The Contemporary Review, Volume 36, September 1879

THE SOCIAL PHILOSOPHY AND RELIGION OF COMTE.

IV.

In my last article I considered the subjective synthesis of Comte, or in other words, his attempt to systematize human knowledge in relation to the moral life of man.For it is his view, as we have seen, that science can never yield its highest fruit to man unless it be systematized—i.e., unless its different parts be connected together and put in their true place as parts of one whole. Scattered lights give no illumination; it is the esprit d'ensemble, the general idea in which our knowledge begins and ends, that ultimately determines the scientific value of each special branch of knowledge.But while synthesis is necessary, it is not necessary, according to Comte, that the synthesis should be objective.The error of mankind in the past has been that they supposed themselves able to ascertain the real or objective principle, which gives unity to the world, and able, therefore, to make their system of knowledge an ideal repetition of the system of things without them.Such a system, however, is entirely beyond our reach.The conditions of our lot, and the weakness of our intelligence, make it impossible for us to tell what is the real principle of unity in the world, or even whether such a principle exists.The attempts to discover it, made by Theology and Metaphysics, have been nothing more than elaborate anthropomorphisms, in which men gave to the unknown and unknowable reality, a form which was borrowed from their own.They saw in the clouds about them an exaggerated and distorted reflection of themselves, and regarded this Brocken spectre as the controlling power whose activity was the source and explanation of everything.Positivism, on the other hand, arises whenever men learn to recognize the nature of this illusion, and to confine their ambition within that which is really the limit of their intelligence.All that we can know is the resemblances and successions of phenomena, and not the things in themselves that are their causes; and if we seek to find a principle of unity for these phenomena, we must find it within and not without. We must organize knowledge with reference to our own wants, rather than with reference to the nature of things. We must regard everything as a means to an end, which is determined by some inner principle in ourselves—not as if we supposed that the world and all that is in it were made for us, or found its centre in us—but simply because this is the only point of view from which we can systematize knowledge, as it is indeed the only point of view from which we need care to systematize it.

It may be asked why system is necessary at all, why we should not be content with a fragmentary consciousness of the world, without attempting to gather the dispersed lights of science to one central principle. To critics like J. S. Mill, Comte's effort after system seems to be the result of an "original mental twist very common in French thinkers," of "an inordinate desire of unity." "That all perfection consists in unity, Comte apparently considers to be a maxim which no sane man thinks of questioning: it never seems to enter into his conceptions that any one could object ad initio, and ask, Why this universal systematizing, systematizing, systematizing?Why is it necessary that all human life should point but to one object, and be cultivated into a system of means to a single end?"[26] To this Mr. Bridges answers that unity in Comte's sense is "the first and most obvious condition which all moral and religious renovators, of whatever time or country, have by the very nature of their office set themselves to fulfil."[27] In other words, all moral and spiritual life depends upon the harmony of the individual with himself and with the world. A divided life is a life of weakness and misery, nor can life be divided intellectually, without being, or ultimately becoming, divided morally. Such unity, indeed, does not exclude—and in a being like man who is in course of development cannot altogether exclude—difference and even conflict. In the most steadily growing intellectual life there are pauses of difficulty and doubt; in the most continuous moral progress there are conflicts with self and others. But such doubts and difficulties will not greatly weaken or disturb us, so long as they are partial, so long as they do not affect the central principles of thought and action, so long as there is still some fixed faith which reaches beyond the disturbance, some certitude which is untouched by the doubt. If, however, we once lose the consciousness that there is any such principle, or if we try to rest on a principle which we at the same time feel to be inadequate, our spiritual life, in losing its unity or harmony with itself, must at the same time lose its purity and energy. It must become fitful and uncertain, the sport of accidental influences and tendencies; it must lower its moral and intellectual aims. This, in Comte's view, is what we have seen in the past. The decay of the old faiths, and of the objective synthesis based upon them, has emancipated us from many illusions, but it has, as it were, taken the inspiration out of our lives. It has made knowledge a thing for specialists who have lost the sense of totality, the sense of the value of their particular studies in relation to the whole; and it has made action feeble and wayward by depriving men of the conviction that there is any great central aim to be achieved by it. And these results would have been still more obvious, were it not that men are so slow in realizing what is involved in the change of their beliefs were it not that the habits and sympathies developed by a creed continue to exist long after the creed itself has disappeared. In the long run, however, the change of man's intellectual attitude to the world must bring with it a change of his whole life. As the creed which reconciled him to the world and bound him to his fellows ceases to affect him, he must be thrown back upon his own mere individuality, unless he can find another creed of equal or greater power to inspire and direct his life. And mere individualism is nothing, but anarchy. That this is so, was not indeed manifest to those who first expressed the individualistic principle: on the contrary, they seemed to themselves to have, in the assertion of individual right, not only an instrument for destroying the old faith and the old social order, but also the principle of a better faith, and the means of reconstructing a better order. But to us who have outlived the period when it could be supposed that the destruction of old, involves in itself the construction of new, forms of life and thought, it cannot but be obvious that the principles of private judgment and individual liberty are nothing more than negations. For as the real problem of our intellectual life is how to rise to a judgment which is more than private judgment, so the real problem of our practical life is how to realize a liberty that is more than individual license. It is in this sense that Comte says that the last three centuries have been a period of the insurrection of the intellect against the heart, a phrase by which he means to indicate at once the gain and the loss of the revolutionary movement; its gain, in so far as it emancipated the intelligence from superstitious illusions, and its loss, in so far as it destroyed the faith which was the bond of social union, without substituting any other faith in its room. At the same time, the expression points to a peculiarity of Comte's Psychology, which affects his whole view of the history, and especially of the religious history, of man; and it is therefore necessary to subject it to a careful examination.

Is it possible for the intellect to be in insurrection against the heart?In a sense already indicated this is possible.It is possible, in short, that the moral and intellectual spirit of a belief may still control the life of one who, so far as his explicit consciousness is concerned, has renounced it.Rooted as the individual is in a wider life than his own, it is often but a small part of himself that he can bring to distinct consciousness.Further, so little are most men accustomed to self-analysis; that they are seldom aware what it is that constitutes the inspiring power of their beliefs. Generally, at least in the first instance, they take their creed in gross, without distinguishing between essential and unessential elements. They confuse, in one general consecration of reverence, its primary principles, and the local and temporary accidents of the form in which it was first presented to them, and they are as ready to accept battle à l'outrance for some useless outwork as for the citadel itself. And, for the same reason, they are ready to think that the citadel is lost when the outwork is taken; to suppose, e.g., that the spiritual nature of man is a fiction if he was not directly made by God out of the dust of the earth, or that the Christian view of life has ceased to be true if a doubt can be thrown on the possibility of proving miracles.Yet however little the individual may be able to separate the particulars which are assailed from the universal with which they are accidentally connected, his whole nature must rebel against the sacrifice which logical consistency seems in such a case to demand from him.It is a painful experience when the first break is made in the implicit unity of early faith, and it is painful just in proportion to the depth of the spiritual consciousness which that faith has produced in the individual.Unable to separate that which he is obliged to doubt from that in which lies the principle of his moral, and, even of his intellectual, life, he is "in a strait betwixt two;" and no course seems to be open to him which does not involve the surrender, either of his intellectual honesty, or of that higher consciousness which alone "makes life worth living," Such a crisis is commonly described as a division between the heart and the head, for in it the articulate or conscious logic is on the side of disbelief, and the resisting conviction generally takes the form of a feeling, an impulse, an intuition, which the individual has for himself, but which he is unable to communicate in the same force to another.And, as such feelings and intuitions of the individual are necessarily subject to continual variation of intensity and clearness, so the struggle between doubt and faith may be long and difficult, the objections, which at one time seem as nothing, at another time appearing to be almost irresistible.Not seldom the result is a broken life, in which youth is given to revolt, and the rest of existence to a faith which vainly strives to be implicit.There is, indeed, no final and satisfactory issue from such an endless internal debate and conflict, until the "heart" has learned to speak the language of the "head,"—i.e., until the permanent principles which underlay and gave strength to faith have been brought into the light of distinct consciousness, and until it has been discovered how to separate them from the accidents, with which at first they were necessarily identified.The hard labour of distinguishing, in the traditions of the past, between the germinative principles, out of which the future must spring, and those external forms and adjuncts, which every day is making more incredible, must be undertaken by any one who would restore the broken unity of man's life.We begin our existence under the shadow and influence of a faith which is given to us, as it were; in our sleep; but in no age, and in this age less than any other, can man possess a spiritual life as a gift from the past without reconquering it for himself.

In this sense, then, we can understand how Comte might speak of an insurrection of the intelligence against the heart, which must be quelled ere the normal state of humanity could be restored; for this would be only another way of saying that, in the modern conflict of faith and reason, the substantial truth, or at least the most important truth, had, up to Comte's own time, been on the side of the former.In this view, the deep unwillingness of those nourished in the Christian or Catholic faith to yield to the logical battery of the Encyclopædists was not merely the result of an obscurantist hatred of light; it was also in great part due to a more or less definite sense of the moral, if not the intellectual, weakness of the principles which the Encyclopædists maintained.For, while the insurrection was justified in so far as it asserted the claims of the special sciences, it was to be condemned in so far as it involved the denial of all synthesis whatever, and also in so far as it was blind to the elements of truth in the imperfect synthesis of the past.It thus tended to destroy the spirit of totality and the sense of duty (l'esprit d'ensemble et le sentiment du devoir).[28] It practically denied the existence of any universal principle which could connect the different parts of knowledge with each other, of any general aim which could give unity to the life of man. Its analytic spirit was fatal, not only to the fictions of theology, but also to that growing consciousness of the solidarity of men of which theology had been the accidental embodiment. The reluctance of religious men to admit the claims of what appeared to be, and, indeed, to a certain extent was, light, was thus due to a more or less distinct perception that their own creed, amid all its partial errors, contained a central truth more important than all the partial truths of science. In clinging to the past they were preserving the germ of the future, and the final victory of science could not come until this germ had been disengaged from the husk of superstition under which it was hidden. Till that was done, the logic of the heart in clinging to its superstitions was better than the logic of the head in rebelling against them. In other words, the implicit reason of faith was wiser than the explicit reason of science.

But this is not all that Comte means.For him the appeal to the heart is not merely the appeal to feelings and intuitions, which are the result of the past development of human intelligence, and especially of the long discipline by which the Christian Church has moulded the modern spirit; it is an appeal to the altruistic affections as original or "innate" tendencies in man which are altogether independent of his intelligence.It is not that the reason of man often speaks through his feelings, but that feeling and reason have in themselves different, and even it may be opposite, voices. In this sense, the attempt has often been made in modern times to stop the invasions of critical reflection by setting up the heart as an independent authority. From the Lutheran theologian who said, "Pectus theologum facit," down to Mr. Tennyson who declares that whenever he heard "the voice—Believe no more,"

"A warmth within the breast would melt
The freezing reason's colder part,
And like a man in wrath, the heart
Stood up and answered, 'I have felt:'"

appeals have constantly been made to the feelings to resist the intrusion of doubt.Such appeals, however, cannot be regarded as otherwise than provisional and self-defensive."The heart knoweth its own bitterness, and a stranger doth not intermeddle with its joy;" but just for that reason it has no general content or independent authority of its own.Whether the "I feel it" mean little or much, depends upon the individual who utters it.It may be the concentrated expression of a long life of culture and discipline, or it may be the loud but empty voice of untrained passion and prejudice.The "unproved assertions of the wise and experienced," as Aristotle tells us, have great value, especially in ethical matters; but it is not because they are unproved assertions, but because we otherwise know that the speakers are wise and experienced.To appeal to the heart in general, without saying "whose heart," either means nothing, or it means an appeal to the natural man—i.e., man as he is before he has been sophisticated by culture and experience; but of the natural man, in this sense, nothing can be said.The further we go back in the history of the individual or the race the more imperfect does their utterance or manifestation become; and when we reach the beginning, we find that there is no manifestation or utterance at all.The natural man of Rousseau was simply an ideal creation, inspired with that intense and even morbid consciousness of self, and that fixed resolve to submit to no external law, which were characteristic of Rousseau himself, and which in him were the last product and quintessence of the individualism of the eighteenth century.The simplicity of this ideal figure was not the first simplicity of nature, but the simplicity of a spirit which has returned upon itself and asserted itself against the world; a kind of simplicity which never existed, at least in the same form, before the great Protestant revolt.The unhistorical character of this idea becomes doubly evident when we find that, as time goes on, and the spirit of the age alters, the qualities of the natural man are also changed.To St.Simon and Fourier, as to Rousseau, man is good by nature, and it is bad institutions or bad external influences which are the source of all the ills that flesh is heir to.But while with the latter the natural man is a solitary, whose chief good lies in the preservation of his independence, with the former he is essentially social, and what is wanted for his perfection and happiness is only to contrive an outward organization in which his social sympathies shall have free play. Comte, as we might expect, rises above these imperfect theories, in so far as he refuses to attribute all the evils of humanity to its external circumstances; but he does not get rid of the essential error which was common to them all, the error of seeking for the explanation of the higher life of humanity in the feelings of the natural man—feelings which are prior to, and independent of, the exercise of his reason, and which supply all the possible motives for that exercise. There are, in his view, two sets of "innate" feelings or desires, between which man's life is divided—the egoistic and the altruistic tendencies, each separate from the others as well as from the intelligence, and having its "organ" in a separate part of the brain. The egoistic feelings at first exist in man in far greater strength than the altruistic; but by the reaction of circumstances, and the influence of men upon each other, the latter have in the past gradually attained to greater power; and it is the ideal of the future to make their victory complete. Meanwhile, the intelligence is necessarily the instrument of desire, and its highest good is to be the instrument of altruistic as opposed to egoistic desire. For it has at best only a choice of masters, and the emancipation of the intelligence from the heart could mean only its becoming a slave of personal vanity. Comte's appeal, therefore, is still to the natural man, or rather to one element in him, which, however, as he acknowledges, is never so weak as it is in man's earliest or most natural state.

The psychology implied in this theory is substantially that which found its fullest expression in Hume's Treatise on Human Nature.Hume, with that tendency to bring things to a distinct issue which is his best characteristic, declares boldly that "reason is, and ought to be, the slave of the passions, and can never pretend to any other office than to serve and obey them."The passions or desires are tendencies of a definite character which exist in man from the first; the awaking intelligence cannot add to their number, or essentially change their nature.It can only take account of what they are, and calculate how best to satisfy them."We speak not strictly and philosophically when we talk of the combat of reason and passion," for reason in itself determines the true and false, but it sets nothing before us as an end to be pursued and avoided.It does not constitute or transform the desires, which are given altogether apart from it, and the will is but the strongest desire.When we say that reason controls the passions what we mean is simply that a strong but calm tendency of our nature, which has reference to some remote object, overcomes some violent impulse towards a present delight; but for intelligence, in the strict sense of the word, to war with passion is a simple impossibility.

The modifications which Comte makes in this view of motive are comparatively trifling.He does not, indeed, like Hume, call reason the slave of the passions; rather he says that "l'esprit doit être le ministre du cœur, mais jamais son esclave;" but this change of language does not involve any important modification of Hume's theory.The intelligence has to give to the heart all kinds of information about the objects through which it may find satisfaction, but after all the end itself has to be determined solely by feeling and desire.In Comte's language the intellect is a "slave," when theology makes it acknowledge the existence of supernatural beings who are agreeable to our desires, but who have no reality as objects of experience; it is a "master," when it pursues its inquiries into the phenomena of the objective world, at the bidding of an errant curiosity, without reference to the well-being of man; it is in its true place as a "servant" when it studies the objective world freely, but only with reference to the end fixed for it by the affections."L'univers doit être étudié non pour lui-même, mais pour l'homme, ou plutôt pour l'humanité;" and this, Comte thinks, will not be done if the intelligence be left to itself, but only if it be made subordinate to the heart. To say, therefore, that the intelligence is not to be a slave but a servant, implies merely that it is to be left free to collect information about the means of satisfying the desires, without having its judgment anticipated by the imagination or the heart; but that, on the other hand, it must keep strictly to its position as an instrument to an end out of itself. For if it once emancipates itself from the yoke of feeling, it soon becomes altogether lawless, and disperses its efforts in every direction in the satisfaction of a vain curiosity. The intelligence, as the scholastic theologians said, is in itself, or when left to itself, a source of anarchy and confusion; it must be, not indeed the serva, but the ancilla fidei, or it defeats its own ends.The intellectual life, as such, is an unsocial, even a selfish existence; for, as reason is guided by no definite objective aim derived from itself, it must find its real motive in the satisfaction of personal vanity and self-conceit, whenever it is not subjected to the yoke of the altruistic affections.

This theory (which, as we shall see, underlies Comte's whole conception of history) suggests two questions.It leads us to ask, in the first place, whether the tendencies of the intellectual life are thus dispersive and opposed to the social tendencies?and, secondly, whether the social tendencies in the form which they take with man, are not necessarily determined to be what they are by his intelligence?The former question really resolves itself into another: Is the intelligence of man a mere formal power of apprehending what is presented to it from without, so that when it is left to itself it must lose itself in the infinite multiplicity of individual objects in the external world?or does it carry with it any synthetic principle, any idea of the whole, to which it necessarily and inevitably seeks to bring back the difference of things?Against Comte's assertion that the natural tendency of the intelligence is to lose itself in difference without end, we might quote the well-known saying of Bacon, that the tendency of the "intellectus sibi permissus" is rather towards a premature synthesis."Intellectus humanus ex proprietate sua facile supponit majorem ordinem et æqualitatem in rebus quam invenit." Surely, if we may speak of tendencies of the intellectual life as separated from the life of feeling, the tendency to unity and the universal belongs to it quite as much as the tendency to difference and the particular; just as in the life of feeling the tendency to isolation and self-assertion against others is combined with the tendency to society and union with others. From the first moment of intellectual life the world is to us a unity; subjectively a unity, as all its varied phenomena are gathered up in the consciousness of one self, and objectively a unity, as every object and event is definitely placed in relation to the other objects and events in one space and one time. The development of knowledge is, no doubt, the continual detection of new differences and distinctions in things, but the phenomena which are distinguished from other phenomena are at the same time put in relation to them. Nor can the intelligence find complete satisfaction until this relation is discovered to be necessary, and thus difference passes into unity again. Individual minds, indeed, may be more of the Aristotelian, or more of the Platonist, order, may tend more to divide what at first is presented as unity, or to unite what at first is presented as difference. But it is absurd to talk of either tendency as belonging to the intelligence in itself, since it is utterly beyond, or rather beneath, the powers of thought to conceive either of an undifferentiated unity, or of a chaos of differences without some kind of relation. Descending to particulars, we may bring Comte as a witness against himself; for while he declares that the sciences which deal with the inorganic world are mainly analytic in their tendencies, he at the same time maintains that the sciences of Biology and, still more, of Sociology and Morals, are synthetic, since they deal with objects in which the whole is not a mere aggregation or resultant of the parts, but in which rather the parts can be understood only in and through the whole. Hence it would seem that the dispersive tendencies of science are confined to lower steps of the scientific scale; and that the final science (as was shown more particularly in a previous article) admits and necessitates a synthesis, which is not merely subjective, but also objective. For Comte does not hold that we are to regard other men merely as means, or to seek to understand them only so far as is necessary for the gratification of some desire in ourselves as individuals. We are, on the contrary, to seek to know man in and for himself; and when we do so know him, we find that he is essentially social, and that the individual, as such, is a mere "fiction of the metaphysicians." Here, again, therefore, we find that Comte's system ends in a compromise between opposite tendencies of thought. His subjective synthesis proved after all to be objective, at least so far as mankind were concerned; and in like manner his opposition of the intellect to the heart turns out to be only partial; for when the intelligence is directed to psychology and sociology, it gives us an idea of humanity, according to which all men are "members one of another." The warfare of the heart and the intelligence thus resolves itself into another expression of that dualism between the world and man, which we found to be an essential characteristic of Comte's system.

The second question—whether the altruistic affections of man do not imply, or are not necessarily connected with, the development of his reason or self-consciousness—is even more important.Comte, like Hume, took all the desires, higher and lower, as tendencies given apart from the reason, which can only devise the means of satisfying them, and is, therefore, necessarily their servant.Reason itself on this view does not essentially affect the character of those tendencies which it obeys."Cupiditas est appetitus cum ejusdem conscientia," said Spinoza, and he then went on to speak as if the "conscientia" made no change in the character of the "appetitus." But if we think of appetites or desires—some of them tending to the good of the individual, others to the good of the species—as existing in an animal which is not conscious of a self, these appetites will neither be selfish nor unselfish in the sense in which we apply these terms to man. Where there is no ego there can be no alter-ego, and therefore neither egoism nor altruism. The idea of the self as a permanent unity to which all the different tendencies are referred, and the rise in consequence of a new desire of pleasure, distinct from the desires of particular objects, are essential to egoism. The idea of an alter-ego, i.e., of a community with others which makes their interests our own, and hence the rise of a love for them,—which is not merely disinterested as the animal appetites are disinterested, because they tend directly to their objects without any thought of self, but disinterested in the sense that the thought of self is conquered or absorbed, is essential to altruism. Each of these tendencies may in its matter, or rather in its first matter, coincide with the appetites; viewed from the outside, they may seem to be nothing higher than hunger or thirst, or sexual or parental impulse, but their form is different. They are changed as by a chemical solvent, which dissolves and renews them; nay, as by a new principle of life, whose first transformation of them is nothing but the beginning of a series of transformations both of their matter and their form; so that, in the end, the simple direct tendency to an object—the uneasiness which sought its cure without reflection either upon itself or upon anything else—becomes changed, on the one side, into a gigantic ambition and greed, which would make the whole world tributary to the lust of the individual, and, on the other, into a love of humanity in which self-love is altogether transcended or absorbed. Neither of these, however, nor any lower form of either, is in such wise external to reason, that we can talk of them as determining it to an end which is not its own. Both are simply the expression in feeling of that essential opposition of the self to the not self, and at the same time that essential unity of the self with the not self, which are the two opposite, but complementary, aspects of the life of reason. And the progressive triumph of altruism over egoism, which constitutes the moral significance of history, is only the result of the fact that an individual, who is also a conscious self, cannot find his happiness in his own individual life, but only in the life of the whole to which he belongs. A selfish life is for him a contradiction. It is a life in which he is at war with himself as well as with others, for it is the life of a being who, though essentially social, tries to find satisfaction in a personal or individual good. The "intelligence" and the "heart" equally condemn such a life; it is not only a crime but a blunder. For a spiritual being as such is one who can only save his life by losing it in a wider life, one who must die to himself in order that he may live. In the progress of man's spirit, therefore, there is no necessary or possible schism between the two parts of his being; but, on the contrary, the development of each is implied in the development of the other. It is the more comprehensive idea, as well as the higher social purpose, which always triumphs; and if what is called intellectual culture sometimes seems to have the worse, it is because it is a superficial or formal culture, and does not really represent the most comprehensive idea.

This leads us to observe that the opposition of the heart to the intelligence is Comte's key to the whole history of the past, especially in relation to religion.Theology is to him a system growing out of a natural, though partially erroneous, hypothesis, a hypothesis which in its first appearance was well suited to excite the nascent intelligence and satisfy the primary affections of man, but which, in its further development, tended to secure moral and social ends at the expense of truth, and became more and more irrational as it became more and more useful.Fetichism, the first religion, was the spontaneous result of man's primitive tendency to exaggerate the likeness of all things to himself.It is "less distant from Positivity" than any other sort of theology,[29] for its error is only that it supposes the existence of life wherever it finds activity—an error which can "easily be brought to the test of verification" and corrected. "We can show it to be an error, and so get rid of it." But Polytheism, seeking for greater generality, refers phenomena to beings who are not identified with them, to "indirect wills belonging to beings purely imaginary," whose "existence can no more be decisively disproved than it can be demonstrated." Further, Polytheism extended to the order of man's life that kind of explanation which Fetichism necessarily confined to nature, because the latter sought to explain everything by man, and never thought of man himself as requiring explanation. But this, while it had the advantage of bringing human life within the domain of speculation, at the same time reduced theology into a palpable instance of reasoning in a circle. For "humanity cannot legitimately be included in the synthesis of causes, from the very fact that its type is found in man."[30] Last of all came Monotheism, concentrating still further the theological explanation of the universe, but rendering it still more incoherent and irrational, for "the conception of a single God involves a type of absolute perfection complete in each of the three aspects of human nature, affection, thought, and action. Now such a conception unavoidably contradicts itself, for either this all-powerful Being must be inferior to ourselves, morally or intellectually, or else the world which he created must be free from those radical imperfections which, in spite of Monotheistic sophistry, have been always but too evident. And even were this second alternative admissible, there would remain a yet deeper inconsistency. Man's moral and mental faculties have for their object to subserve practical necessities, but an omnipotent Being can have no occasion either for wisdom or for goodness."[31]

What reconciles mankind, and especially the leaders of mankind, to these intellectually unsatisfactory conceptions of God, is their practical value in extending and strengthening the social bond.Polytheism was superior to Fetichism, because it lent itself to the formation of that wider community, which we call the State, whereas Fetichism tended rather to confine the sympathies of men to the narrower limits of the family.And Monotheism was the necessary basis of that still wider society which binds men to each other simply as men, and apart from any special ties of blood or language.This at least was the case so long as the truth of the unity of humanity had not yet assumed a scientific form, and therefore still needed an external support.But when the sciences of sociology and morals arise, this external scaffolding ceases to be necessary, and must even become injurious, as, indeed, Theology was from the first imperfectly adapted to the social end it was made to subserve.

This last point deserves special attention.According to Comte, Theology, and above all Monotheistic Theology, is a system whose direct influence is altogether unfavourable to the social tendencies, although indirectly, by the course of history, and through the wise modifications to which it has been subjected by the leaders and teachers of mankind, it has become the main instrument in developing altruism.The increasing generality of theological belief, indeed, was a necessary condition of the establishment of social unity; but, by directing the eyes of men not to themselves, but to supernatural beings, by making the event of life turn on the favour or disfavour of such beings, rather than on the social action and reaction of men upon each other, and by reducing this world into a secondary position, so that its concerns were subordinated to those of another world, Theology tended to dissolve rather than to knit closer the bonds of society.The relation of the individual to God isolated him from his fellows.Especially was this the case with the Christian form of Monotheism, with its tremendous future rewards and penalties, and the direct relation which it established between the soul of the individual and the infinite Being. "The immediate effect of putting personal salvation in the foremost place was to create an unparalleled selfishness, a selfishness rendering all social influences nugatory, and thus tending to dissolve public life."[32] "The Christian type of life was never fully realized except by the hermits of the Thebaid," who, "by narrowing their wants to the lowest standard, were able to concentrate their thoughts without remorse or distraction on the attainment of salvation."[33] What else, indeed, but egoism could be awakened by the worship of a God who is himself the supreme type of egoism? For "the desires of an omnipotent Being, being gratified as soon as formed, can consist in nothing but pure caprices. There can be no appreciable motive either from within or from without. And above all, these pure caprices must of necessity be purely personal; so that the metaphysical formula, To live in self for self, would be alike applicable to the two extreme grades of the vital scale. The type of divinity thus approximates to the lowest stage of animality, the only shape in which life is purely individual, because it is reduced to the one function of nutrition."[34] The natural result of such a religion was, therefore, to discourage the altruistic affections, and, indeed, Monotheism has systematically denied that such affections form part of the nature of man.

The alchemy which, according to Comte, turned this poison into an elixir vitæ, was found in the altruistic affections of the teachers of mankind, which led them to limit and modify the doctrine they taught, so as to subserve man's moral improvement.This, however, would not have been sufficient, if these teachers had not at an early period ceased to be a theocracy, or, in other words, if the practical government of mankind had not been wrested from their hand by the military classes.By this change, which contained in itself the germ of the separation of the Church from the State, of theory from practice, of counsel from command, the priests, prophets, or philosophers, who were the intellectual leaders of men, were reduced to that position of subordination in which alone they can concentrate their attention upon their proper work.For the influences of the intellect, like those of the affections, must be indirect if they are to be pure."No power, especially if it be theological, cares to modify the will, unless it finds itself powerless to control action."[35] But when the theoretic class were subordinated to the practical class, they became the natural allies of the women, and, like them, had to substitute counsel for command. At first, indeed, their subjection was too absolute, for the military aristocracies of Greece and Rome did not leave to the priesthood sufficient independence, or at least sufficient authority, to permit even of counsel. But with the rise of Catholic Monotheism, supported as it was by a new revelation based upon an incarnation of God, the separation of Church and State was definitely established, and the intellectual life was put in its proper relation to the life of action.

The consequence is that the theological priesthood have continually sought to counteract the natural influences of their theological doctrines by making additions which were inconsistent with its "absolute" principle, but which rendered it better fitted for the purpose of binding men together.This was especially the case under Monotheism, where, as we have seen, such counteraction was most necessary.From this source arose a series of supplementary doctrines, generally tending to connect God with man, and men with each other.St.Paul, "the real founder of Christianity," took the first step in reducing Monotheism into a shape in which it could act as an "organic" doctrine, and his successors followed steadily in the same path.If the omnipotence of God raised him above all human sympathy, and tended to destroy human sympathy in his worshippers, the doctrines of the Trinity and the Incarnation again brought him near to them, and taught them to reverence a humanity which was thus raised into unity with God.In the Feast of the Eucharist all men celebrated and enjoyed their unity with this exalted and deified humanity.The same influence, in its further development, led to the adoration of the saints, and above all of the Virgin Mother, in whom Christian devotion really worshipped humanity, in its simplest and tenderest affections.Finally, if benevolent sympathies were denied to nature, St.Paul found a place for them by attributing them to grace, "which Thomas à Kempis admirably defines as the equivalent of love—gratia sive dilectio—divine inspiration being substituted for human impulse."[36] And the struggle between egoism and altruism was expressed in the doctrines of the Fall and Redemption of mankind.[37] Thus the social passion, which, according to the theory, could not be found in humanity, was conceived to flow from a divine influence, and became ennobled, at least as a means of salvation, in the eyes of those who would otherwise have suppressed it. At the same time, as Comte also contends, these additions or corrections of the original doctrine were inconsistent or imperfect in themselves, and inadequate to the social purpose for which they were destined; and they naturally disappeared whenever, by the emancipation of the intelligence, the immense egoism, which Monotheism consecrated in God and favoured in man, was let loose from the bonds in which the Church had confined it. Protestantism was the first indication of this change; for Protestantism is but an organized anarchy, in which the only elements of order are derived from an instinctive conservatism, clinging to the fragments of a past doctrinal system, which, in principle, has been abandoned. It contains no organic elements of its own—no positive contribution to the progressive life of humanity; it is simply the first imperfect result of that metaphysical individualism which, in its ultimate form, freed from all the limits of the Catholic system, expressed itself theoretically in Rousseau and Voltaire, and practically in the French Revolution. The hope of mankind, however, lies in the new synthesis of Positivism, which alone can give due value to the innate altruistic sympathies of man, and which therefore alone can place on a permanent scientific basis that social order which the mediæval Church attempted in vain to found on the essentially egoistic and anarchic doctrine of Monotheism.

The fundamental conception, then, which underlies Comte's view of progress is, that every past religion, with the partial exception of Fetichism, has been an amalgam of two radically inconsistent elements, one of which only was due to the theological principle itself; while the other was due, partly to the practical instinct of its priests, which led them to modify the logical results of that principle in conformity with the social wants of man; and partly also to their subordinate position, which obliged them to use the spiritual means of conviction and persuasion instead of the ruder weapons of material force.To criticise fully this position would be to re-write Comte's history of religion.It will be sufficient here to point out that his view of modern history begins in a false interpretation of Christianity, and ends in an equally false interpretation of the Protestant Reformation.

Christianity from its origin has two aspects or elements; and if we compare it with earlier religions, we may call these its Pantheistic and its Monotheistic elements.But these elements are not, as Comte asserts, joined together by a mere external necessity.They are necessarily connected in the inner logic of the system; nor can we regard one of them as more or less essential than the other.In the simplest words of the Gospels we find already expressed a sense of reconciliation with God, and therefore with the world and self, which is alien to pure Monotheism, though there is some faint anticipation of it in the later books of the Old Testament.For a spiritual Monotheism, while it awakens a consciousness of the holiness of God, and the sinfulness of the creature, tends to make fear prevail over love, and the sense of separation over the sense of union.The idea of the unity of the Divine and the human—an original unity which yet has to be realized by self-sacrifice—and the corresponding idea that the individual or natural life must be lost in order to save it, were set before humanity, as in one great living picture, in the life and death of Christ.And what was thus directly presented to the heart and the imagination in an individual, was universalized in the writings of St.Paul and St.John: in other words, it was liberated from its peculiar national setting, and used as a key to the general moral history of man.The Messiah of the Jews was exalted into the Divine Logos, and the Cross became the symbol of an atonement and reconciliation between God and man, which has been made "before the foundation of the world," yet which has to be made again in every human life.The work of the first three centuries was to give to this idea such logical expression as was then possible, in the doctrines of the Incarnation and the Trinity. It is true that this idea of the unity of man with God was not immediately carried out to any of the consequences which might seem to be contained in it. It remained for a time a religion, and a religion only; it did not show itself to be the principle of a new social or political order of life. Rather it accepted the old order represented by the Roman Empire, and even consecrated it as "ordained of God," only demanding for itself that it should be allowed to purify the inner life of men. Such a separation of the things of Cæsar and the things of God was then inevitable; for it is impossible that a new principle can ever be received simply and without alloy into minds, which are at the same time occupying themselves with its utmost practical or even theoretical consequences. In this sense there is great truth in what Comte says about the value of the separation of the spiritual from the temporal authority. The power of directly realizing a new religious principle, just because it draws away attention from the principle itself to the details of its practical application, is likely to prevent that application being either effective or even a true expression of the principle. Such practical inferences cannot safely be drawn by direct logical deduction; they will be made with certainty and effect only by spirits which the principle has remoulded. The decided withdrawal of the Christian Church from the sphere of "practical politics" was, therefore, not merely a necessity forced upon it from without; it was a condition which its best members gladly accepted, because without it the inner transformation of man's life by the new doctrine would have been impossible. If Christianity had raised an insurrection of slaves, it never could have put an end to slavery.

But while this withdrawal was necessary, it contained a great danger; for the inner life cannot be separated from the outer life without becoming narrowed and distorted. Confined to the sphere of religion and private morality, the doctrine of unity and reconciliation necessarily became itself the source of a new dualism. What had been at first merely neglect of the world was gradually changed into hostility to worldly interests; and the germs of a positive morality, reconciling the flesh and the spirit—which appear in the New Testament—were neglected and overshadowed in the growth of asceticism. Christianity, even in its first expression, had a negative side towards the natural life of man; while it lifted man to God, it yet taught that humanity "cannot be quickened except it die." But the mediæval Church, while it constantly taught that humanity in its desires and tendencies must die, had almost forgotten to hope that it could be quickened. Its highest morality—the morality of the three vows—was the negation of all social obligations; its science was the interpretation of a fixed dogma received on authority; its religion tended to become an external service, an opus operatum, a preparation for another world, rather than a principle of action in this.Its highest act of worship, the Eucharist, in which was celebrated the revealed unity of men with each other and with God, was reserved in its fulness for the clergy, and even with them was finally reduced to an external act by the doctrine of transubstantiation, in which poetry "became logic," and in becoming logic, ceased to be truth.

Now, Comte, seeing the working of this negative tendency in mediæval Catholicism, and regarding it as the natural work of Monotheism, is obliged to treat all the positive side of Christianity as an external addition suggested by the practical wisdom of the clergy.St.Paul is supposed by him to have invented (and Comte's language would ever suggest that he consciously invented[38]) the doctrine of grace, in order to reconsecrate those social affections which Monotheism, in its condemnation of nature, had either denied to exist, or, what is nearer the truth, had treated as having no moral value.But this only shows how imperfectly Comte grasped the Pauline conception of the moral change which religion produces.The idea that the immediate untamed and undisciplined will of the natural man is not a principle of morality, and that therefore man must die to live, must rise above himself to be himself, is one which has in it nothing discordant with the claims of social feeling.It is the commonplace of every powerful writer on practical ethics, from the Gospels to Thomas à Kempis, and from Luther to Goethe.

"Und so lang du das nicht hast
Dies-es: Stirb und Werde,
Bist du nur ein trüber Gast
Auf der dunkeln Erde."

St.Paul adds that this death to self is possible only to him in whom another than his own natural will lives; "so then it is not I that live, but Christ that liveth in me."Comte would probably accept the sentence with the substitution of humanity for Christ.But either substitution involves the negation of the natural tendencies, whether individual or social, in their immediate natural form; and Comte himself, when he placed not only the sexual but even the maternal impulse among those that are merely "personal," virtually acknowledged that the natural or instinctive basis of the altruistic affections is not in itself moral.[39] But because he begins with a psychology which treats the egoistic and altruistic desires, and again the intellect and the heart, as distinct and independent entities, he is unable to do justice to an account of moral experience which involves that they are essentially related elements in one whole, or necessarily connected stages of its development.

In the form in which it was first presented, the teaching of Christianity was undoubtedly ambiguous, as, indeed, every doctrine in its first general and abstract form must be.We cannot then call it either social or anti-social, without limitations; it is anti-social and ascetic, because of its negative relations to the previous forms of life and culture; it is social and positive in so far as in its primary doctrine of the unity of the divine and human—of divinity manifested in man and humanity made perfect through suffering—it contains the promise and the necessity of a development by which nature and spirit shall be reconciled. The progressive tendency of Christendom was based on the fact that from the earliest times the followers of Christ were placed in the dilemma, either of denying their primary doctrine of reconciliation between God and man and going back to pure Monotheism, or of advancing to the reconciliation of all those other antagonisms of spirit and nature, the world and the Church, which arose out of the circumstances of its first publication. And modern history is more than anything else the history of the long process whereby this logical necessity manifested itself in fact. The negative spirit of the Middle Age, its asceticism, its dualism, its formalism, its tendency to transform the moral opposition of natural and spiritual into an external opposition between two natural worlds, present and future, and thus to substitute "other-worldliness" for worldliness, instead of substituting unworldliness for both—all these characteristics were the natural results of the fact that the idea of Christianity, in its first abstract form, could not include, and therefore necessarily became opposed to, the forms of social life and organization with which it came into contact. But while the early Christians looked for the realization of the kingdom of Heaven in some immediate earthly future, and the Middle Age postponed it to another life, Christ had already taught the truth, which alone can turn either of these hopes into something more than the expression of an egoistic desire—the truth that "the kingdom of God is within us." The reaction of the social necessities of mediæval society on the doctrine—which Comte quite correctly describes as leading to the gradual elevation of humanity and of human interests—found its main support in the principles of the doctrine itself, so soon as its lessons had been absorbed into the mind of the people. The irresistible force of the movement, whereby the intelligence was emancipated from authority, and the claims of the family and the State were asserted against the Church, lay above all in this, that Christianity itself was felt to involve the consecration of human life in all its interests and relations. Luther's appeal to the New Testament and to the earliest ages of Christianity was in some ways unhistorical, but it expressed a truth. Protestantism was not a return to the Christianity of the first century; it was an assertion of the relation of the individual to God, which was itself made possible only by the long work of Latin Catholicism. But the development of a doctrine, if it has in it any germ of truth which is capable of development, involves a continual recurrence to its first, and therefore its most general, expression. The elements successively developed in the Catholic and the Protestant, the Latin and the Germanic forms of Christianity, were both present in the original germ, and the exaggerated prominence given in the former to the negative side of Christianity could not but lead, in the development of thought, to a similarly exaggerated manifestation of its positive side. But it is nearly as absurd to say, as Comte does, that the true logical outcome of Christianity is to be found in the "life of the hermits of the Thebaid," as it would be to say that its true logical outcome is to be found in those vehement assertions of nature—naked and unashamed—as its own sufficient warrant, which poured almost with the force of inspiration from the lips of Diderot. Both extremes are equally removed from that special moral temper and tone of feeling which we can alone call Christian—the former by its want of sympathy and tenderness, no less than the latter by its want of purity and self-command. Reassertion of nature through its negation, or to put it more simply, the purification of the natural desires by the renunciation of their immediate gratification, is the idea that is more or less definitely present in all phases of the history of Christianity; and, though swaying from one side to the other, the religious life of modern times has never ceased to present both aspects. Even a St. Augustine recoiled from the Manichæism by which nature was regarded, not simply as fallen from its original idea, but as essentially impure. And, on the other hand, even Rousseau's Savoyard vicar, who has got rid of the negative or ascetic element, as completely as is possible for any one still retaining any tincture of Christianity or even of religion, and who insists so strongly on the text that "the natural is the moral," is yet forced to recognize that nature has two voices, and that the raison commune has to overcome and transform the natural inclinations of the individual. In the life of its Founder, the Christian Church has always had before it an individual type of that harmony of the spiritual and natural life, which it is its ideal to realize in all the wider spiritual relations of man; nor, till that ideal is reached, can it be said that the Christian idea is exhausted, or that the place is vacant for a new religion, however great may be the changes of form and expression through which Christianity must pass under the changed conditions of modern life.

That Comte was not able to discern this, arose, as we have seen, from the fact that he held a kind of Manichæism of his own. To him the egoistic and altruistic desires were two kinds of innate tendencies, both of which exist in man from the first, though with a great preponderance on the side of egoism. Moral improvement simply consists in altering the original proportions in favour of altruism, and moral perfection would be the complete extinction of egoism (which with Comte would naturally mean the extinction of all the desires classified as personal). Hence there is a distinctly ascetic tendency in some of the precepts of the Politique Positive,—i.e., asceticism begins to appear, not simply as a transitionary process through which certain natural desires are to be purified, but as a deliberate attempt to extinguish them.A deeper analysis would have shown that the desires in themselves, as mere natural impulses, are neither egoistic nor altruistic, neither bad nor good; and that while, as they appear in the conscious life, they are necessarily at first poisoned with egoism, yet that the ego is not absolutely opposed to the alter ego, but rather implies it. A spiritual or self-conscious being is one who can find himself, nay who can find himself only, in the life of others: and when he does so find himself, there is no natural desire which for itself he needs to renounce as impure; no natural desire which may not become the expression of the better self, which is ego and alter ego in one. But Comte, unable from the limitations of his psychology to see the true relation of the negative and the positive side of ethics, is obliged to treat the ascetic tendency of Christianity as involving a denial of the existence, or the moral value, of the social sympathies; and on the other hand, to regard the efforts of the Christian Church to cultivate those sympathies, as the result of an external accommodation. His view of Christianity, in short, practically coincides with the definition of virtue given by Paley; it is "doing good to man, in obedience to the will of God, with a view to eternal happiness." It is the pursuit of a selfish end by means in themselves unselfish, with the pleasures and pains of another world introduced as the link of connection; and it must therefore leave bare selfishness in its place, so soon as doubt is cast upon these supernatural rewards and punishments. Hence Comte is just neither to Catholicism nor to Protestantism; considering that the former was only indirectly social, and that the latter is merely the first step in a scepticism which, taking away the fears and hopes of another world, must at the same time take away the last limit upon selfishness. And, just because he is unable to understand either the negative tendencies of the former, or the positive tendencies of the latter, phase of modern life, he has an imperfect appreciation of that social ideal to which both are leading, and which must combine in itself the true elements of both. As, however, it is the temptation of writers on social subjects to be least just to the tendencies of the time which preceded their own, and against whose errors they have immediately to contend, so we find that Comte is fairer towards Catholicism than he is towards Protestantism, or towards that individualism which grew out of Protestantism, and which he is pleased to call Metaphysics. The latter he sees solely on their destructive side, as successive stages in the modern movement of revolt, without appreciating the constructive elements involved in them. Hence also he is led, in his attitude towards this great movement, to all but identify himself with Catholic writers like De Maistre; and his own scheme of the future is essentially reactionary. The restoration of the spiritual power to its mediæval position was a natural proposal for one who saw in the Protestant revolt nothing more than an insurrectionary movement, which might clear the way for a new social construction, but which in itself was the negation of all government whatever.

For what was Protestantism?To the Protestant it seemed to be simply a return to the original purity of the Christian faith; to the Catholic, it seemed to be a fatal revolt against the only organization by which Christianity could be realized. Really it partook of both characters. It involved at once a dangerous misconception of the social conditions, under which alone the religious life can be realized and developed, and a deeper and truer apprehension of that religion, which first recognized the latent divinity or universal capacity of every spiritual being as such, and which, therefore, seemed to impose upon every individual man the right or rather the duty of living by the witness of his own spirit. Comte saw only the former of these aspects of it. Hence he regarded the French Revolution as a practical refutation of the individualism which grew out of the Protestant movement, and not, as it was in truth, a critical event, which should force men to distinguish and separate its true and its false elements. And he drew from it the lesson that the individual has no moral or religious life of his own, but that it is only in proportion as he transcends his own individuality and lives the life of humanity, that his own spiritual life can have any depth or riches in it. Like Burke he could say, "We are afraid to put men to live and trade each on his own private stock of reason, because we suspect that the stock in each man is small, and that the individuals would do better to avail themselves of the general bank and capital of nations and of ages." But because he discerned this, he regarded the effort of Protestantism to throw individuals back upon themselves as merely tending to empty their minds of all valuable contents, and to deliver them over to their own individual caprice. Private judgment and popular government are to him only other forms of expression for intellectual and political anarchy; and his remedy for the moral diseases of modern times is the restoration of that division of the spiritual and temporal authorities, which existed in the Middle Ages. But there is another aspect of the Protestant movement and of these apparently anarchical doctrines, to which Comte pays no attention. Catholicism, as we have seen, had developed one aspect of Christianity, until, by its exclusive prominence, the principle of Christianity itself was on the point of being lost. It had changed the opposition of laity and clergy, world and Church, from a relative into an absolute one; it had presented its doctrine, not as something which the spirit of the individual may ultimately verify for itself, but as something to which it must permanently submit without any verification. It had made the worship into an opus operatum instead of a means through which the feelings of the worshipper could be at once drawn out and expressed. Now, it is as opposed to these tendencies that the Protestant movement had its highest importance. It would, no doubt, be intellectual anarchy, for every individual to claim to judge for himself, on subjects for which he has not the requisite training or discipline; but it is a slavery scarcely less corrupting in its effect than anarchy, when he is made to regard the difference between himself and his teachers as a permanent and absolute one. In the former case, he has no sufficient feeling of his want to make him duly submissive to teaching; in the latter, he has no sufficient consciousness of his capacity to awake a due reaction of his thought upon the matter received from his teachers. Again, the decline of the sovereignty of the people would be the negation of all rule, if it meant that the uninstructed many should govern themselves by their own insight, and that the instructed few should simply be their servants and their instruments. But where the people are not recognized as the ultimate source of power, where their consent is not in any regular way made necessary to the proceedings of their governors, they are by that very fact kept in a perpetual tutelage, and cannot possibly feel that the life of the State is their own life. Now, the most important effect of the Protestant movement was just this, that it awakened in each individual the consciousness of his universal nature, in other words the consciousness that there is no external power or sovereignty, divine or human, to which he has absolutely and permanently to submit, but that every outward claim of authority must ultimately be justified by the inner witness of the spirit. The freedom of man is that his obedience to the State, to the Church, even to God, is the obedience of his natural to his spiritual self. The essential truth of the Reformation lay in its republication of the doctrine that the voice of God speaks within and not only without us, and indeed that "it is only by the God within that we can comprehend the God without." And the nations, which had learned that lesson in religion, soon hastened to apply it to the social and political order of life. It is undoubtedly a dangerous lesson, as may be seen, not only in the tendency of many Protestant sects to put the inner life in opposition to the outer, and so to deprive the former of all wider contents and interests; but also in the ultimate substitution, by Rousseau and others, of the assertion of the natural, for the assertion of the spiritual, man. In such extreme cases we find the mere capacity of man for a higher life treated as if it were the higher life itself; forgetting that the capacity is nothing unless it be realized, and that its realization requires the surrender of individual liberty and private judgment to the guidance and teaching of those, in whom that realization has already taken place. But it is not the less true that the consciousness of the capacity, and the consequent sense of the duty of becoming, not merely a slave or instrument, but an organ, of the intellectual and moral life of mankind, is the essential basis of modern life. "Henceforth, I call you not servants, for the servant knoweth not what his lord doeth; but I have called you friends," is a word of Christ which scarcely began to be verified till the Reformation. And while its verification cannot mean the negation of that division of labour upon which society rests,—cannot mean that each one should know and judge, any more than that each one should do, everything for himself,—it at least means that every power and authority should henceforth be, in the true sense of the word, spiritual, and rest for its main support upon the opinion of those who obey it.It is because he has not appreciated this truth that Comte so decidedly breaks with the democratic spirit of modern times, and seeks to set up an aristocracy in the State and a monarchy in the Church. Yet the spirit of the age is, after all, too strong for him, and while he refuses to the governed any regular and legitimate way of reacting upon the powers that govern them, he recognizes that the ultima ratio, the final remedy for misgovernment, lies in their irregular and illegitimate action.As regards the State, he declares that "the right of insurrection is the ultimate resource with which no society should allow itself to dispense."[40] And as regards the Church he says that if "the High Priest of Humanity, supported by the body of the clergy, should go wrong, then the only remedy left would be the refusal of co-operation, a remedy which can never fail, as the priesthood rests solely on conscience and opinion, and succumbs, therefore, to their adverse sentence." The civil government, in fact, can bring the spiritual power to a dead-lock, by "suspending its stipend, for in cases of serious error, popular subscriptions would not replace it, unless on the supposition of a fanaticism scarcely compatible with the Positive faith, where there is enthusiasm for the doctrines, rather than for the teachers."[41] Comte also desiderates among the proletariate a strong reactive influence of public opinion, by which the officers, both of Church and State, are to be kept to their work. But if this is desirable, why should the proletariate have no regular means of making their will felt? An "organic" theory of the constitution of society must surely provide every real force with a legitimate form of expression; if a social theory embodies the idea of revolution in it, it is self-condemned.

Comte's social ideal is in many respects a close reproduction of the mediæval system, with its régime dispersif of feudalism in secular politics, and its concentration of Papal authority in the Church. For him, the growth of national States to their present dimensions, and, on the other hand, the increasing division of labour in the realm of thought, are equally steps in the wrong direction. Still more strongly, if possible, does he reprobate that interference of the State with spiritual matters, such as the education of the people and its religious life, which has been the natural consequence of the failure of the mediæval Church to maintain its old authority. Notwithstanding his worship of humanity, the idea of a "parliament of man, a federation of the world," by which all the powers of mankind should be united for the attainment of the highest material and spiritual good, has no attraction for him. To reduce the State to the dimensions of a commune, and to confine it to the care of purely material interests, is his first political proposal. France, England, and Spain (and we may now add Germany and Italy) are, in his view, "factitious aggregates without solid justification," and they will only become "free and durable States," when they are broken up into fragments, each with a population of two or three millions, and a territory not exceeding that of Belgium or Tuscany. The "West" will thus be divided into seventy republics, and the earth into five hundred, and the main work of the patriciate will be to direct and regulate the industrial life of the community; each member of the banker triumvirate, who are to be at the head of the State, having one of the great industrial departments under his special superintendence. On the other hand the unity of humanity is to be represented solely by the spiritual power, in whose hands is to be left the whole work of extending science, teaching the people, and exercising a moral censorship over all Governments and individuals. And while this spiritual power is, for practical purposes, to be strictly organized on the model of the mediæval Church, it is also, like that Church, to remain, for scientific purposes, inorganic. In other words, it is to admit no scientific division of labour, but every one, like a mediæval doctor, is to profess all science, adding to this the priestly office, which, with Comte, includes both the cure of souls and of bodies.

To criticize the details of this scheme seems to be unnecessary after what has been already said.It is not to be denied that the division of Church and State in the Middle Age was a most important and even necessary condition of progress.Christianity could never have been impressed upon the minds of men, if its concrete application and development had been too rapid.The essential condition of such development was that men should not concern themselves too prematurely with it.For the consequences of a moral and religious principle cannot be reached by direct logical deductions; it is like a living germ, in which, by no analysis or dissection, you can discover the lineaments of the future plant.To know what it really is, or involves, you must plant it in the minds of men, and let it grow.Hence the mediæval Church was strong in its weakness, and it was its very victories over the temporal power that were its greatest danger.It became corrupt and lost its hold upon the minds of men, just when it seemed to have established its right to an absolute supremacy.Comte, following De Maistre, attaches great importance to the position of the Popes as arbiters between the Sovereigns and nations of mediæval Europe.But he forgets that, in claiming and maintaining this position the Popes were distinctly ceasing to be a spiritual power, if it be the function of a spiritual power to inculcate principles rather than to use them to solve present difficulties.A power interfering in this way with the immediate struggle of interests, could not but be invaded by the passions they excite, and it was the more certain to be corrupted by these passions, because it conceived them to be evil, and pretended altogether to renounce them.The mediæval authority of the Church might have its value, as an anticipation of the peaceful federation of the nations under one supreme Government, but it was at the same time the first step towards the erasing of the distinction between the temporal and the spiritual power.

The truth seems to be that the distinction, of secular and spiritual powers, except in the sense already indicated, is essentially irrational, and that the attempt to realise it in practice must involve, as it did involve in the Middle Ages, a continual internecine struggle.To set up two regularly constituted powers face to face with each other, one claiming man's allegiance in the name of his spiritual, and the other in the name of his temporal, interests, is to organize anarchy.So long as man's body and soul are inseparable, it will be impossible to divide the world between Cæsar and God; for in one point of view all is Cæsar's, and in another all is God's.In the Middle Ages the conflict of two despotisms was necessary to the growth of freedom; but, when government ceases to be despotic, the need for such division of power passes away.The relative separation between the speculative and the practical classes—between the scientific and moral teachers of mankind, on the one hand, and the statesmen or administrators who have to discover what immediate changes in the organization of life have become necessary, on the other—is a division of labour which can surely be attained without breaking up the unity of the social body.It is not desirable that the philosopher, or priest, or man of science, should be king—and we may even acknowledge that if he were king he would probably be a very bad one;—on the other hand, it is desirable that he should have his due influence, as the teacher of those general truths out of which all practical improvement must ultimately spring.But the natural difference of the tastes and capacities of men should, in a well-organized State, be sufficient to secure due influence to those who are the natural representatives of man's spiritual interests (whether they be religious, philosophic, or scientific), without tempting them from their proper task of discovering and teaching the truth, to the less appropriate work of determining how much of it comes within "the sphere of practical politics."Comte, indeed, by organizing them as an independent power apart from, and outside of, the State, would make such a perversion extremely probable.A hierarchy of priests, under a despotic Pope, would soon cease to be, in any sense, a spiritual power; and this would be only the more certain if, by the Comtist denunciation of specialism, they were prohibited from any division of labour according to capacity in their own peculiar sphere of scientific research.For by this prohibition their attention would be drawn more and more from the truth of their doctrines to their immediate practical effects, not to mention that, in the case of all but a few comprehensive minds, the natural result would be an omniscient superficiality, which would be the enemy of all real culture.For he who knows one thing well may find the whole in the part; but he who knows the whole superficially, inevitably reduces it to the level of something partial and subjective.Deprived of its natural aim, the Comtist Church of the future would inevitably throw itself, with all its energy, into the task of directly influencing the practical life of men, and there it would find itself in the presence of a number of communal States, none of them large enough to offer any effective resistance. Positivism must indeed alter human nature, if such a priesthood would not seek to make itself despotic, especially if it could wield such a formidable weapon as the Positivist excommunication is supposed to be.[42]

The truth is that Comte commits the same error which misled Montesquieu and his followers, when they supposed that the great security of a free State lay in the separation of the legislative, executive, and judicial powers,—i.e., in treating the different organs through which the common life expresses itself as if they were independent organisms. In doing so, they forgot that, if such a balance of power was realised, the effect must either be an equilibrium in which all movement must cease, or a struggle in which the unity of the State would be in danger of being lost.The true security against the dangers involved, on the one hand, in the direct application of theory to practice, and, on the other hand, in the separation of practice from theory, must lie, not in giving them independent positions as spiritual and temporal powers, but in the organic unity of the society—communal, national, or, if it may be, universal—to which the representatives of both belong.And organic unity, though it does not mean any special form of government, means at least two things: in the first place, that each great class or interest should have for itself a definite organ, and should therefore be able to act on the whole body in a regular and constitutional manner, so as to show all its force without revolutionary violence; and, in the second place, that no class or interest should have such an independent position, that there is no legal or constitutional method of bringing it into due subordination.But Comte, losing his balance in his jealousy of the individualistic and democratic movement of modern society, has built up a social ideal, which fails in both these points of view.And he is consequently obliged, against his will, to contemplate revolution and war as necessary resources of the Constitution.

It would not be fair to conclude these articles, which have necessarily been devoted in great part to criticism and controversy, without expressing a sense of the power and insight which are shown in the works of Comte, especially in the Politique PositiveControversy itself, it must be remembered, is a kind of homage; for, as Hegel says, "It is only a great man that condemns us to the task of explaining him."But if we can sometimes look down upon such men, it becomes us to remember that we stand upon their shoulders.Comte seems to me to occupy, as a writer, a position in some degree similar to that of Kant.He stands, or rather moves, between the old world and the new, and is broken into inconsistency by the effort of transition.Like Kant, he is embarrassed to the end by the ideas with which he started, and of which he can never free himself so as to make a new beginning. Comte had only a small portion of that power of speculative analysis which characterized his great predecessor, but he had much of his tenacity of thought, his power of continuous construction; and he had the same conviction of the all-importance of morals, and the same determination to make all his theoretic studies subordinate to the solution of the moral problem. Also, partly because he lived at a later time, and in the midst of a society which was in the throes of a social revolution, and partly because of the keenness and strength of his own social sympathies, he gives us a kind of insight into the diseases and wants of modern society, which we could not expect from Kant, and which throws new light upon the ethical speculations of Kant's idealistic successors. To believe that his system, as a whole, is inconsistent with itself, that his theory of historical progress is insufficient, and that his social ideal is imperfect, need not prevent us from recognizing that there are many valuable elements in his historical and social theories, and that no one who would study such subjects can afford to neglect them. A mind of such power cannot treat any subject without throwing much light upon it, which is independent of his special system of thought, and, above all, without doing much to show what are the really important difficulties in it which need to be solved. And, especially in such subjects, to discover the right question is to be half-way to the answer. Further, as Comte himself somewhere says, it is an immense advantage in studying any complex subject to have before us a distinct and systematic attempt to explain it; for it is only by criticism upon criticism that we can expect to reach the truth, in which all its varied sides and aspects are brought to a unity.

Edward Caird.

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THE PROBLEM OF THE GREAT PYRAMID.

A few months ago I endeavoured to trace out, in these pages, the probable origin of the week, as a measure of time, by a method which has not hitherto, so far as I know, been followed in such cases. I followed chiefly a line of à priori reasoning, considering how herdsmen and tillers of the soil would be apt at a very early period to use the moon as a means of measuring time, and how in endeavouring so to use her they would almost of necessity be led to employ special methods of subdividing the period during which she passes through her various phases. But while each step of the reasoning was thus based on à priori considerations, its validity was tested by the evidence which has reached us respecting the various methods employed by different nations of antiquity for following the moon's motions. It appears to me that the conclusions to which this method of reasoning led were more satisfactory, because more trustworthy, than those which have been reached respecting the week by the mere study of various traditions which have reached us respecting the early use of this widespread time measure.

I now propose to apply a somewhat similar method to a problem which has always been regarded as at once highly interesting and very difficult, the question of the purpose for which the pyramids of Egypt, and especially the pyramids of Ghizeh, were erected.But I do not here take the full problem under consideration.I have, indeed, elsewhere dealt with it in a general manner, and have been led to a theory respecting the pyramids which will be touched on towards the close of the present paper.Here, however, I intend to deal only with one special part of the problem, that part to which alone the method I propose to employ is applicable—the question of the astronomical purpose which the pyramids were intended to subserve.It will be understood, therefore, why I have spoken of applying a somewhat similar method, and not a precisely similar method; to the problem of the pyramids. For whereas in dealing with the origin of the week, I could from the very beginning of the inquiry apply the à priori method, I cannot do so in the case of the pyramids. I do not know of any line of à priori reasoning by which it could be proved, or even rendered probable, that any race of men, of whatever proclivities or avocations, would naturally be led to construct buildings resembling the pyramids. If it could be, of course that line of reasoning would at the same time indicate what purposes such buildings were intended to subserve. Failing evidence of this kind, we must follow at first the à posteriori method; and this method, while it is clear enough as to the construction of pyramids, for there are the pyramids themselves to speak unmistakably on this point, is not altogether so clear as to any one of the purposes for which the pyramids were built.

Yet I think that if there is one purpose among possibly many which the builders of the pyramids had in their thoughts, which can be unmistakably inferred from the pyramids themselves, independently of all traditions, it is the purpose of constructing edifices which should enable men to observe the heavenly bodies in some way not otherwise obtainable.If the orienting of the faces of the pyramids had been effected in some such way as the orienting of most of our cathedrals and churches—i.e., in a manner quite sufficiently exact as tested by ordinary observation, but not capable of bearing astronomical tests,—it might reasonably enough be inferred that having to erect square buildings for any purpose whatever, men were likely enough to set them four-square to the cardinal points, and that, therefore, no stress whatever can be laid on this feature of the pyramids' construction.But when we find that the orienting of the pyramids has been effected with extreme care, that in the case of the great pyramid, which is the typical edifice of this kind, the orienting bears well the closest astronomical scrutiny, we cannot doubt that this feature indicates an astronomical purpose as surely as it indicates the use of astronomical methods.

But while we thus start with what is to some degree an assumption, with what at any rate is not based on à priori considerations, yet manifestly we may expect to find evidence as we proceed which shall either strengthen our opinion on this point, or show it to be unsound. We are going to make this astronomical purpose the starting-point for a series of à priori considerations, each to be tested by whatever direct evidence may be available; and it is practically certain that if we have thus started in an entirely wrong direction, we shall before long find out our mistake. At least we shall do so, if we start with the desire to find out as much of the truth as we can, and not with the determination to see only those facts which point in the direction along which we have set out, overlooking any which seem to point in a different direction. We need not necessarily be in the wrong track because of such seeming indications. If we are on the right track, we shall see things more clearly as we proceed; and it may be that evidence which at first seems to accord ill with the idea that we are progressing towards the truth, may be found among the most satisfactory evidence obtainable. But we must in any case note such evidence, even at the time when it seems to suggest that we are on the wrong track. We may push on, nevertheless, to see how such evidence appears a little later. But we must by no means forget its existence. So only can we hope to reach the truth or a portion of the truth, instead of merely making out a good case for some particular theory.

We start, then, with the assumption that the great pyramid, called the Pyramid of Cheops, was built for this purpose, inter alia, to enable men to make certain astronomical observations with great accuracy; and what we propose to do is to inquire what would be done by men having this purpose in view, having, as the pyramid builders had, (1) a fine astronomical site, (2) the command of enormous wealth, (3) practically exhaustless stores of material, and (4) the means of compelling many thousands of men to labour for them.

Watching the celestial bodies hour by hour, day by day, and year by year, the observer recognizes certain regions of the heavens which require special attention, and certain noteworthy directions both with respect to the horizon and to elevation above the horizon.

For instance, the observer perceives that the stars, which are in many respects the most conveniently observable bodies, are carried round, as if they were rigidly attached to a hollow sphere, carried around an axis passing through the station of the observer (as through a centre) and directed towards a certain point in the dome of the heavens.That point, then, is one whose direction must not only be ascertained, but must be in some way or other indicated.Whatever the nature of an astronomer's instruments or observatory, whether he have but a few simple contrivances in a structure of insignificant proportions, or the most perfect instruments in a noble edifice of most exquisite construction and of the utmost attainable stability, he must in every case have the position of the pole of the heavens clearly indicated in some way or other.Now, the pole of the heavens is a point lying due north, at a certain definite elevation above the horizon.Thus the first consideration to be attended to by the builder of any sort of astronomical observatory, is the determination of the direction of the true north (or the laying down of a true north-and-south line), while the second is the determination, and in some way or other the indication of the angle of elevation above the north point, at which the true pole of the heavens may lie.

To get the true north-and-south line, however, the astronomer would be apt at first, perhaps, rather to make mid-day observations than to observe the stars at night.It would have been the observation of these which first called his attention to the existence of a definite point round which all the stars seem to be carried in parallel circles; but he would very quickly notice that the sun and the moon, and also the five planets, are carried round the same polar axis, only differing from the stars in this: that, besides being thus carried round with the celestial sphere, they also move upon that sphere, though with a motion which is very slow compared with that which they derive from the seeming motion of the sphere itself. Now, among these bodies the sun and moon possess a distinct advantage over the stars. A body illuminated by either the sun or the moon throws a shadow, and thus if we place an upright pointed rod in sunlight or moonlight, and note where the shadow of the point lies, we know that a straight line from the point to the shadow of the point is directed exactly towards the sun or the moon, as the case may be. Leaving the moon aside as in other respects unsuitable, for she only shines with suitable lustre in one part of each month, we have in the sun's motions a means of getting the north-and-south line by thus noting the position of the shadow of a pointed upright. For being carried around an inclined axis directed northwards, the sun is, of course, brought to his greatest elevation on any given day when due south. So that if we note when the shadow of an upright is shortest on any day, we know that at that moment the sun is at his highest or due south; and the line joining the centre of the upright's base with the end of the shadow at that instant lies due north-and-south.

But though theoretically this method is sufficient, it is open, in practice, to a serious objection.The sun's elevation, when he is nearly at his highest, changes very slowly; so that it is difficult to determine the precise moment when the shadow is shortest.But the direction of the shadow is steadily changing all the time that we thus remain in doubt whether the sun's elevation has reached its maximum or not.We are apt, then, to make an error as to time, which will result in a noteworthy error as to the direction of the north-and-south line.

For this reason, it would be better for any one employing this shadow method to take two epochs on either side of solar noon, when the sun was at exactly the same elevation, or the shadow of exactly the same length,—determining this by striking out a circle around the foot of the upright, and observing where the shadow's point crossed this circle before noon in drawing nearer to the base, and after noon in passing away from the base.These two intersections with the circle necessarily lie at equal distances from the north-and-south line, which can thus be more exactly determined than by the other method, simply because the end of the shadow crosses the circle traced on the ground at moments which can be more exactly determined than the moment when the shadow is shortest.

Now, we notice in this description of methods which unquestionably were followed by the very earliest astronomers, one circumstance which clearly points to a feature as absolutely essential in every astronomical observing station. (I do not say "observatory," for I am speaking just now of observations so elementary that the word would be out of place.) The observer must have a perfectly flat floor on which to receive the shadow of the upright pointer. And not only must the floor be flat, but it must also be perfectly horizontal. At any rate, it must not slope down either towards the east or towards the west, for then the shadows on either side of the north-and-south line would be unequal. And though a slope towards north or south would not affect the equality of such shadows, and would therefore be admissible, yet it would clearly be altogether undesirable; since the avoidance of a slope towards east or west would be made much more difficult if the surface were tilted, however slightly, towards north or south. Apart from this, several other circumstances make it extremely desirable that the surface from which the astronomers make their observations should be perfectly horizontal. In particular, we shall see presently that the exact determination of elevations above the eastern and western horizons would be very necessary even in the earliest and simplest methods of observation, and for this purpose it would be essential that the observing surface should be as carefully levelled in a north-and-south as in an east-and-west direction.

We should expect to find, then, that when the particular stage of astronomical progress had been reached, at which men not only perceived the necessity of well-devised buildings for astronomical observation, but were able to devote time, labour, and expense to the construction of such buildings, the first point to which they would direct their attention would be the formation of a perfectly level surface, on which eventually they might lay down a north-and-south or true meridional line.

Now, of the extreme care with which this preliminary question of level was considered by the builders of the great pyramid, we have singularly clear and decisive evidence.For all around the base of the pyramid there was a pavement, and we find the builders not only so well acquainted with the position of the true horizontal plane at the level of this pavement, but so careful to follow it (even as respects this pavement, which, be it noticed, was only, in all probability, a subsidiary and quasi-ornamental feature of the building), that the pavement "was varied in thickness at the rate of about an inch in 100 feet to make it absolutely level, which the rock was not."[43]

But now with regard to the true north-and-south direction, although the shadow method, carried out on a truly level surface, would be satisfactory enough for a first rough approximation, or even for what any but astronomers would regard as extreme accuracy, it would be open to serious objections for really exact work. These objections would have become known to observers long before the construction of the pyramid was commenced, and would have been associated with the difficulties which suggested, I think, the idea itself of constructing such an edifice.

Supposing an upright pointed post is set up, and the position of the end of the shadow upon a perfectly level surface is noted; then whatever use we intend to make of this observation, it is essential that we should know the precise position of the centre of the upright's base, and also that the upright should be truly vertical. Otherwise we have only exactly obtained the position of one end of the line we want, and to draw the line properly we ought as exactly to know the position of the other end. If we want also to know the true position of a line joining the point of the upright and the shadow of this point, we require to know the true height of the upright. And even if we have these points determined, we still have not a material line from the point of the upright to the place of its shadow. A cord or chain from one point to the other would be curved, even if tightly stretched, and it would not be tightly stretched, if long, without either breaking or pulling over the upright. A straight bar of the required length could not be readily made or used: if stout enough to lie straight from point to point it would be unwieldy, if not stout enough so that it bent under its own weight it would be useless.

Thus the shadow method, while difficult of application to give a true north-and-south horizontal line, would fail utterly to give material indications of the sun's elevation on particular days, without which it would be impossible to obtain in this manner any material indications of the position of the celestial pole.

A natural resource, under these circumstances—at least a natural resource for astronomers who could afford to adopt the plan—would be to build up masses of masonry, in which there should be tubular holes or tunnellings pointing in certain required directions.In one sense the contrivance would be clumsy, for a tunnelling once constructed, would not admit of any change of position, nor even allow of any save very limited changes in the direction of the line of view through them.In fact, the more effective a tunnelling would be in determining any particular direction, the less scope, of course, would it afford for any change in the direction of a line of sight along it.So that the astronomical architect would have to limit the use of this particular method to those cases in which great accuracy in obtaining a direction line and great rigidity in the material indication of that line's position were essential or at least exceedingly desirable.Again, in some cases presently to be noticed, he would require, not a tubing directed to some special fixed point in the sky, but an opening commanding some special range of view.Yet again it would be manifestly well for him to retain, whenever possible, the power of using the shadow method in observing the sun and moon; for this method in the case of bodies varying their position on the celestial sphere, not merely with respect to the cardinal points, would be of great value. Its value would be enhanced if the shadows could be formed by objects and received on surfaces holding a permanent position.

We begin to see some of the requirements of an astronomical building such as we have supposed the earlier observers to plan.

First, such a building must be large, to give suitable length to the direction lines, whether along edges of the building or along tubular passages or tunnellings within it.Secondly, it must be massive in order that these edges and passages might have the necessary stability and permanence.Thirdly, it must be of a form contributing to such stability, and as height above surrounding objects (even hills lying at considerable distances) would be a desirable feature, it would be proper to have the mass of masonry growing smaller from the base upwards.Fourthly, it must have its sides carefully oriented, so that it must have either a square or oblong base with two sides lying exactly north and south, and the other two lying exactly east and west.Fifthly, it must have the direction of the pole of the heavens either actually indicated by a tunnelling of some sort pointed directly polewards, or else inferable from a tunnelling pointing upon a suitable star close to the true pole of the heavens.

The lower part of a pyramid would fulfil the conditions required for the stability of such a structure, and a square or oblong form would be suitable for the base of such a pyramid.We must not overlook the fact that a complete pyramid would be utterly unsuitable for an astronomical edifice.Even a pyramid built up of layers of stone and continued so far upwards that the uppermost layer consisted of a single massive stone, would be quite useless as an observatory.The notion which has been entertained by some fanciful persons, that one purpose which the great pyramid was intended to subserve, was to provide a raised small platform high above the general level of the soil, in order that astronomers might climb night after night to that platform, and thence make their observations on the stars, is altogether untenable.Probably no fancy respecting the pyramids has done more to discredit the astronomical theory of these structures than has this ridiculous notion; because even those who are not astronomers and therefore little familiar with the requirements of a building intended for astronomical observation, perceive at once the futility of any such arrangement, and the enormous, one may almost say the infinite disproportion between the cost at which the raised small platform would have been obtained, and the small advantage which astronomers would derive from climbing up to it instead of observing from the ground level.Yet we have seen this notion not only gravely advanced by persons who are to some degree acquainted with astronomical requirements, but elaborately illustrated.Thus, in Flammariou's "History of the Heavens," there is a picture representing six astronomers in eastern garb, perched in uncomfortable attitudes on the uppermost steps of a pyramid, whence they are staring hard at a comet, naturally without the slightest opportunity of determining its true position in the sky, since they have no direction lines of any sort for their guidance. Apart from this, their attention is very properly directed in great part to the necessity of preserving their equilibrium. In only one point in fact does this picture accord with à priori probabilities—namely, in the great muscular development of these ancient observers. They are perfectly herculean, and well they might be, if night after night they had to observe the celestial bodies from a place so hard to reach, and where attitudes so awkward must be maintained during the long hours of the night.

It is perfectly clear, and is in fact one of the chief difficulties of the astronomical theory of the pyramids, that it would only be when these buildings were as yet incomplete that they could subserve any useful astronomical purposes; nevertheless we must not on this account suffer ourselves at this early stage of our inquiry to be diverted from the astronomical theory by what must be admitted to be a very strong argument against it. We have seen that there is such decisive and even demonstrative evidence in favour of the theory that the pyramids were not oriented in a general, still less in a merely casual, manner, and this is, in reality, such clear evidence of their astronomical significance, that we must pass further on upon the line of reasoning which we have adopted—prepared to turn back indeed if absolutely convincing evidence should be found against the theory of the astronomical purpose of the pyramids, but anticipating rather that, on a close inquiry, a means of obviating this particular objection may before long be found.

Let us suppose, then, that astronomers have determined to erect a massive edifice, on a square or oblong base properly oriented, constructing within this edifice such tubular openings as would be most useful for the purpose of indicating the true directions of certain celestial objects at particular times and seasons.

Before commencing so costly a structure they would be careful to select the best possible position for it, not only as respects the nature of the ground, but also as respects latitude.For it must be remembered that, from certain parts of the earth, the various points and circles which the astronomer recognizes in the heavens occupy special positions and fulfil special relations.

So far as conditions of the soil, surrounding country, and so forth are concerned, few positions could surpass that selected for the great pyramid and its companions.The pyramids of Ghizeh are situated on a platform of rock, about 150 feet above the level of the desert.The largest of them, the Pyramid of Cheops, stands on an elevation free all around, insomuch that less sand has gathered round it than would otherwise have been the case.How admirably suited these pyramids are for observing stations is shown by the way in which they are themselves seen from a distance.It has been remarked by every one who has seen the pyramids that the sense of sight is deceived in the attempt to appreciate their distance and magnitude. "Though removed several leagues from the spectator, they appear to be close at hand; and it is not until he has travelled some miles in a direct line towards them, that he becomes sensible of their vast bulk and also of the pure atmosphere through which they are viewed."

With regard to their astronomical position, it seems clear that the builders intended to place the great pyramid precisely in latitude 30°, or, in other words, in that latitude where the true pole of the heavens is one-third of the way from the horizon to the point overhead (the zenith), and where the noon sun at true spring or autumn (when the sun rises almost exactly in the east, and sets almost exactly in the west) is two-thirds of the way from the horizon to the point overhead.In an observatory set exactly in this position, some of the calculations or geometrical constructions, as the case may be, involved in astronomical problems, are considerably simplified.The first problem in Euclid, for example, by which a triangle of three equal sides is made, affords the means of drawing the proper angle at which the mid-day sun in spring or autumn is raised above the horizon, and at which the pole of the heavens is removed from the point overhead.Relations depending on this angle are also more readily calculated, for the very same reason, in fact, that the angle itself is more readily drawn.And though the builders of the great pyramid must have been advanced far beyond the stage at which any difficulty in dealing directly with other angles would be involved, yet they would perceive the great advantage of having one among the angles entering into their problems thus conveniently chosen.In our time, when by the use of logarithmic and other tables, all calculations are greatly simplified, and when also astronomers have learned to recognize that no possible choice of latitude would simplify their labours (unless an observatory could be set up at the North Pole itself, which would be in other respects inconvenient), matters of this sort are no longer worth considering, but to the mathematicians who planned the great pyramid they would have possessed extreme importance.

To set the centre of the pyramid's future base in latitude 30°, two methods could be used, both already to some degree considered—the shadow method, and the Pole-star method.If at noon, at the season when the sun rose due east and set due west, an upright A C were found to throw a shadow C D, so proportioned to A C that A C D would be one-half of an equal-sided triangle, then, theoretically, the point where this upright was placed would be in latitude 30°.As a matter of fact it would not be, because the air, by bending the sun's rays, throws the sun apparently somewhat above his true position.Apart from this, at the time of true spring or autumn, the sun does not seem to rise due east, or set due west, for he is raised above the horizon by atmospheric refraction, before he has really reached it in the morning, and he remains raised above it after he has really passed below—understanding the word "really" to relate to his actual geometrical direction. Thus, at true spring and autumn, the sun rises slightly to the north of east, and sets slightly to the north of west. The atmospheric refraction is indeed so marked, as respects these parts of the sun's apparent course, that it must have been quickly recognized. Probably, however, it would be regarded as a peculiarity only affecting the sun when close to the horizon, and would be (correctly) associated with his apparent change of shape when so situated. Astronomers would be prevented in this way from using the sun's horizontal position at any season to guide them with respect to the cardinal points, but they would still consider the sun, when raised high above the horizon, as a suitable astronomical index (so to speak), and would have no idea that even at a height of sixty degrees above the horizon, or seen as in direction D A, Fig. 1, he is seen appreciably above his true position.

Adopting this method—the shadow method—to fix the latitude of the pyramid's base, they would conceive the sun was sixty degrees above the horizon at noon, at true spring or autumn, when in reality he was somewhat below that elevation.Or, in other words, they would conceive they were in latitude 30° north, when in reality they were farther north (the mid-day sun at any season sinking lower and lower as we travel farther and farther north).The actual amount by which, supposing their observations exact, they would thus set this station north of its proper position, would depend on the refractive qualities of the air in Egypt.But although there is some slight difference in this respect between Egypt and Greenwich, it is but small; and we can determine from the Greenwich refraction tables, within a very slight limit of error, the amount by which the architects of the great pyramid would have set the centre or the base north of latitude 30°, if they had trusted solely to the shadow method.The distance would have been as nearly as possible 1125 yards, or say three furlongs.

Now, if they followed the other method, observing the stars around the pole, in order to determine the elevation of the true pole of the heavens, they would be in a similar way exposed to error arising from the effects of atmospheric refraction.They would proceed probably somewhat in this wise:—Using any kind of direction lines, they would take the altitude of their Polar star (1) when passing immediately under the pole, and (2) when passing immediately above the pole.The mean of the altitudes thus obtained would be the altitude of the true pole of the heavens.Now, atmospheric refraction affects the stars in the same way that it affects the sun, and the nearer a star is to the horizon, the more it is raised by atmospheric refraction.The Pole-star in both its positions—that is when passing below the pole, and when passing above that point—is raised by refraction, rather more when below than when above; but the estimated position of the pole itself, raised by about the mean of these two effects, is in effect raised almost exactly as much as it would be if it were itself directly observed (that is, if a star occupied the pole itself, instead of merely circling close round the pole).We may then simplify matters by leaving out of consideration at present all questions of the actual Pole-star in the time of the pyramid builders, and simply considering how far they would have set the pyramid's base in error, if they had determined their latitude by observing a star occupying the position of the true pole of the heavens.

They would have endeavoured to determine where the pole appears to be raised exactly thirty degrees above the horizon.But the effect of refraction being to raise every celestial object above its true position, they would have supposed the pole to be raised thirty degrees, when in reality it was less raised than this.In other words, they would have supposed they were in latitude 30°, when, in reality, they were in some lower latitude, for the pole of the heavens rises higher and higher above the horizon as we pass to higher and higher latitudes.Thus they would set their station somewhat to the south of latitude 30°, instead of to the north, as when they were supposed to have used the shadow method.Here again we can find how far they would set it south of that latitude.Using the Greenwich refraction table (which is the same as Bessel's), we find that they would have made a much greater error than when using the other method, simply because they would be observing a body at an elevation of about thirty degrees only, whereas in taking the sun's mid-day altitude in spring or autumn, they would be observing a body at twice as great an elevation.The error would be, in fact, in this case, about 1 mile 1512 yards.

It seems not at all unlikely that astronomers, so skilful and ingenious as the builders of the pyramid manifestly were, would have employed both methods.In that case they would certainly have obtained widely discrepant results, rough as their means and methods must unquestionably have been, compared with modern instruments and methods.The exact determination from the shadow plan would have set them 1125 yards to the north of the true latitude; while the exact determination from the Pole-star method would have set them 1 mile 1512 yards south of the true latitude.Whether they would thus have been led to detect the effect of atmospheric refraction on celestial bodies high above the horizon may be open to question.But certainly they would have recognized the action of some cause or other, rendering one or other method, or both methods, unsatisfactory If so, and we can scarcely doubt that this would actually happen (for certainly they would recognize the theoretical justice of both methods, and we can hardly imagine that having two available methods, they would limit their operations to one method only), they would scarcely see any better way of proceeding than to take a position intermediate between the two which they had thus obtained. Such a position would lie almost exactly 1072 yards south of true latitude 30° north.

Whether the architects of the pyramid of Cheops really proceeded in this way or not, it is certain that they obtained a result corresponding so well with this that if we assume they really did intend to set the base of the pyramid in latitude 30°, we find it difficult to persuade ourselves that they did not follow some such course as I have just indicated—the coincidence is so close considering the nature of the observations involved.According to Professor Piazzi Smyth, whose observational labours in relation to the great pyramid are worthy of all praise, the centre of the base of this pyramid lies about 1 mile 568 yards south of the thirtieth parallel of latitude.This is 944 yards north of the position they would have deduced from the Pole-star method; 1 mile 1693 yards south of the position they would have deduced from the shadow method; and 1256 yards south of the mean position between the two last-named.The position of the base seems to prove beyond all possibility of question that the shadow method was not the method on which sole or chief reliance was placed, though this method must have been known to the builders of the pyramid.It does not, however, prove that the star method was the only method followed.A distance of 944 yards is so small in a matter of this sort that we might fairly enough assume that the position of the base was determined by the Pole-star method.If, however, we supposed the builders of the pyramid to have been exceedingly skilful in applying the methods available to them, we might not unreasonably conclude from the position of the pyramid's base that they used both the shadow method and the Pole-star method, but that, recognizing the superiority of the latter, they gave greater weight to the result of employing this method.Supposing, for instance, they applied the Pole-star method three times as often as the shadow method, and took the mean of all the results thus obtained, then the deduced position would lie three times as far from the northern position obtained by the shadow method as from the southern position obtained by the Pole-star method.In this case their result, if correctly deduced, would have been only about 156 yards north of the actual present position of the centre of the base.

It is impossible, however, to place the least reliance on any calculation like that made in the last few lines. By à posteriori reasoning such as this one can prove almost anything about the pyramids. For observe, though presented as à priori reasoning, it is in reality not so, being based on the observed fact, that the true position lies more than three times as far from the northerly limit as from the southern one. Now, if in any other way, not open to exception, we knew that the builders of the pyramid used both the sun method and the star method, with perfect observational accuracy, but without knowledge of the laws of atmospheric refraction, we could infer from the observed position the precise relative weights they attached to the two methods. But it is altogether unsafe, or, to speak plainly, it is in the logical sense a perfectly vicious manner of reasoning, to ascertain first such relative weights on an assumption of this kind, and having so found them, to assert that the relation thus detected is a probable one in itself, and that since, when assumed, it accounts precisely for the observed position of the pyramid, therefore the pyramid was posited in that way and no other. It has been by unsound reasoning of this kind that nine-tenths of the absurdities have been established on which Taylor and Professor Smyth and their followers have established what may be called the pyramid religion.

All we can fairly assume as probable from the evidence, in so far as that evidence bears on the results of à priori considerations, is that the builders of the great pyramid preferred the Pole-star method to the shadow method, as a means of determining the true position of latitude 30° north. They seem to have applied this method with great skill considering the means at their disposal, if we suppose that they took no account whatever of the influence of refraction. If they took refraction into account at all they considerably underrated its influence.

Piazzi Smyth's idea that they knew the precise position of the thirtieth parallel of latitude, and also the precise position of the parallel, where, owing to refraction, the Pole-star would appear to be thirty degrees above the horizon, and deliberately set the base of the pyramid between these limits (not exactly or nearly exactly half-way, but somewhere between them), cannot be entertained for a moment by any one not prepared to regard the whole history of the construction of the pyramid as supernatural. My argument, let me note in passing, is not intended for persons who take this particular view of the pyramid, a view on which reasoning could not very well be brought to bear.

If the star method had been used to determine the position of the parallel of 30° north latitude, we may be certain it would be used also to orient the building.Probably indeed the very structures (temporary, of course) by which the final observations for the latitude had been made, would remain available also for the orientation.These structures would consist of uprights so placed that the line of sight along their extremities (or along a tube perhaps borne aloft by them in a slanting position) the Pole-star could be seen when immediately below or immediately above the pole.Altogether the more convenient direction of the two would be that towards the Pole-star when below the pole.The extremities of these uprights, or the axis of the upraised tube, would lie in a north-and-south line considerably inclined to the horizon, because the pole itself being thirty degrees above the horizon, the Pole-star, whatever star this might be, would be high above the horizon even when exactly under the pole.No star so far from the pole as to pass close to the horizon would be of use even for the work of orientation, while for the work of obtaining the latitude it would be absolutely essential that a star close to the pole should be used.

A line along the feet of the uprights would run north-and-south.But the very object for which the great astronomical edifice was being raised, was that the north-and-south line amongst others should be indicated by more perfect methods.

Now at this stage of proceedings, what could be more perfect as a method of obtaining the true bearing of the pole than to dig a tubular hole into the solid rock, along which tube the Pole-star at its lower culmination should be visible?Perfect stability would be thus insured for this fundamental direction line.It would be easy to obtain the direction with great accuracy, even though at first starting the borings were not quite correctly made.And the further the boring was continued downwards towards the south the greater the accuracy of the direction line thus obtained.Of course there could be no question whatever in such underground boring, of the advantage of taking the lower passage of the Pole-star, not the upper.For a line directly from the star at its upper passage would slant downwards at an angle of more than thirty degrees from the horizon, while a line directly from the star at its lower passage would slant downwards at an angle of less than thirty degrees; and the smaller this angle the less would be the length, and the less the depth of the boring required for any given horizontal range.

Besides perfect stability, a boring through the solid rock would present another most important advantage over any other method of orienting the base of the pyramid.In the case of an inclined direction line above the level of the horizontal base, there would be the difficulty of determining the precise position of points under the raised line; for manifest difficulties would arise in letting fall plumb-lines from various points along the optical axis of a raised tubing.But nothing could be simpler than the plan by which the horizontal line corresponding to the underground tube could be determined.All that would be necessary would be to allow the tube to terminate in a tolerably large open space; and from a point in the base vertically above this, to let fall a plumb-line through a fine vertical boring into this open space.It would thus be found how far the point from which the plumb-line was let fall lay, either to the east or to the west of the optical axis of the underground tunnel, and therefore how far to the east or to the west of the centre of the open mouth of this tunnel.Thus the true direction of a north-and-south line from the end of the tube to the middle of the base would be ascertained.This would be the meridian line of the pyramid's base, or rather the meridian line corresponding to the position of the underground passage directed towards the Pole-star when immediately under the pole.

A line at right angles to the meridian line thus obtained would lie due east and west, and the true position of the east-and-west line would probably be better indicated in this way than by direct observation of the sun or stars. If direct observation were made at all, it would be made not on the sun in the horizon near the time of spring and autumn, for the sun's position is then largely affected by refraction. The sun might be observed for this purpose during the summer months, at moments when calculation showed that he should be due east or west, or crossing what is technically the prime verticalPossibly the so-called azimuth trenches on the east side of the great pyramid may have been in some way associated with observations of this sort, as the middle trench is directed considerably to the north of the east point, and not far from the direction in which the sun would rise when about thirty degrees (a favourite angle with the pyramid architects) past the vernal equinox.But I lay no stress on this point.The meridian line obtained from the underground passage would have given the builders so ready a means of determining accurately the east and west lines for the north and south edges of the pyramid's base, that any other observations for this purpose can hardly have been more than subsidiary.

It is, of course, well known that there is precisely such an underground tunnelling as the considerations I have indicated seem to suggest as a desirable feature in a proposed astronomical edifice on a very noble scale.In all the pyramids of Ghizeh, indeed, there is such a tunnelling as we might expect on almost any theory of the relation of the smaller pyramids to the great one.But the slant tunnel under the great pyramid is constructed with far greater skill and care than have been bestowed on the tunnels under the other pyramids.Its length underground amounts to more than 350 feet, so that, viewed from the bottom, the mouth, about four feet across from top to bottom on the square, would give a sky range of rather less than one-third of a degree, or about one-fourth more than the moon's apparent diameter.But, of course, there was nothing to prevent the observers who used this tube from greatly narrowing these limits by using diaphragms, one covering up all the mouth of the tube, except a small opening near the centre, and another correspondingly occupying the lower part of the tube from which the observation was made.

It seems satisfactorily made out that the object of the slant tunnel, which runs 350 feet through the rock on which the pyramid is built, was to observe the Pole-star of the period at its lower culmination, to obtain thence the true direction of the north point.The slow motion of a star very near the pole would cause any error in time, as when this observation was made, to be of very little importance, though we can understand that even such observations as these would remind the builders of the pyramid of the absolute necessity of good time-measurements and time-observations in astronomical research.

Finding this point clearly made out, we can fairly use the observed direction of the inclined passage to determine what was the position of the Pole-star at the time when the foundations of the great pyramid were laid, and even what that Pole-star may have been. On this point there has never been much doubt, though considerable doubt exists as to the exact epoch when the star occupied the position in question. According to the observations made by Professor Smyth, the entrance passage has a slope of about 26° 27', which would have corresponded, when refraction is taken into account, to the elevation of the star observed through the passage, at an angle of about 26° 29' above the horizon. The true latitude of the pyramid being 29° 58' 51", corresponding to an elevation of the true pole of the heavens, by about 30° 1/2' above the horizon, it follows that if Professor Smyth obtained the true angle for the entrance passage, the Pole-star must have been about 3° 31-1/2' from the pole. Smyth himself considers that we ought to infer the angle for the entrance passage from that of other internal passages, presently to be mentioned, which he thinks were manifestly intended to be at the same angle of inclination, though directed southwards instead of northwards. Assuming this to be the case, though for my own part I cannot see why we should do so (most certainly we have no à priori reason for so doing), we should have 26° 18' as about the required angle of inclination, whence we should get about 3° 42' for the distance of the Pole-star of the pyramid's time from the true pole of the heavens. The difference may seem of very slight importance, and I note that Professor Smyth passes it over as if it really were unimportant; but in reality it corresponds to somewhat large time-differences. He quotes Sir J. Herschel's correct statement, that about the year 2170 B.C. the star Alpha Draconis, when passing below the pole, was elevated at an angle of about 26° 18' above the horizon, or was about 3° 42' from the pole of the heavens (I have before me, as I write, Sir J. Herschel's original statement, which is not put precisely in this way); and he mentions also that somewhere about 3440 B.C. the same star was situated at about the same distance from the pole. But he omits to notice that since, during the long interval of 1270 years, Alpha Draconis had been first gradually approaching the pole until it was at its nearest, when it was only about 3-1/2' from that point, and then as gradually receding from the pole until again 3° 42' from it, it follows that the difference of nine or ten minutes in the estimated inclination of the entrance passage corresponds to a very considerable interval in time, certainly to not less than fifty years. (Exact calculation would be easy, but it would be time wasted where the data are inexact.)

Having their base properly oriented, and being about to erect the building itself, the architects would certainly not have closed the mouth of the slant tunnel pointing northwards, but would have carried the passage onwards through the basement layers of the edifice, until these had reached the height corresponding to the place where the prolongation of the passage would meet the slanting north face of the building. I incline to think that at this place they would not be content to allow the north face to remain in steps, but would fit in casing stones (not necessarily those which would eventually form the slant surface of the pyramid, but more probably slanted so as to be perpendicular to the axis of the ascending passage.) They would probably cut a square aperture through such slant stones corresponding to the size of the passage elsewhere, so as to make the four surfaces of the passage perfectly plane from its greatest depth below the base of the pyramid to its aperture, close to the surface to be formed eventually by the casing stones of the pyramid itself.

Now, in this part of his work, the astronomical architect could scarcely fail to take into account the circumstance that the inclined passage, however convenient as bearing upon a bright star near the pole when that star was due north, was, nevertheless, not coincident in direction with the true polar axis of the celestial sphere. I cannot but think he would in some way mark the position of their true polar axis. And the natural way of marking it would be to indicate where the passage of his Pole-star above the pole ceased to be visible through the slant tube. In other words he would mark where a line from the middle of the lowest face of the inclined passage to the middle of the upper edge of the mouth was inclined by twice the angle 3° 42' to the axis of the passage. To an eye placed on the optical axis of the passage, at this distance from the mouth the middle of the upper edge of the mouth would (quam proximé) show the place of the true pole of the heavens. It certainly is a singular coincidence that at the part of the tube where this condition would be fulfilled, there is a peculiarity in the construction of the entrance passage, which has been indeed otherwise explained, but I shall leave the reader to determine whether the other explanation is altogether a likely one. The feature is described by Smyth as "a most singular portion of the passage—viz. , a place where two adjacent wall-joints, similar, too, on either side of the passage, were vertical or nearly so; while every other wall-joint, both above and below, was rectangular to the length of the passage, and, therefore, largely inclined to the vertical." Now I take the mean of Smyth's determinations of the transverse height of the entrance passage as 47.23 inches (the extreme values are 47.14 and 47.32), and I find that, from a point on the floor of the entrance passage, this transverse height would subtend an angle of 7° 24' (the range of Alpha Draconis in altitude when on the meridian) at a distance 363.65 inches from the transverse mouth of the passage. Taking this distance from Smyth's scale in Plate xvii. of his work on the pyramid ("Our Inheritance in the Great Pyramid"), I find that, if measured along the base of the entrance passage from the lowest edge of the vertical stone, it falls exactly upon the spot where he has marked in the probable outline of the uncased pyramid, while, if measured from the upper edge of the same stone, it falls just about as far within the outline of the cased pyramid as we should expect the outer edge of a sloped end stone to the tunnel to have lain.

It may be said that from the floor of the entrance passage no star could have been seen, because no eye could be placed there.But the builders of the pyramid cannot reasonably be supposed to have been ignorant of the simple properties of plane mirrors, and by simply placing a thin piece of polished metal upon the floor at this spot, and noting where they could see the star and the upper edge of the tunnel's mouth in contact by reflection in this mirror, they could determine precisely where the star could be seen touching that edge, by an eye placed (were that possible) precisely in the plane of the floor.

I have said there is another explanation of this peculiarity in the entrance passage, but I should rather have said there is another explanation of a line marked on the stone next below the vertical one.I should imagine this line, which is nothing more than a mark such "as might be ruled with a blunt steel instrument, but by a master hand for power, evenness, straightness, and still more for rectangularity to the passage axis," was a mere sign to show where the upright stone was to come.But Professor Smyth, who gives no explanation of the upright stone itself, except that it seems, from its upright position, to have had "something representative of setting up, or preparation for the erecting of a building," believes that the mark is as many inches from the mouth of the tunnel as there were years between the dispersal of man and the building of the pyramid; that thence downwards to the place where an ascending passage begins, marks in like manner the number of years which were to follow before the Exodus; thence along the ascending passage to the beginning of the great gallery the number of years from the Exodus to the coming of Christ; and thence along the floor of the grand gallery to its end, the interval between the first coming of Christ and the second coming or the end of the world, which it appears is to take place in the year 1881.It is true not one of these intervals accords with the dates given by those who are considered the best authorities in Biblical matters,—but so much the worse for the dates.

To return to the pyramid.

We have considered how, probably, the architect would plan the prolongation of the entrance passage to its place of opening out on the northern face.But as the pyramid rose layer by layer above its basement, there must be ascending passages of some sort towards the south, the most important part of the sky in astronomical research.

The astronomers who planned the pyramid would specially require four things.First, they must have the ascending passage in the absolutely true meridian plan; secondly, they would require to have in view, along a passage as narrow as the entrance tunnel, some conspicuous star, if possible a star so bright as to be visible by day (along such a tunnel) as well as by night; thirdly, they must have the means of observing the sun at solar noon on every day in the year; and fourthly, they must also have the entire range of the zodiac or planetary highway brought into view along their chief meridional opening.

The first of these points is at once the most important and the most difficult.It is so important, indeed, that we may hope for significant evidence from the consideration of the methods which would suggest themselves as available.

Consider:—The square base has been duly oriented.Therefore, if each square layer is placed properly, the continually diminishing square platform will remain always oriented.But if any error is made in this work the exactness of the orientation will gradually be lost.And this part of the work cannot be tested by astronomical observations as exact as those by which the base was laid, unless the vertical boring by which the middle of the base, or a point near it, was brought into connection with the entrance passage, is continued upwards through the successive layers of the pyramidal structure.As the rock rises to a considerable height within the interior of the pyramid,[44] probably to quite the height of the opening of the entrance passage on the northern slope, it would only be found necessary to carry up this vertical boring on the building itself after this level had been reached. But in any case this would be but an unsatisfactory way of obtaining the meridian plane when once the boring had reached a higher level than the opening of the entrance passage; for only horizontal lines from the boring to the inclined tunnelling would be of use for exact work, and no such lines could be drawn when once the level of the upper end of the entrance passage had been passed by the builders.

A plan would be available, however (not yet noticed, so far as I know, by any who have studied the astronomical relations of the great pyramid), which would have enabled the builders perfectly to overcome this difficulty.

Suppose the line of sight down the entrance passage were continued upwards along an ascending passage, after reflection at a perfectly horizontal surface—the surface of still water—then by the simplest of all optical laws, that of the reflection of light, the descending and ascending lines of sight on either side of the place of reflection, would lie in the same vertical plane, that, namely, of the entrance passage, or of the meridian.Moreover, the farther upwards an ascending passage was carried, along which the reflected visual rays could pass, the more perfect would be the adjustment of this meridional plane.

To apply this method, it would be necessary to temporarily plug up the entrance passage where it passed into the solid rock, to make the stone-work above it very perfect and close fitting, so that whenever occasion arose for making one of the observations we are considering, water might be poured into the entrance passage, and remain long enough standing at the corner (so to speak) where this passage and the suggested ascending passage could meet, for Alpha Draconis to be observed down the ascending passage. Fig. 2 shows what is meant. Here D C is the descending passage, C A the ascending passage, C the corner where the water would be placed when Alpha Draconis was about to pass below the pole. The observer would look down A C, and would see Alpha Draconis by rays which had passed down D C, and had been reflected by the water at C. Supposing the building to have been erected, as Lepsius and other Egyptologists consider, at the rate of one layer in each year, then only one observation of the kind described need be made per annum. Indeed, fewer would serve, since three or four layers of stone might be added without any fresh occasion arising to test the direction of the passage C A.