iii of California i Regional r Facility FAMILIAR SCIENCE WORKS BY MR. PROCTOR. EASY STAR LESSONS FOR YOUNG LEARNERS. With Star Maps for Every Night in the Year, Drawings of the Constellations, &c. By RICHARD A. PROCTOR. Crown 8vo. cloth extra, 6s. MYTHS AND MARVELS OF ASTRONOMY. By RICHARD A. PROCTOR. Crown 8vo. cloth extra, 6s. PLEASANT WAYS IN SCIENCE. By RICHARD A. PROCTOR. Crown 8vo. cloth extra, 6s. ROUGH WAYS MADE SMOOTH : a Series ot Familiar Essays on Scientific Subjects. By RICHARD A. PROCTOR. Crown 8vo. cloth extra, 6s. OUR PLACE AMONG INFINITIES : a Series of Essays contrasting our Little Abode in Space and Time with the Infinities Around us. By RICHARD A. PROCTOR. Crown 8vo. cloth extra, 6.?. THE EXPANSE OF HEAVEN : a Series of Essays on the Wonders of the Firmament. By RICHARD A. PROCTOR. Crown 8vo. cloth extra, 6s. WAGES AND WANTS OF SCIENCE WORKERS. By RICHARD A. PROCTOR. Crown 8vo. it. 6d. ' Mr. Proctor, of all writers of our time, best conforms to Matthew A mold's conception of a man of culture, in that he strives to humanize knowledge and divest it of whatever is liarsh, crude, or technical, and so makes it a source of happiness and brightness for all.' WESTMINSTER REVIEW. CHATTO & WINDUS, Piccadilly, W. FAMILIAR SCIENCE STUDIES RICHARD A. PROCTOR AUTHOR OF 1 ROUGH WAYS MADE SMOOTH ' ' THE POETRY OF ASTRONOMY ' ' THE EXPANSE OF HEAVEN ' ETC. ' Let knowledge grow front more to more ' TENNYSON Bonbon CHATTO & WINDUS, PICCADILLY 1882 All rights reserved LONDON : PRINTED BY SPOTTISWOODE AND CO., NEW-STREET SQUARE AND PARLIAMENT STREET PREFACE. THE ESSAYS in the present volume are taken chiefly from the Times, Scribner's Magazine, the Gentleman s Magazine, Belgravia, the Contemporary Review, and the Corn/till. I have little to say of them that I have not already said of other essays of mine which have been republished in book form. My object in writing them has been to give clear and simple but also correct accounts of scientific matters likely to be interesting to the general public. RICHARD A. PROCTOR. LONDON : December 1881. 111714.4 CONTENTS. PAGE NOTES ON INFINITY I SCIENCE AND RELIGION 30 A MENACING COMET 35 METEORIC DUST . . . . . . . .47 BIELA'S COMET AND METEORS 53 MOVEMENTS OF JUPITER'S CLOUD MASSES . . . .60 THE ORIGIN OF THE WEEK 77 THE PROBLEM OF THE GREAT PYRAMID . . . .104 THE PYRAMIDS OF GHIZEH 143 SUN-SPOTS AND FINANCIAL PANICS . . * . . . . 170 COLD AND WET 191 OUR WINTERS . . 201 ABOUT LOTTERIES 207 BETTING ON RACES 234 A GAMBLING SUPERSTITION . . . . . . . 254 THE FIFTEEN PUZZLE 273 ETNA 295 WEATHER FORECASTS 313 SOME STRANGELY FULFILLED DREAMS 322 SUSPENDED ANIMATION . . 345 OUR ASTRONOMERS ROYAL . . . . . . . 374 PHOTOGRAPHS OF -A GALLOPING HORSE. . . . . 402 FAMILIAR SCIENCE STUDIES. NOTES ON INFINITY. WERE it not for the infinities by which he is surrounded, man might believe that all knowledge is within his power at least, that every kind of knowledge is. to a greater or less degree, masterable. Men have analysed, one by one, the mysteries which surround the very great and the very little. On the one hand they have penetrated farther and farther into the star-depths, and have brought from beyond the re- motest range of the telescope information not only as to the existence, but as to the very constitution of the orbs which people space. We know the actual elements which build up worlds and suns on the outskirts of our present domain in space ; and that domain is widening year by year, and century by century, as telescopes of greater power are con- structed and greater skill acquired in their use. On the other hand, men have not only analysed the minutest struc- ture of organic matter, have not only dealt with the move- ments of molecules and even of atoms, but they have in- quired into the motions taking place in a medium more ethereal than matter as commonly understood a medium utterly beyond our powers of direct research, and whose characteristics are only indirectly inferred from the study of effects produced by its means. Such is the extreme present range of man's researches in the direction of the vast pn the one hand and the minute on the other ; and at first sight 2 FAMILIAR SCIENCE STUDIES. this range seems to include all that is or can be. For if the portions of the universe to which man cannot now penetrate, or may never be able to penetrate, resemble in the general characteristics of their structure and constitution the portions which he can examine, then, though he may examine but a part, he has in reality sampled the whole. And again, if the intimate structure of matter forming the visible universe, and the structure of that far subtler matter which forms the ether of space, represent the ultimate tex- ture so to speak of the universe, then in the analysis of che minute also man has attained a similar success. We might thus recognise the possibility of that which a French philosopher has called the ' Scientific Apotheosis of Man : ' in this sense, that, so far as quality of knowledge is con- cerned (as distinct from range of knowledge), men may be- come as gods, knowing all things, and even in the fulness of time able to discern good from evil, distinguishing that real good which exists in what, with our present knowledge, seems like absolute evil. But so soon as we consider the infinite, the absolute necessity, according to our conceptions, of infinity of space and time if not of matter and energy, we recognise not only that there is much to which our researches can never be extended, but that the knowledge which is unattainable infinitely transcends that which is attainable. Take, for instance, the infinity of space. If we could suppose that the extremest possible range of telescopic vision fell short to some degree only of the real limits of the universe, we might not unreasonably believe that the unattainable parts were not unlike the portions over which our survey extends. But when we consider what infinity of space really means, we are compelled to admit that the portion of the universe which we have examined, or can conceivably examine, is absolutely as nothing a mere mathematical point compared with the actual universe. This being so, it would be utterly unreason- able to suppose that what we know of the universe affords any measurable indication of the structure of the rest. The part NOTES ON INFINITY. 3 we know being as nothing compared with the whole, to assume that the remainder resembles it, is as unreasonable as it would be for a man who had seen but a single thread of a piece of cloth to attempt to infer from it the pattern of the whole. If such a man assumed that the whole piece was of one colour and made throughout of the same kind of thread, he would be much in the position of the man of science who should assume that the infinity of space surrounding the finite portion which we have examined, consists throughout of systems of suns single, multiple, and clustered attended by systems of planets. So again of the infinity of time. We know of certain processes which are taking place in that particular portion of time in which our lives are set, or over which our reasoning powers range ; inferring from the present what has happened in the remote past or will happen in the distant future. We trace back our earth to its beginning 'in tracts of fluent heat,' or pass farther back to what Huxley has called the ' nebulous cubhood ' of the solar system, or even attempt to conceive how the system of multitudinous suns filling the depths of space may have been formed by processes of development. And looking forward to the future, we trace out the progress of processes arising from those earlier ones, recognising apparently the ultimate surcease of every form of life, the life of all creatures living upon worlds, of worlds themselves, of solar systems, of systems of such systems, and of even higher orders of systems. If time were but finite, if we could conceive either a beginning or an end of absolute time, we might fairly enough suppose that processes such as these, and the subordinate processes associated with them, were the fulfilment of time. But time being infinite, of necessity we have no more reason for supposing that what we thus recognise in our domain of time re- sembles what takes place in other portions of time, than a man who listened for a single second to a concerted piece of music would have for imagining that the notes he heard B 2 4 FAMILIAR SCIENCE STUDIES. during that second were continued throughout the whole performance. Combining the consideration of the infinity of space with that of the infinity of time, we have no better right to consider that we understand the operation of the mighty mechanism of the universe, than one who for less than a second should be shown the least conceivable portion of a mighty machine would have thereafter to assert that he understood its entire workings. The saying of Laplace (whom, however, Swedenborg anticipated) that ' what we know is little, while the unknown is immense,' may truly be changed into this, that the known is nothing, the unknown infinite ; for whatever is finite, however great, bears to the infinite a ratio infinitely small, or is to the infinite as nothing. A million, equally with a single unit, is as nothing com- pared with a number infinitely large ; a million years, equally with a single second, is as nothing compared with eternity. The whole of what modern astronomy calls the universe is, equally with the minutest atom, as nothing compared with infinite space. ' System of nature!' exclaims Carlyle justly; ' to the wisest man, wide as is his vision, nature remains of quite infinite depth, of quite infinite expansion, and all ex- perience thereof limits itself to some few computed cen- turies and measured square miles.' Let us consider, however, whether, after all, we must admit that space is infinite or time eternal. Remembering that space and time are forms of thought, and that the ideas of infinite space and infinite time are inconceivable, may it not be that, though we cannot escape the inconceivable by rejecting these infinities, we may nevertheless be able to substitute some other conditions less utterly oppressive than they are ? So far as time is concerned, no attempt has been made, so far as I know, in this direction. It does not seem easy to imagine how time can be regarded as other than infinite. We should have entirely to change our conception of time, for instance, before we could regard it as self-repeating. NOTES ON INFINITY. 5 We can readily conceive the idea of a sequence of events being continually repeated, and thus assign a cyclical cha- racter to occupied time. But if we thus imagined that all the events now taking place had occurred many times before and will occur many times again, always in the same exact sequence, the cycles thus imagined would only be new and larger measures of absolute time. Though infinitely ex- tended in duration, according to our conceptions, they could no more be regarded as bearing a measurable ratio to time itself than the seconds or minutes into which we divide the part of time in which we live bear a measurable ratio to the duration, past, present, and future, of the visible uni- verse. I am not, indeed, prepared to admit that a more suc- cessful effort has hitherto been made, or can be made, to indicate the possibility that space may not be infinite. Some eminent masters of mathematical analysis, whose acumen and profundity are justly celebrated, have expressed their acceptance of certain views, presently to be described, which suggest the possibility that space may be finite ; but I find nothing either in their reasonings on this special subject, or in their writings generally, to suggest that they have the same mastery of geometrical as they have of analytical relations in mathematics. Nay, I venture to say that no competent geometrician who examines their reasoning can fail to recog- nise a confusion of thought, an indistinctness of mental vision, so soon as they pass from the verbal and mathe- matical expression of space relations, to the consideration of those relations themselves. Before considering the position they endeavour to maintain, let us briefly inquire into the general considerations which present themselves when we contemplate the relations of space as they appear to our conceptions. It must be admitted at the outset (and no doubt in this we may recognise a reason for the diversity of view which appears to exist), that no theory of the finiteness of space can possibly be more utterly inconceivable than the idea of 6 FAMILIAR SCIENCE STUDIES. infinite space itself. And by inconceivable I do not mean merely that which is beyond our power of picturing men- tally ; for many things which not only exist, but can be measured and gauged, cannot possibly be pictured in our minds. No man, for instance, can form a clear mental picture of the dimensions of our earth, still less of Jupiter's or of the Sun's ; while the distances of the stars distances which dwarf even the dimensions of the Sun into insignifi- cance are, in the ordinary use of the words, absolutely inconceivable. Yet, though we cannot picture these dimen- sions, we find no difficulty in admitting their actual existence. They are merely multiples of dimensions with which we are already familiar. But absolute infinity of space is unlike aught that the mind of man has hitherto been able to con- ceive. Aristotle well indicated this in his celebrated argu- ment for the finiteness of the universe, that argument of which Sir J. Herschel truly said that, though unanswerable, it never yet convinced mortal man. The straight line joining any two points in space, be they inhere they may, is finite, because it has two definite terminations ; therefore the uni- verse itself is finite. Equally unanswerable, however, though also equally unsatisfactory, is the retort in favour of the infinity of space. The straight line joining any two points in space, be they where they may, can be produced to any distance in the same straight line, 1 in either direction, and 1 It is singular that the elementary ideas of geometry are introduced at the very beginning of any inquiry into the subject of infinity of space. The three postulates of the geometry of the line and circle present to us : First, Aristotle's argument for a finite universe : secondly, the counter-argument for infinity of space ; and thirdly, the thought of Augustine (commonly attributed to Pascal) that the universe has its centre everywhere and its circumference nowhere. Let it be granted, says the first postulate, that a straight line may be drawn from any one point to any other point ; the second says, let it be granted that any finite line may be produced to any distance in the same straight line ; the third, let it be granted that a circle may be described with any centre and at any distance from that centre. The first is Aristotle's statement ; the second is the counter-statement ; the third is equivalent NOTES ON INFINITY. 7 therefore no point on the produced line on either side can be regarded as its extremity j such lines being therefore in- finite, the universe is infinite. But it may be well to consider what we mean by a straight line the absolute straight line of geometry. It is held by many mathematicians that our conceptions of points, lines, surfaces, figures, and so forth, in space are entirely de- rived from our experience of material points, lines, surfaces, figures, and so on. Assuming this to be so, what is the con- ception of straightness in a line joining two points ? It ap- pears to me that when we trace back the conception to its origin, we find the idea of a straight line joining two points to be that of a line, such that, if the eye were so placed that the two points appeared to coincide, the line itself, thus seen endwise, would appear as a point. This, if not the only independent test that can be applied to any material line, in order to determine its straightness, is certainly the best. Stretching a fine thread is either not a perfect test or not an independent test. If the two points are on a flat surface we can stretch a string from one to the other, because the flat surface affords suitable resistance to the string's tendency to bend ; but the flatness of the surface is a quality of pre- cisely the same kind as the straightness of the line, and un- less we are assured that the surface is flat we cannot be sure that the stretched string is not curved. Without a supporting surface we may be absolutely certain that the string is curved, to the assertion that every point in the whole of space may be taken as a centre, and that there are no limits whatever to the distance at which a circle may be described around any point as centre. In like manner with the definitions and axioms. The idea of infinity is implicitly involved, and all but explicitly indicated, in the definition of parallel straight lines ; and before we can accept the doctrine of the possible existence of a fourth dimension in space, through which doctrine alone (so far as can be seen) the infinity of the universe can be questioned, we must reject the axiom that two straight lines cannot enclose a space ; or rather the wider axiom which Euclid should have adopted (since he makes, in reality, repeated use of it), that two straight lines which coincide in two points coincide in all points. 8 FAMILIAR SCIENCE STUDIES. however slightly ; for the string, having weight, hangs (no matter how strongly it may be pulled) in the curve called the catenary no force, however great, being able to pull any string, however short, into absolute straightness. An objec- tion might be urged, in like manner, against the visual test ; because air is a transparent medium, and no finite portion of air being ever of constant heat and density throughout, the rays of light must always be bent, however slightly, in traversing any portion of air, however minute so that, in fact, we cannot look quite straight through even a stratum of air only a single inch in thickness. The visual test, how- ever, is independent, and, imagining vision to take place through a vacuum, we can at least conceive this test being absolutely perfect. The idea, then, of a finite straight line may be regarded as that of a line which, looked at endwise, would appear as a point. And we may extend this con- ception to lines of indefinitely enormous length. Thus, suppose there are two stars optically close together, though really separated by many million times the distance which separates our sun from us, and that, owing to the motion of one or both they draw optically nearer together until at length they appear as one, and this by so perfect an accord- ance of direction that, if telescopic power could be enormously increased, the centres of their two discs would be optically coincident : then a straight line joining these two centres would be one which, if it were a material line visible through the substance of the nearer star, would be optically reduced to a point supposing for the sake of argu- ment that the two stars, after being carried by their proper motions into the required positions, were reduced to rest. The italicised words may seem unnecessary, but in point of fact they are only a part of what is necessary by them- selves they are absolutely insufficient. If a telescopist living for a few odd millions of years could from a fixed standpoint watch two stars gradually approaching by their proper motion until they apparently coincided, one lying at an enormous distance beyond the other, and at that very NOTES ON INFINITY. 9 instant those swiftly moving stars were brought to rest, they would not really be in a straight line with the observer's eye. For he would see the nearer in the direction it had many years ago, when its light began the journey towards him ; while he would see the farther in the direction which it had at a much more remote epoch. And it would be these two positions, which the two stars occupied, not at the same time, but at times widely remote, which would be in a right line with the observer's eye. If two stars really were brought by their proper motions into a straight line with the eye of an observer at a remote station, they would not seem to be coincident, and if they were then suddenly reduced to rest the observer would see them still apparently in motion, drawing nearer and nearer together until they ap- parently coincided. We see, then, that this optical test of the straightness of the line joining two points requires that the points should be at rest. I may here digress for a few moments to notice one very singular consequence of the effect of motion just men- tioned. Conceive the production of a straight line joining two points to be effected under the visual test, the eye itself being the tracing point. The eye is first placed so that the nearer point (close to the eye) is coincident appar- ently with the more remote, and then the eye recedes with infinite velocity, or at least with a velocity exceeding many million times the velocity of light. Then it would seem at first as though the eye must of necessity travel in a straight line ; but in reality this would only be the case if the two points were either absolutely or relatively at rest. If not, then, paradoxical though it may seem, it is nevertheless true that the eye would have to travel in a series of whorls forming a mighty, spiral, the path of the eye at a very great distance from the two points being almost at right angles to a really straight line joining the eye and the centre of gravity of the moving points (around which they would make their revolutions). io FAMILIAR SCIENCE STUDIES. The relation here considered is rather a singular one in itself (apart, I mean, from all question of infinity). It may be illustrated by a phenomenon which occurred in December 1874, and will occur again in December 1882 a transit of Venus. Suppose we see the disc of Venus at any instant projected as a round black spot on the very centre of the Sun's face. Then one would say at the first view that at that moment the eye and the centres of the Sun and Venus were in a straight line. But this would not be exactly the case. For we see the Sun at any moment, not in his real direction, but in that towards which he lay some nine minutes before, light having taken that time in travelling to us from him ; and we see Venus at any moment, not in her real direction, but in that towards which she lay when the Sun's light passed her. As her distance from us varies widely, so the displacement due to the journey light has to take from her to reach us varies widely in relative amount, though, being always small, ordinary observation perceives no remarkable irregularity in her motions. 1 When she is 1 If light did not travel with a velocity enormously exceeding that of the planets in their orbits, they would seem to move very irregularly (at least, until the cause of the irregularity had been discovered) ; we should sometimes see Mars, for example, where he was a month or so before, sometimes where he was a year or so before i.e., sometimes twenty or thirty millions of miles, sometimes two or three hundred millions of miles, from his true place. As it is, light crosses the greatest distance separating us from Mars in about twenty minutes, and the least in about four minutes, so that the irregularity in his apparent motions never amounts to more than the distance he traverses in about 16 minutes, or a little more than 14,000 miles. If light travelled at the same rate as sound, it would have been absolutely impossible for men to interpret the apparent planetary motions, and the most erroneous ideas would inevitably have prevailed respecting the real motions. Even if the velocity of light had amounted to 20 or 30 miles per second, instead of its real value about 186,000 miles per second the true theory of the planetary movements would have seemed absolutely in- consistent with what the eyes would have seen. Even as it is, astro- nomy is directly opposed to the doctrine that seeing is believing. We see every celestial body, not where it is, but where it was. It is hardly NOTES ON INFINITY. II between the Earth and Sun, light takes about 2^ minutes in reaching us from Venus ; and therefore we see her where she was z minutes before. All that we can say, then, from the observed fact that Venus is seen at any moment, ap- parently at the very centre of the Sun's disc, is that a straight line from the eye to the place Venus occupied 2^ minutes before is in the same direction as a straight line from the eye to the sun eight minutes before the moment of the observation. But the Earth is at the moment itself on the axis of Venus's shadow cone. This axis, then, cannot be a straight line. Similar reasoning applies to all the planets, including the Earth. They do not throw straight shadows into space. This is the point to which I have wished to lead the reader's attention. The axis of a planet's shadow is the path which would be pursued by the eye in the case before considered, if the planet were taken for the nearer and the Sun for the more remote of the two objects ; and instead of this axis of the shadow lying, as one would expect, upon straight lines extending radially from the Sun, it is curved with a constantly increasing deflection, until in depths very remote from the sun it actually sweeps out fig- ures shaped almost like circles ! The shadow travels radially just as the light from the Sun does, simply because it lies be- tween regions of light both receding radially from the Sun. Hence the place reached by the shadow which tiadbeen just behind a planet in one part of its course will lie in the same direction from the Sun, only at a much greater distance, when the planet has performed any part of its circuit or any num- ber of circuits. This being true for every position of the planet, it follows readily that when we connect together the various positions reached by the outward- travelling shadow, at any moment, they form a mighty shadow-spiral extending in a series of whorls infinitely into space, or at least to a distance corresponding to that which light has necessary to remark that astronomy, in predicting the motions of the celestial bodies, as well as the occurrence of eclipses, transits, occulta- tions, and so on, takes this circumstance fully into account. 12 FAMILIAR SCIENCE STUDIES. traversed since first the planet became an opaque body, or the Sun began to pour light upon the planet (whichever of these two events was the later) in other words, since first the planet cast a shadoiv. Thus, let, ^1/2/3/4 be the path of a planet about the Sun S, and let the planet be at/,, then the shadow extends outwards from/!. Let us see what Shape of a Planet's shadow. shape it will have. The shadow which had been behind the planet when last at/, has gone to PI,/, PI being the dis- tance traversed by light during one revolution of the planet. That which was behind the planet when last at/ 2 has gone to P 2 ,/ 2 P 2 being the distance traversed by light in three- quarters of a revolution. Similarly, we get P 3 for the place NOTES ON INFINITY. 13 reached by the shadow which had been behind the planet when last at/ 3 ,/ 3 P 3 being the distance traversed by light during half a revolution ; and P 4 for the place reached by the shadow which had been behind the planet when last at / 4 ,/ 4 P 4 being the distance traversed by light in a quarter of a revolution of the planet. The shadow's axis then lies along the curve/! P 4 P 3 P 2 Pj. But this is not the whole shadow. The shadow which had been behind the planet when last time but one at/!, has been all the time travelling outwards, and is now at Qi, Pj Q! being equal to/ t P! ; and similarly we get other points of another whorl Q 4 Q 3 Q_2 QD tne radial breadth a b, between the two whorls being everywhere equal to the distance traversed by light during one revolution of the planet. Outside this whorl there is another, another beyond that, and so on for as many whorls, in all, as the planet has made revolutions since it first began to cast a shadow. The radial breadth between two successive whorls is always the distance traversed by light during a revolution of the planet, and as the distance of the whorls increases this breadth bears a smaller and smaller proportion to the size of the whorl, whose shape therefore becomes more and more nearly circular, though of course there is always the gap PI Qi between the two ends. In the case of our earth this gap is equal to light's journey in a year, or to about one-third of the distance separating us from the nearest fixed star ; yet the greatest radius of the whorl corresponding to the year 88 1 of our era exceeds the least in no greater degree than 1,000 exceeds 999. It is strange to reflect that this mighty shadow-whorl is even now conveying into depths of space, so remote that to our conceptions their distance is infinite, a material record of the actual beginning of our earth's existence as a shadow- throwing body. All the other planets of our own system, and whatever worlds there are circling around the multitu- dinous suns peopling space, have in like manner their vast whirling shadows, various in shape according to the varying motions of the planets, and greater or less in their extension 14 FAMILIAR SCIENCE STUDIES. according to the greater or less duration of planetary life. These mighty interlacing shadows are all the time in motion with a velocity altogether beyond our conceptions, yet so minute, compared with the dimensions of the shadow, that hundreds of years produce no appreciable change in the shape of the remoter whorls. It will be understood, of course that the shadows are not such shadows as human vision could perceive. Neither light-waves nor the absence of light-waves in the sether of space could be recognised as we recognise light and darkness. Only when some opaque object is placed in any region of space can ordinary vision determine whether light is passing there or not. Moreover, the shadows I have been speaking of are not black sha- dows even in this sense. They are only regions of space where the light which would else have arrived from the Sun has been to some finite, but very small, degree reduced through the interposition of a planet. Yet it is easy to conceive that beings living in the universe of rether, as we live in our universe of matter, might clearly perceive these shadows these regions where the sether is less or more disturbed by the undulations forming what we call light ; and if we adopt the thought of Leibnitz, that the universe is the sensorium of God, then these mighty interlacing shadows swiftly rushing through His omnipresent brain con- vey to His mind such evidence as their shape and nature can afford respecting the past history of the worlds peopling space. Here, also, let this strange point be noted. If a Being thus sentient, through and by all space, conceived the idea of straight lines after the manner described above regarding, to wit, the prolongation of the line joining two points as that line in space from every point of which at the moment the two points would seem as one then in His mind straight lines would correspond with the shadow axes just dealt with, and would only be really straight if the points were at rest. To His conceptions, then always on the assumption I have just made the straight line joining the sun and earth would, if produced far enough, become NOTES ON INFINITY. 15 almost circular, and form an endless spiral. Still referring to His conceptions of such a line, not to the real shadows be- fore dealt with, it would not matter whether the line joining the earth and sun were produced beyond the earth or beyond the sun ; in either case it would extend outwards into space in an infinite series of whorls. Thus two mighty series of interlacing whorls l would be mistakenly conceived of as a straight line. It is something like this error which the advocates of the new ideas concerning space suggest as possibly affecting the ordinary geometrical conceptions respecting straight lines and so falsifying all our ideas respecting the universe. Conceive, they say, the primary geometrical ideas of crea- tures living in a world of one dimension. They would know nothing of breadth or thickness, but of linear exten- sion only. And we can readily imagine that such creatures might conceive their world infinite in extension ; because all lines in it must be supposed capable of being indefinitely produced, still remaining in it. Yet in reality the universe in which such creatures existed mightbe finite even as respects its single dimension ; for the line in which these imaginary creatures lived might be curved, and, returning into itself, be limited in actual length. Thus while a line could be infinitely produced in this singly dimensioned world, the world itself in which such infinite extension of lines could be effected would be finite. Conceive, again, the case of a world of two dimensions only length and breadth without thickness. The creatures in this world would be mere surfaces, and their ideas would necessarily be limited to surfaces. All those portions of our geometry which relate to plane fig- ures and plane curves would lie within their grasp, while 1 The student of geometry will not need to be told that a spiral formed in the manner illustrated in the figure is what is called the spiral of Archimedes, and that for completeness it requires the second infinite series, travelling the other way round, but in other respects precisely like the first series, whorl for whorl. Each whorl of one series cuts each whorl of the other onoe, and once only. 1 6 FAMILIAR SCIENCE STUDIES. not only would they be unable to deal with questions relat- ing to solids or curved surfaces, or curved lines not lying in one plane, but the very idea of a third dimension would be utterly inconceivable by them. Now, while these creatures might have, as we have, the conception of straight lines, and might postulate, as we do, that such lines when finite may be indefinitely produced, so that they would have ideas like ours respecting infinite extension in length and breadth, it might very well be that the surface in which they lived, being curved and re-entering into itself, would no more be infinite than the surface of a globe or an egg. Moreover, and this is a point very specially insisted upon by those whose reasoning I am reproducing, it might well be that different portions of the curved surface in which they resided might be differently curved (as the end of an egg is differently curved from the middle parts), and geometrical relations derived from the experience of creatures living in one portion of this curved surface might not by any means correspond with those which they would have deduced had their lot been cast in another portion of the same surface. For instance, in the case of two triangles belonging to one portion of the surface, two sides enclosing an angle of one might be severally equal to two sides enclosing an angle of the other, and the perfect equality of the two triangles might be tested by superposition in our region of this surface world ; but a triangle having two sides and the enclosed angle respectively equal to those of another in a different part of that world, might not admit of being superposed on this last. This can easily be shown by drawing two triangles, one on the end of an egg and the other on the middle of the egg, each triangle having two sides of given length and at a given inclination : it will be found that if the corre- sponding pieces of shell are cut out they cannot be exactly superposed. Not only is this so, but if two triangles, each having two sides of given length and at a given inclination, be drawn in different positions on the middle of the egg, they cannot be superposed, simply because at that part of NOTES OiV INFINITY. 17 the egg the curvatures in different directions are different. A line drawn lengthwise with respect to the egg belongs to a larger curve than a line drawn square to it. On the contrary, at the two ends of the egg, and there alone, the curvatures in all directions are alike, and therefore at either of these spots triangles of the kind described could be superposed, but not elsewhere. Thus the geometry of one part of such a surface differs essentially from the geometry of other parts, and creatures living on a portion of a surface of that kind would be altogether mistaken in supposing that throughout their world the same geometrical laws held which experience derived from their own region of that world seemed to suggest. The application of all this is obvious. We live in a world of three dimensions, and cannot conceive the exist- ence of a fourth dimension. Length, breadth, and thickness seem, of necessity, to be the only possible measures of space. But as creatures living in a world of one dimension would be mistaken in assuming, as they unquestionably would, that there could be no other dimension as, again, creatures living in a world of two dimensions would be mis- taken in assuming that a third dimension was impossible so may we be mistaken in assuming that there can be no other dimension than length, breadth, and thickness. Hence those who adopt the reasoning I have described believe in the possible existence of a fourth dimension in space. Nor can any reason be perceived why a fifth or sixth dimension or an infinite number of dimensions, may not be regarded as possible, if the reasoning be only admitted on which has been based the possibility of a fourth dimension. Again, as creatures living in a world of one dimension or of two dimensions might mistakenly imagine their world infinite in extension in its single dimension or in its two di- mensions whereas in one case it might be any closed curve, and in the other any continuous curved surface so may we also be mistaken in supposing our world infinite in extension throughout its three dimensions. It may in some c i8 FAMILIAR SCIENCE STUDIES. way (which we can no more conceive than creatures pos- sessed with the idea that they lived in a world of two dimen- sions could conceive the idea of the curvature of their world, which, of course, involves really a third dimension) possess a kind of curvature which makes it a world of four dimen- sions (or more), and may be no more infinite than the cir- cuit of a ring or the surface of a globe is infinite. Yet again, the geometry of creatures living on a curved line or on a curved surface, but who supposed they lived on a straight line or a plane surface, would pro tanto be inexact. For instance, creatures living on the surface of a sphere enormously large compared with their own dimensions, would readily deduce the relation that the three angles of a triangle are equal to two right angles, for their plane geome- try would be as ours ; yet this relation would not be strictly true for their world, the three angles of a triangle described on a spherical surface being constantly in excess of two right angles. In like manner the relations of our geo- metry, linear, plane, and solid, may be inexact. The lines we consider straight lines may in reality be curved. Our parallel lines may in reality, if only produced far enough, meet on both sides, just as two parallel lines marked on a sphere meet necessarily if produced, and in fact enclose a space. Or, instead of that, a contrary relation may hold, and whereas, according to our present geometry, a straight line through a given point must occupy a certain definite position if it is not to meet another straight line (in the same plane), however far it may be produced, it may be that in reality the former line might be swung round through some finite though small angle, and in every one of the positions it thus assumed possess the property of parallelism, never meet- ing the other line, however far both might be produced. 1 1 This is no mere reductio ad absitrdum. Lobatchowsky, who has been compared by a skilful student of the new ideas with Copernicus, has framed a system of geometry on this very assumption. Before quoting Professor Clifford's account of Lobatchowsky's work in this direction, I venture to quote Clifford's remarks on the general question, in order that the reader may not imagine that what I have [said above NOTES ON INFINITY. 19 Thus, by conceiving the possibility of a fourth dimension in space, we find ourselves freed from the difficulties which our present geometrical conceptions force upon us. The universe need no longer be regarded as infinite. The straight lines which had been so troublesome are no longer troublesome, because they are no longer straight, but share the curvature of space. We may produce them as much as we please, but they all come round to the same point again. respecting the new geometry is drawn from my own imagination only. I remind the reader that Professor Clifford was a skilful analytical mathematician, and that he was professedly expounding the ideas of Helmholtz, Riemann, Lobatchowsky, and others of admitted skill in mathematics. ' The geometer of to-day,' says Clifford, ' knows nothing about the nature of actually existing space at an infinite distance ; he knows nothing about the properties of this present space in a past or a future eternity. He knows, indeed, that the laws assumed by Euclid are true with an accuracy that no direct experiment can approach, not only in this place where we are, but in places at a distance from us that no astronomer has conceived ; but he knows this as of Here and Now ; beyond his range is a There and Then of which he knows nothing at present, but may ultimately come to know more. So there is a real parallel between the work of Copernicus and his successors on the one hand, and the work of Lobatchowsky and his successors on the other. In both of these the knowledge of immensity and eternity is replaced by knowledge of Here and Now. And in virtue of these two revela- tions' (the italics are mine), ' the idea of the Universe, the Macrocosm, the All, as subject of human knoivledge, and therefore of human interest, has fallen to pieces.'' Now the work of Lobatchowsky is thus described by Clifford : ' He admitted that two straight lines cannot enclose a space, or that two lines which once diverge go on diverging for ever. But he left out the postulate about parallels ' (viz. that there is one position, and one only, in which a straight line drawn ^hrough a point is parallel to a given straight line). ' Lobatchowsky supposed instead that there was a finite angle through which the second line might be turned after the point of intersection had disappeared at one end before it reappeared at the other.' This angle depends on the distance of the point from the line in such sort that the three angles of a triangle shall always be less than two right angles by a quantity proportional to the area of the triangle. 'The whole of this geometry,' proceeds Clifford, ' is worked out in the style of Euclid, and the most interesting conclu- sions are arrived at.' c 2 20 FAMILIAR SCIENCE STUDIES. This at least will happen 'on the supposition that the curva- ture of all space is nearly uniform and positive ' (that is, of the same nature as the curvature of a nearly globe-shaped surface considered with reference to the portion of space enclosed within it ; for, considered with reference to ' all outside,' the curvature of a globe is negative). Professor Clifford thus sums up the benefits arising from these new ideas on the supposition just mentioned : ' In this case, the universe, as known, is again a valid conception, for the extent of space is a finite number of cubic miles. And this comes about in a curious way. If you were to start in any direction whatever, and move in that direction in a perfectly straight line, accord- ing to the definition of Leibnitz, after travelling a most prodigious dis- tance, to which ' the distance of the nearest star ' ' would be only a few steps, you would arrive at this place. Only, if you had started up- wards, you would appear from below. Now, one of two things would be true. Either, when you had got half-way on your journey, you came to a place which is opposite to this, and which you must have gone through, whatever direction you started in ' (just as, in whatever direction an insect might travel from any point on a sphere, he would pass through the point opposite from his starting-place, and that when he was half-way round) ; ' or else all paths you could have taken diverge entirely from each other till they meet again at this place ' (just as the various paths by which an insect might proceed from any point on an anchor ring, moving always directly forwards, would all bring him back to his starting-place, but would have no other point in common). ' In the former case, every two straight lines meet in two points ; in the latter, they meet only in one. Upon this supposition of a positive cur- vature, the whole of geometry is far more complete and interesting ; the principle of duality, instead of half-breaking down over metric relations, applies to all propositions without exception. In fact, I do not mind confessing that I personally have often found relief from the 1 I have here departed from the text, but, that I may not be sus- pected of vitiating the passage, I quote Clifford's exact words : ' a most prodigious distance,' he says, 'to which the parallactic unit 200,000 times the diameter of the earth's orbit would be only a few steps.' I must confess I cannot see the advantage of inventing a word, and giving a roundabout explanation of it, when the thing really signified is ex- tremely simple. Science does not require to be thus fenced round from ordinary apprehension by sesquipedalian verbal stakes. NOTES ON INFINITY. 21 dreary infinities of homaloidal space' (that is, space where straight lines arc straight, and planes plane; from the Greek 6fj.a\6s, level) 'in the consoling hope that, after all, this other may be the true state of things. ' Now, with all respect for the distinguished mathemati- cians who have adopted the method of reasoning which I have briefly sketched, and which Professor Clifford thus eloquently sums up, I submit that the whole train of reason- ing is geometrically objectionable, and that the very words in which those who adopt it are compelled to clothe their arguments and to express their conclusions should suffice to show this. To begin with, although it is unquestionably true that our ideas respecting the geometrical point, line, plane, circle, and so forth, are originally derived from ex- perience, they in truth transcend experience. Thus, as the ancient geometers are said to have drawn figures on sand to illustrate their reasoning, and these figures were necessarily altogether imperfect representations of the figures as geo- metrically defined, we can imagine a gradually increasing accuracy in draughtsmanship, until at length only such lines as Rutherford has been able to draw on glass 10,000, if I remember rightly, to the inch might be used, or even lines very much finer. Yet the lines so drawn only differ in degree, so far as their departure from geometrical perfection is concerned, from the lines drawn on sand. We can imagine a continual increase of fineness until at length the eiTors from exactness would be less than those ethereally occupied spaces, between the ultimate atoms of bodies, which lie beyond the range of our microscopes. We might con- ceive a yet further increase of fineness, until irregularities in the actual constitution of the ether itself took the place of the gross irregularities of the lines once drawn on the sand. Or such irregularities might in turn be conceived to be re- duced to their million-millionth parts. Yet we are still as remote as ever from the geometrical line, simply because that is a conception suggested by ordinary lines, not a reality which can under any circumstances actually exist. And so of the straightness of lines, the planity of surfaces, and 22 FAMILIAR SCIENCE STUDIES. other like geometrical conceptions : they are transcendental- isms suggested (only) by experience, not in reality comparable with them any more than infinity of space is comparable with mere immensity. To say, therefore, that geometrical lines, surfaces, and so forth, may be imperfect because sj^ce itself may be discontinuous, is to assert of them that pos- sibly they may not be geometrical lines, but only exceedingly delicate lines of the ordinary kind. To say again that geometrically straight lines may have their straightness vitiated by the curs'ature of space, is to say that they are not geometrically straight lines, but curved. I was about to say that it is as inconceivable that a straight line can, when produced far enough, return into itself, as to say that two things of any kind being added to two other things of the same kind, make three or five things of that kind, and not four ; but I remember that, among other objections to the validity of our primary conceptions, one has been urged against the mistaken notion that ex necessitate two and two make four. There may be regions of space or portions of eternity where, when two things are added to two, the sum is greater or less than four, and where in general our funda- mental ideas about number may be altogether incorrect ; and in those or other regions or times straight lines may be curved, and level surfaces uneven. Space also may there and then be discontinuous, the interstices being neither void nor occupied space ; and time may proceed discontinuously, being interrupted by intervals which are neither void nor occupied time. It can only be in those regions of space and in those portions of eternity that beings exist who can conceive the possibility of the creatures spoken of by Helmholtz, Clifford, and others, as having only length with- out, breadth or thickness, or only length and breadth without thickness. Here and now I apprehend that, though we may speak of such creatures, we cannot possibly conceive of them as actually existent. We might on this account, indeed, dismiss the one-dimen- sioned and two-dimensioned creatures and their mistaken NOTES ON INFINITY. 23 notions, which cannot possibly affect ourselves who are un- able to conceive either them or their notions. But we may admit for the sake of argument the possible existence and the possible mistakes of such creatures, and yet find no reason whatever to admit the possibility of a fourth dimen- sion in space. Take the creatures living in a surface. So long as the experience of such creatures was not opposed to the requirements of plane geometry, their conceptions and their experience would alike conform to the relations of our plane geometry. But if, after gradually widening their ex- perience, they discovered that these relations were not strictly fulfilled that, for instance, the three angles of a triangle were appreciably greater than two right angles when the triangle was very large the existence of a third dimen- sion would present itself to their conceptions, simply because it had in effect, as their geometricians would explain, become sensible to their experience. Its possibility would never have been beyond their power of conception, and it is not at all clear that such creatures, even without the lessons of actual experience, might not conceive the possible existence of matter on one side or the other of the surface in which they lived. In fact, it is not easy to see what should prevent them. Moreover, when they had made the discovery of a third dimension in their own world, by finding in fact that the surface in which they lived was not plane, they would be unable to 'find relief from the dreary infinities of homaloidal space in the consoling hope ' that their world, being curved, might therefore contain a finite number of square miles. They would simply have found that what had seemed the universe to them was in point of fact not the universe ; that the infinities of length and breadth which they had imagined as existing in their world lay really outside of it, in company with another infinity of which they had before (on Helm- holtz's assumption as to their mental condition) formed no conception. If we are really to admit with Plelmholtz and Clifford the possible existence of creatures of one dimension or of two dimensions, and also to accept as certain the 24 FAMILIAR SCIENCE STUDIES. theory of these mathematicians that creatures of this kind could form no conception of dimensions other than those of their own persons, then we must accept all the consequences of these (unfortunately inconceivable) conceptions. Not only must we assert with Helmholtz and Clifford that these creatures would have been mistaken at first in supposing their world necessarily infinite in the dimensions it possessed, but we must admit that they would have been mistaken later in supposing that the finiteness of their world was any proof of the finiteness of length and breadth. They would quite erroneously have come to the conclusion that they had mastered their old difficulties about infinite extension in these dimensions. The consoling hope which would buoy them up after their discovery would be an entirely deceptive one. Their world would be simply a spherical, spheroidal, or otherwise-shaped surface in space, surrounded on all sides by infinities, not only of length and breadth, but of depth also. Their second mistake would, in fine, be as prepos- terous as \vould have been the theory, could sane geographers ever have entertained it, that when our own earth had been shown to be a globe, the plane of the horizon had been proved not to be infinite, but to contain a finite number of square miles. If we must accept so much of the argument advanced by Helmholtz and supported by Clifford, the true analogue of the reasoning of the bi-dimensionists, on the part of us who are tri-dimensionists, would be this that we may one day discover the part of the universe we inhabit to be finite, the length and breadth and depth of our universe lying within the real infinities of length and breadth and depth, while to these infinities a fourth infinity, of a kind which we are at present unable to conceive, would by that discovery have been added to those which we already find sufficiently overwhelming. Thus the ' consoling hope ' of Professor Clifford, rightly apprehended, is in reality but a fresh cause of despair. In fact, it is easy to perceive on a priori grounds that this must be the case. For if we imagine a linear creature NOTES ON INFINITY. 25 of advanced ideas arguing with less thoughtful fellow-lines as to the existence of breadth as well as length, we see that his argument would run somewhat on this wise : ' You im- agine mistakenly, my linear friends, that all points lie in our line ; but there may be, and I believe for my own part there are, points not in our line at all.' He would not say, ' on one side of it or on the other/ simply because the concep- tion of sides to their linear universe could not have been formed by his hearers So with the planar folk. An ad- vanced surface would reason that all lines and points were not necessarily in their world, but might be above or below their level. This idea, of points outside the linear world in one case, or of points and lines outside the surface world in the other, would be an absolutely essential preliminary to any argument in favour of the possible curvature of a world of either kind, and therefore of the possible finiteness of either world. We can only make the analogy complete by reasoning that possibly there may be points outside what we call space, thence prove the possible curvature of space, and so infer the finiteness of space. But the possible finiteness of space established by the assumption that there may be points outside of it, is not consoling to those who find the infinities of homaloidal space dreary ; and the fourth dimension called upon to relieve us from the dreary infinities of length, breadth, and depth, would only intro- duce a more awful infinity, just as surface infinity is in- finitely vaster than linear infinity, and infinity of volume infinitely vaster than infinity of surface. Fortunately, length, breadth, and depth are the only conceivable infinities of space. The fearful quadri-dimensional infinity is as one of the spirits from the vasty deep over which Glendower boasted that he possessed controlling power. We may speak of infinities thus unknown, but, so far as conceiving them is concerned, ' they will not come when we do call for them.' I have said that the very words in which the advocates of the new ideas respecting space are compelled, not only to clothe their arguments, but to express their ideas, suffice to 26 FAMILIAR SCIENCE STUDIES. show that those ideas are geometrically objectionable ; and, so far as their arguments are concerned, I think I have proved this. As for their conclusion, it seems only neces- sary to point out, that to say the extent of space is a finite number of cubic miles, is in reality equivalent to saying that it has a limiting surface : now, the mind is unable to con- ceive a surface which has not space on both sides of it. Thus there must, according to our conceptions, be space outside the surface supposed to include all space which is absurd. I may add, though the argument is complete already, that whether a straight line as defined by Leibnitz can or cannot, when produced sufficiently far, return to the point to which it started, it is certain that the straight line as defined by Euclid cannot do so, nor can the straight line as conceived by Newton, or probably by any mathe- matician of geometrical tendencies. For Euclid defines a straight line as lying evenly between its extreme points ; and a straight line which extends from one point and after an enormous journey returns, no matter by what course, to a point close by its starting-point (not to carry it on to the starting-point itself) cannot possibly be regarded as lying evenly between the starting-point and the point close by, which points are its extremities. And Newton, as we know, regarded a straight line as produced by the continuous motion of a point tending continually in one unchanged direction ; whereas a point which, after no matter how long after leaving a fixed point, is found travelling towards that point, can certainly not be regarded as travelling in the same direction all the time, but, on the contrary, its course must in the interim have changed through four right angles. But after all, the infinities which surround us not only the infinities of time and space, but the infinities also of matter, of energy, and of vitality, the infinity of the minute as well as the infinity of the vast though inexpressibly awful, are not in truth 'dreary.' It is, in fact, in such infinities alone that we find an answer to the misgivings that arise continually within us as our knowledge widens. Were NOTES ON INFINITY. 27 the universe finite in extent or in duration, the discoveries by which science is continually widening her domain in space and time would perplex us even more than they do at present. We should have to believe in the constant enormous expenditure of forms of force which there is no replacing, and whose transmutation to other forms implies a real waste of energy, if only the total supply of force is finite. As the action of processes of evolution is more clearly recognised, and seen to extend over longer and longer periods of time, we should seem to be continually tending towards the belief that from the very beginning there has been only evolution. If time were regarded as finite, then the vast range of time over which the vision of science extends would seem dreary indeed, because, so far as the eye of science extends, no direct evidence of a First Cause could be perceived. So also of the minute. If men could really penetrate to the ultimate constitution of matter if they could perceive the operations of Nature within the corpuscles we should find no means of conceiving how possibly the seemingly wasted energies of the perceptible universe may have their use in processes affecting matter beyond our powers of perception. And it is only by imagining some such employment of the apparently lost energies of our universe that we can be led to the belief that our universe in turn receives constant supplies of energy from processes lost to our perceptions because of their vast- ness, as the processes taking place within the ether are lost to us because of their minuteness. Lastly, were it not for the infinities which are beyond our powers of conception, as well as of perception, we should be logically forced, as it seems to me, into direct antagonism to the doctrine of a Being working in and through all things and during all time. For, step by step, knowledge has passed onwards from the development of leaf and limb to the development of plant and animals, thence to the development of races and species, of flora and fauna, onwards still to the development of the earth and her fellow-worlds, the development of solar 28 FAMILIAR SCIENCE STUDIES. systems ; and science bides her time to recognise the laws of development according to which systems of solar systems, and even systems of higher orders, have come into existence. In like manner, science has learned to look beyond the death of individuals and races, to contemplate the death of worlds, and systems of worlds, and systems of systems, to the death eventually of all, and more than all, the known portions of the universe. Had we to do with the finite only, in time and space, and in all that time and space contain, we might well shudder at the dreary wastes thus presented to us space, time, matter, power, and vitality, all ulti- mately the spoil of Death. Even if we could recognise a Supreme Being existing amid these desolations, we could not reverence mere immensity of extent and duration with- out control over the progress of events and without purpose which could be conceived. But seeing that it is not immen- sity, but infinity, we have to deal wilh, and perceiving that our knowledge, no matter how widely it may extend its domain, still has in reality but an evanescent range for the immense is nothing in presence of the infinite we are no longer forced to this 'abomination of desolation.' Being able to grasp the finite only, whereas the universe is infinite, reason compels us to admit that we can know absolutely nothing of the scheme of the universe. It must ever remain as unfathomable as the infinite depths of space, as immea- surable as the infinite domain of time. We may reject this theory or that theory of supervision or control, or plan or purpose, or whatsoever name we choose to give to the un- knowable relations between all things and their God. When men assure us that God wills this, or designs that, or will bring about somewhat else, and still more when men pretend to tell us the nature or ways of God, we may, from the teachings of Nature, be able utterly to reject the doctrines thus propounded. But we cannot go further, and reject the general doctrine with which these special doctrines have been associated. We can say truly that the idea of a per- sonal God, whatsoever attributes may be assigned to such a NOTES ON INFINITY. 29 Being, is not only unintelligible, but utterly unimaginable ; and that those who tell us that they can conceive of such a Being, know not what they say ; but we cannot reject the doctrine because it is inconceivable, for we have seen that we cannot reject the doctrines of infinity of time and infinity of space. Nay, so far are we from being justified in rejecting the belief in a Supreme Being because we cannot conceive such a Being, that, on the contrary, no being of which we could conceive could possibly be the God of the utterly inconceivable universe. That God must of necessity be Himself inconceivable. The most earnest believers, as well as the exactest students of science, can have butf., 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 106 FAMILIAR SCIENCE STUDIES. 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 in- dicates 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 a 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 a priori considerations, each to be tested by whatever direct evidence may be available ; and it is practi- cally 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 determina- tion 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 on 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 par- ticular theory. THE PROBLEM OF THE GREAT PYRAMID. 107 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 astrono- mical observations with great accuracy ; and what we pro- pose to do is to inquire what would be done by men having this purpose in view, having, as the pyramid builders had, (i) 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 recognises 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 instru- ments 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 sta- bility, 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 io8 FAMILIAR SCIENCE STUDIES. 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 astro- nomer 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 seem- ing 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 eleva tion, when he is nearly at his highest, changes very slowly ; THE PROBLEM OP THE GREAT PYRAMID. 109 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 observ- ing 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 neces- sarily 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 astrono- mers, 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 ad- missible, yet it would clearly be altogether undesirable ; since the avoidance of a slope towards east or west would no FAMILIAR SCIENCE STUDIES. 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 observa- tions 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 obser- vation, and for this purpose it would be essential that the observing surface should be as carefully levelled in a north- and-south as well as in an east-and-west direction. We should expect to find, then, that when the particular stage of astronomical progress had been readied, at which men not only perceived the necessity of well-devised build- ings for astronomical observation, but were able to devote time, labour, and expense to the construction of such build- ings, the first point to which they would direct their atten- tion 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 pave- ment, 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 proba- bility, 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.' l 1 It seems to me not improbable that the level was de'ermined by simply flooding (though to a very small depth only, of course) the en- tire area to be levelled not only the pavement level, but higher levels as the pyramid was raised layer by layer. By completing the outside of each layer first, an enclosed space capable of receiving the water THE PROBLEM OF THE GREAT PYRAMID. in But now with regard to the true north- and- south direc- tion, 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 ob- jections 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 asso- ciated 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 ex- actly 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 could 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 would be formed (the flooding being required once only for each layer), and when the level had been taken, the water could be allowed to run off by the interior passages to the well which Piazzi Smyth considers to be symbolical of the ' bottomless pit.' ii2 FAMILIAR SCIENCE STUDIES. 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 direc- tion 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 astrono- mical 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. THE PROBLEM OF THE GREAT PYRAMID. 113 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 though 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 point- ing 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 star.-?, 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 i Ii 4 FAMILIAR SCIENCE STUDIES. 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 Flammarion's ' History of the Heavens, 3 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 cf 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 a 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 awk- ward 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 incom- plete that they could subserve any useful astronomical purposes ; nevertheless we must not on this account suffer our- selves 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 an- THE PROBLEM OF THE GREAT PYRAMID. 115 ticipating rather that, on a close inquiry, a means of obvia- ting 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 lati- tude. For it must be remembered that, from certain parts of the earth, the various points and circles which the astronomer recognises 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 admi- rably 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 pre- cisely in latitude 30, or, in other words, in that latitude where the true pole of the heavens is one-third of the way Ii6 . FAMILIAR SCIENCE STUDIES. 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 astro- nomers have learned to recognise 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 lon- ger worth considering, but to the mathematicians who planned the great pyramid they would have possessed ex- treme 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, theo- retically, the point wh2re this upright was placed would be THE PROBLEM OF THE GREAT PYRAMID. 117 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 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 recognised. 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 B c the horizon, or 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 DA, Fig. i, 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 ele- vation. 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 liS FAMILIAR SCIENCE STUDIES. 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 pyra- mid would have set the centre of the base north of lati- tude 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 (i) 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, atmo- spheric 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 esti- mated 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 THE PROBLEM OF THE GREAT PYRAMID. ng horizon. But the effect of refraction being to raise every celestial object above its true position, they would have sup- posed 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 refrac- tion 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 eleva- tion. The error would be, in fact, in this case, about i 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 i 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 recognised the action of some cause or other, render- ing one or other method, or both methods, unsatisfactory. If so, and we can scarcely doubt that this would actually happen (for certainly they would recognise the theoretical 120 FAMILIAR SCIENCE STUDIES. justice of both methods, and we can hardly imagine that having two available methods, they would limit their opera- tions to one method only), they would scarcely see any bet- ter way of proceeding than to take a position intermediate between the two which they had thus obtained. Such a posi- tion would lie almost exactly 1072 yards south of true lati- tude 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 i 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 ; i mile 1693 yards south of the position they would have de- duced 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 con- clude from the position of the pyramid's base that they used both the shadow method and the Pole-star method, but that, recognising the superiority of the latter, they gave greater THE PROBLEM Of THE GREAT PYRAMID. 121 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 a posteriori reasoning such as this one can prove almost any- thing about the pyramids. For observe, though presented as cl 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 atmo- spheric 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 rea- soning, to ascertain first such relative weights on an assump- tion 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 un- sound reasoning of this kind that nine-tenths of the absurdi- ties 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 d priori considerations, is that the builders of the great pyramid 122 P AMI LIAR SCIENCE STUDIES. 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 posi- tion 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 construc- tion 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 posi- tion 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 in- clined 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 THE PROBLEM OF THE GREAT PYRAMID. 123 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 astro- nomical 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 I2 4 FAMILIAR SCIENCE STUDIES. 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-\vest 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 termed the prime vertical. Possibly 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 THE PROBLEM OF THE GREAT PYRAMID. 125 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 (he 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 seerns 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 ar.d 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 126 FAMILIAR SCIENCE STUDIES. 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", cor- responding to an elevation of the true pole of the heavens, by about 30 ^ above the horizon, it follows that if Pro- fessor Smyth obtained the true angle for the entrance passage, the Pole-star must have been about 3 3i|' 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 a 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 ap- THE PROBLEM OF THE GREAT PYRAMID. 127 preaching the pole until it was at its nearest, when it was only about 33' 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 north- wards, 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 indi- cate where the passage of his Pole-star above the pole ceased to be visible through the slant tube. In other words he 128 FAMILIAR SCIENCE STUDIES. 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 proxinie) 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 deter- mine 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 pas- sage, 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 Dra- conis 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 nnd 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 pas- sage no star could have been seen, because no eye could be THE PROBLEM OF THE GREAT PYRAMID. 129 placed there. But the builders of the pyramid cannot reasonably be supposed to have been ignorant of the sim- ple 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 pecu- liarity 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 rect angularity 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 ' some- thing 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 pyra- mid ; that thence downwards to the place where an ascend- ing 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 con- sidered the best authorities in Biblical matters, but sc much the worse for the dates. To return to the pyramid. K 130 FAMILIAR SCIENCE STUDIES. 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 pas- sage 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 avail- able. Consider : The square base has been duly oriented. Therefore, if each square layer is placed properly, the con- tinually diminishing square platform will remain always oriented. But if any error is made in this work, the exact- ness 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 pas- sage, 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, 1 probably to quite 1 The irregular descending passage long known as the well, which communicates between the ascending passage and the underground chamber, enables us to ascertain how high the rock lises into the pyra- THE PROBLEM OF THE GREAT PYRAMID. 131 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 in 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 pas- sage, 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 adjust- ment of this meridional plane. To apply this method, it would be necessary to tempo- rarily 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 Dra- mid at this particular part of the base. We thus learn that the rock rises in this place, z. any rate, thirty or forty feet above the basal plane. K2 132 FAMILIAR SCIENCE STUDIES. conis 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 A D Towards South. = ^x^ / > Towards North. FIG. 2. 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. It is hardly necessary to remind those who have given any attention to the subject of the pyramid that there is pre- cisely such an ascending passage as C A, and that as yet no explanation of the identity of its angle of ascent with the angle of descent of the passage D C has ever been given. Most pyramidalists content themselves by assuming, as Sir E. Beckett puts it, ' that the same angle would probably be used for both sets of passages, as there was no reason for vary- ing /'/,' which is not exactly an explanation of the relation. Mr. Wackerbarth has suggested that the passages were so adjusted for the purpose of managing a system of balance cars united by ropes from one passage to another ; but this explanation is open, as Beckett points out, to the fatal ob- jection that the passages meet at their lowest point, not at their highest, so that it would be rather a puzzle ' to work out the mechanical idea.' The reflection explanation is not only open to no such objections, but involves precisely such an application of optical laws as we should expect from men as ingenious as the pyramid builders certainly were. In THE PROBLEM OF THE GREAT PYRAMID. 133 saying this, let me explain, I am not commending myself for ingenuity in thinking of the method, simply because such methods are quite common and familiar in the astronomy of modern times. While I find this explanation, which occurred to me even while this paper was in writing, so satisfactory that I feel almost tempted to say, like Sir G. Airy of his explanation of the Deluge as an overflow of the Nile, that ' I cannot enter- tain the slightest doubt' of its validity, I feel that there ought to be some evidence in the descending passage itself of the use of this method. We might not find any traces of the plugs used to stop up, once a year or so, the rock part of the descending passage. For they would be only tem- porary arrangements. But we should expect to find the floor of the descending passage constructed with special care, and very closely fitted, where the water was to be re- ceived. Inquiring whether this is so, I learn not only that it is, but that another hitherto unexplained feature of the great pyramid finds it explanation in this way, the now cele- brated ' secret sign.' Let us read Professor Smyth's account of this peculiar feature : ' When measuring the cross-joints in the floor of the entrance pa?- sage, in 1865, I went on chronicling their angles, each one proving to be very nearly at right angles to the axis, until suddenly one came which was diagonal; another, and that was diagonal too; but, after that, the rectangular position was resumed. Further, the stone mate- i ial carrying these diagonal joints was harder and better than elsewhere in the floor, so as to have saved that part from the monstrous excava- tions elsewhere perpetrated by some moderns. Why, then, did the builders change the rectangular joint angle at that point, and execute such unusual angles as they chose in place of it, in a better material of stone than elsewhere ; and yet with so little desire to call general atten- tion to it, that they made the joints fine and close to that degree that they escaped the attention of all men until 1865 A.D.? The answer came from the diagonal joints themselves, on discovering that the stone between them was opposite to the butt end of the portcullis of the first ascending passage, or to the hole whence the prismatic stone of con- cea'ment through 3000 years had dropped out almost before Al Mamoun's 134 FAMILIAR SCIENCE STUDIES. eyes. Here, therefore, was a secret sign in the pavement of the en- trance-passage, appreciable only to a careful eye and a measurement by angle, but made in such hard material that it was evidently intended to last to the end of human time with the great pyramid, and has done so thus far. ' Whether Professor Smyth is right in considering that this specially-prepared position of the floor was intended not for any practical purpose, but to escape the notice of the care- less, while yet, when the right men ' at last, duly instructed, entered the passage,' this mysterious floor-sign should show them where a ceiling-stone was movable, on perceiving which they ' would have laid bare the beginning of the whole train of those sub-aerial features of construction which are the great pyramid's most distinctive glory, and exist in no other pyramid in Egypt or the world/ I leave the reader to judge. I would remark, only, that, if so, the builders of the pyramid were not remarkably good prophets, seeing that the event befell otherwise, the ceiling-stone dropping out a thousand years or so before the floor-sign was noticed ; wherefore we need not feel altogether alarmed at their own prediction (according to Professor Smyth), that the end of the world is to come in 1881, even as Mother Shipton also is reported to have prophesied. .On the other hand, there seem excellent reasons for adopting the above interpretation of the secret sign ; as showing where the floor of the de- scending passage was purposely prepared for the reception of water, on the still surface of which the Pole-star of the day might be mirrored for one looking down the ascending passage. Albeit, I cannot but think that this ascending passage must also have been so directed as to show some bright star when due south. For if the passage had only given the meridian plane, but without permitting the astronomer to observe the southing of any fixed star, it would have sub- served only one-half its purposes as a meridional instrument. It is to be remembered that, supposing the ascending passage to have its position determined in the way I have described, there would be nothing to prevent its being also made to THE PROBLEM OF THE GREAT PYRAMID. 135 show any fixed star nearly at the same elevation. For it could readily be enlarged in a vertical direction, the floor remaining unaltered. Since it is not enlarged until the great gallery is reached (at a distance of nearly 127 feet from the place where the ascent begins), it follows, or is at least ren- dered highly probable, that some bright star was in view through that ascending passage. Now, taking the date 2170 B.C., which Professor Smyth assigns to the beginning of the great pyramid, or even taking any date (as we fairly may), within a century or so on either side of that date, we find no bright star which would have been visible when due south, through the ascending passage. I have calculated the position of that circle among the stars along which lay all the points passing 26 18' above the horizon when due south, in the latitude of Ghizeh, 2170 years before the Christian era ; and it does not pass near a single conspicuous star. 1 There is only one fourth magni- tude star which it actually approaches namely, Epsilon Ceti ; and one fifth magnitude star, Beta of the Southern Crown. When we remember that Egyptologists almost without 1 There is a statement perfectly startling in its inaccuracy, in a chapter of Blake's ' Astronomical Myths,' derived from Mr. Haliburton's researches, asserting that in the year 2170 B.C., the Pleiades were ' exactly at that height that they could be seen in the direction of the Southward-pointing passage of the pyramid.'' The italics are not mine. As this passage pointed 335, or thereabouts, below (that is south of) the equator, and the Pleiades were then some 35 north of the equator, the passage certainly did not then point to the Pleiades. Nor has there been any time since the world began when the Pleiades were any- where near the direction of the southward pointing passage. In fact they have never been more than 20 south of the equator. The state- ment follows immediately after another to the surprising effect that in the year 2170 B.C. 'the Pleiades really commenced the spring by their midnight culmination.' The only comment an astronomer can make on this startling assertion is to repeat with emphasis the word italicised by Mr. Haliburton (or Mr. Blake?). The Pleiades being then in con- junction with what is now called the first point of Aries, culminated at noon, not at midnight, at the time of the vernal equinox. 136 FAMILIAR SCIENCE STUDIES. exception assert that the date of the builders of the great pyramid must have been more than a thousand years earlier than 2170 B.C., and that Bunsen has assigned to Menes the date 3620 B.C., while the date 3300 B.C. has been assigned to Cheops or Suphis on apparently good authority, we are led to inquire whether the other epoch when Alpha Draconis was at about the right distance from the pole of the heavens may not have been the true era of the commencement of the great- pyramid. Now, the year 3300 B.C., though a little late, would accord fairly well with the time when Alpha Draconis was at the proper distance 3 from the pole of the heavens. If the inclination of the entrance-passage is 26 27', as Professor Smyth made it, the exact date for this would be 3390 B.C. ; if 26 40', as others made it before his measurements, the date would be about 3320 B.C., which would suit well with the date 3300 B.C., since a century either way would only carry the star about a third of a degree towards or from the pole. Now, when we inquire whether in the year 3300 B.C. any bright star would have been visible, at southing, through the ascending passage, we find that a very bright star indeed, an orb otherwise remarkable as the nearest of all the stars, the brilliant Alpha Centauri, shone as it crossed the meridian right down that ascending tube. It is so bright that, viewed through that tube, it must have been visible to the naked eye, even when southing in full daylight. But thirdly we must consider how the builders of the pyramid would arrange for the observation of the sun at noon on every clear day in the year. They would carry up the floor of the ascending passage in an unchanged direction, as it already pointed south of the lowest place of the noon-sun at mid-winter. They would have to enlarge the tunnel into a lofty gallery, to in- crease the vertical range of view on the meridian. It seems reasonable to infer that they would prefer so to arrange matters that the upper end of the gallery would be near the middle of the platform which would form the top of the THE PROBLEM OF THK GREAT PYRAMID. 137 pyramidal structure from the time when it was completed for observational purposes. The height of the gallery would be so adjusted to its length, that the mid-winter's sun would not shine further than the lower end of the gallery (that is, to the upper end of the smaller ascending passage). In fact, as the moon and planets would have to be observed when due south, through this meridional gallery, and as they range further from the equator both north and south than the sun does, it would be necessary that the gallery should extend lower down than the sun's mid-winter noon rays would shine. As it would be a part of the observer's work to note ex- actly how far down the gallery the shadow of its upper southern edge reached, as well as the moment when -the sun's light passed from the western to the eastern wall of the gallery, and other details of the kind ; besides, of course, taking time-observations of the moment when the sun's edge seemed to reach the edge of the gallery's south- ern opening ; and as such observations could not be properly made by men standing on the smooth slanting floor of the gallery, it would be desirable to have cross-benches capable of being set at different heights along the sloping gallery. In some observations, indeed, as where the transits of several stars southing within short intervals of time had to be observed, it would be necessary to set some observers at one part of the gallery, others at another part, and perhaps even to have several sets of observers along the gallery. And this suggests yet another consideration. It might be thought desirable, if great importance was attached (as the whole building shows that great importance must have been attached) to the exactness of the observations, to have several observations of each transit of a star across the mouth of the gallery. In this case, it would be well to have the breadth of the gallery different at different heights, though its walls must of necessity be upright throughout- that is, the walls must be upright from the height where one breadth commences, to the height where the next breadth 138 FAMILIAR SCIENCE STUDIES. commences. With a gallery built in this fashion, it would be possible to take several observations of the same transit, somewhat in the same way that the modern observer watches the transit of a star across each of five, seven, or nine parallel spider threads, in order to obtain a more correct time for the passage of the star across the middle thread, than if he noted this passage alone. How far the grand gallery corresponds with these re- quirements can be judged from the following description given by Professor Greaves in 1638 : 'It is,' he says, 'a very stately piece of work, and not inferior, either in re- spect of the curiosity of art, or richness of materials, to the most sumptuous and magnificent buildings,' and a little fur- ther on he says, ' this gallery, or corridor, or whatever else I may call it, is built of white and polished marble (limestone), the which is very evenly cut in spacious squares or tables. Of such materials as is the pavement, such is the roof and such are the side walls that flank it ; the coagmentation or knitting of the joints is so close, that they are scarcely dis- cernible to a curious eye ; and that which adds grace to the whole structure, though it makes the passage the more slippery and difficult, is the acclivity or rising of the ascent. The height of this gallery is 26 feet' (Professor Smyth's careful measurements show the true height to be more nearly 28 feet), 'the breadth of 6-870 feet, of which 3-435 feet are to be allowed for the way in the midst, which is set and bounded on both sides with two banks (like benches) of sleek and polished stone; each of these hath 1-717 of a foot in breadth, and as much in depth.' These measure- ments are not strictly exact. Smyth made the breadth of the gallery above the banks or ramps, as he calls them, 6 feet loi inches ; the space between the ramps, 3 feet 6 inches ; the ramps nearly about i foot 8 T \f inches broad, and nearly i foot 9 inches high, measured transversely, that is, at right angles to the ascending floor. As to arrangements for the convenience of observers on the slippery and difficult floor of this gallery, we find that THE PROBLEM OF THE GREAT PYRAMID. 139 upon the top of these benches or ramps, near the angle where they meet the wall, ' there are little spaces cut in right- angled parallel figures, set on each side '.opposite one another, intended no question for some other end than ornament? The diversity of width which I have indicated as a desir- able feature in a meridional gallery, is a marked feature of the actual gallery. ' In the casting and ranging of the marbles ' (limestone), ' in both the side walls, there is one piece of architecture,' says Greaves, ' in my judgment very graceful, and that is that all the ceurses or stones, which are but seven (so great are these stones), do set and flag over one another about three inches ; the bottom of the uppermost course overlapping the top of the next, and so in order, the rest as they descend.' The faces of these stones are exactly vertical, and as the width of the gallery diminishes upwards by about six inches for each successive course, it follows that the width at the top is about 3^ feet less than the width, 6 feet ioi inches, at the bottom, or agrees in fact with the width of the space between the benches or ramps. Thus the shadow of the vertical edges of the gallery at solar noon just reached to the edges of the ramps, the shadow of the next lower vertical edges falling three inches from the edges higher up the ramps, those of the next vertical edges six inches from these edges, still higher up, and so forth. The true hour of the sun's south- ing could thus be most accurately determined by seven sets of observers placed in different parts of the gallery, and near midsummer, when the range of the shadows would be so far shortened, that a smaller number of observers only could follow the shadows' motions ; but in some respects, the observations in this part of the year could be more readily and exactly made than in winter, when the shadows' spaces of various width would range along the entire length of the gallery. Similar remarks would apply to observations of the moon, which could also be directly observed. The planets and stars of course could only be observed directly. I 4 o FAMILIAR SCIENCE STUDIES. The grand gallery could be used for the observation of any celestial body southing higher than 26 18' above the horizon ; but not very effectively for objects passing near the zenith. The Pleiades could be well observed. They southed about 63! above the horizon in the year 2140 B.C. or thereabouts when they were on the equinoctial colure. 1 But if I am right in taking the year 3300 B.C. when Alpha Centauri shone down the smaller ascending passage in southing, the Pleiades were about 58 only above the horizon when southing, and therefore even more favourably observable from the great meridional gallery. In passing I may note that at this time, about 3300 years before our era, the equinoctial point (that is, the point where the sun passes north of the equator, and the year begins according to the old manner of reckoning) was midway between the horns of the Bull. So that then, and then alone, a poet might truly speak of spring as the time ' Candidus auratis aperit quum cornibus annum Taurus, ' as Virgil incorrectly did (repeating doubtless some old tradi- tion) at a later time. Even Professor Smyth notices the necessity that the pyramid gallery should correspond in some degree with such a date. ' For,' says he, ' there have been traditions for long, whence arising I know not, that the seven overlappings of the grand gallery, so impressively de- scribed by Professor Greaves, had something to do with the Pleiades, those proverbially seven stars of the primeval world,' only that he considers the pyramid related to memorial 1 This date is sometimes given earlier, but when account is taken of the proper motion of these stars we get about the date above mentioned. I cannot understand how Dr. Ball, Astronomer Royal for Ireland, has obtained the date 2248 B.C., unless he has taken the proper motion of Alcyone the wrong way. The proper motion of this star during the last 4000 years has been such as to increase the star's distance from the equinoctial colure ; and therefore, of course, the actual interval of time since the star was on the colure is less than it would be calculated to be if the proper motion were neglected. THE PROBLEM OF THE GREAT PYRAMID. 141 not observing astronomy, ' of an earlier date than Virgil's.' The Pleiades also, it may be remarked, were scarcely re- garded in old times as belonging to the constellation of the Bull, but formed a separate asterism. The upper end of the great gallery lies very near the vertical axis of the pyramid. It is equidistant, in fact, from the north and south edges of the pyramid platform at this level, but lies somewhat to the east of the true centre of this platform. One can recognise a certain convenience in this arrangement, for the actual centre of the platform would be required as a position from whence observation of the whole sky could be made. Observers stationed there would have the cardinal points and the points midway between them defined by the edges and angles of the square platform, which would not be the case if they were displaced from the centre. Stationed as they would be close to the mouth of the gallery, they would hear the time signallings given forth by the observers placed at various parts of the gallery ; and no doubt one chief end of the exact time-observations, for which the gallery was manifestly constructed, would be to enable the platform observers duly to record the time when various phenomena were noticed in any part of the heavens. This corresponds well with the statement made by Proclus, that the pyramids of Egypt, which, according to Diodorus Siculus, had been in existence during 3600 years, terminated in a platform upon which the priests made their celestial observations. The last-named historian alleges, also ('Biblioth. Hist.' Lib. I.), that the Egyptians, who claimed to be the most ancient of men, professed to be acquainted with the situation of the earth, the risings and settings of stars, to have arranged the order of days and months, and pretended to be able to predict future events, with certainty, from their observations of celestial phenomena. I think that it is in this association of astrology with astro- nomy that we find the explanation of what, after all, remains the great mystery of the pyramid the fact, namely, that all I 4 2 FAMILIAR SCIENCE STUDIES. the passages, ascending, descending, and horizontal, con- structed with such extreme care, and at the cost of so much labour, in the interior of the great pyramid, were eventually (perhaps not very long after their construction) to be closed up. I reject utterly the idea that they could have been constructed merely as memorials. Sir E. Beckett, who seems willing to admit this conception, rejects the notion that the builders of the pyramid recorded ' standard measures by hiding them with the utmost ingenuity.' Is it not equally absurd to imagine that they recorded the date of the great pyramid, by construction, by those most elaborately concealed passages ? Why they should have concealed them after constructing them so carefully, may not be clear. For my own part, I regard the theory that the Pyramid of Suphis was built for astrological observations, relating to the life of that monarch only, as affording the most satisfactory explanation yet advanced of the mysterious circumstance that the building was closed up after his death. Supposing the part of the edifice (fifty layers in all), which includes the ascending and descending passages, to have been erected during his life- time, it may be that some 'reverential or superstitious feeling caused his successors, or the priesthood, to regard the build- ing as sacred after his death to be closed up therefore and completed as a perfect pyramid, polished ad unguem from its pointed summit to the lines along which the four faces meet the smooth pavement. round its base. We might thus explain why each monarch required his own astrological observatory afterwards to become his tomb. Be this as it may, it is certain that the pyramids were constructed for astronomical observations ; and it would, I conceive, be utterly unreasonable to imagine that the costly interior fittings and arrangements, ' not inferior, in respect of curiosity of art or richness of materials, to the most sumptuous and magnificent buildings,' were intended to subserve no other purpose but to be memorials ; and that, too, not until, in the course of thousands of years, the whole mass of the pyramid had begun to lose the exactness of its original figure. 143 THE PYRAMIDS OF GHIZEH. IN my treatise called ' Myths and Marvels of Astronomy ' there are two essays on the great pyramid, one dealing with the strange fancies which have been associated with this building by Professor Piazzi Smyth, Astronomer Royal for Scotland, the other advancing a theory respecting the building which seems to me, on the whole, more probable than any other. In the last essay of this present volume I have considered other relations which had not occurred to me when I wrote those papers. I do not now propose to go over the ground covered by my three former essays, but, following the practice which I have before adopted in like cases, to indicate at full length in the present essay only such points as I have noted since the other papers were written. If in such study as I have given to the subject in the interval I had found any evidence bearing unfavourably upon the views I have advanced in those papers, I should have judged it right to point out clearly and definitely the nature and weight of such evidence, and to withdraw, if the evidence suggested such a course, from positions taken up in error not merely abandoning views which appeared erroneous, but pointing out such errors as I had recognised. Since, on the contrary, the evidence I have obtained and the points which I have noticed in relation to the pyramids, and especially to the great pyramid, appear strikingly to confirm the theory I advanced in the essay entitled ' The Mystery of the Pyramid,' it is but just to indicate the nature of this new or recently noted matter, even as I should have 144 FAMILIAR SCIENCE STUDIES. indicated any adverse evidence. If I should thus appear tenax profiositi, I believe such persistence has its origin in a wish to be just and truthful (qualities which, as we know, Horace associated with tenacity of opinion). I think too that readers of my former papers on the pyramid may find as much interest as I have found myself in the new matter thus submitted to them, respecting the oldest remaining monuments of human labour (except such as are to be re- garded as subjects rather of palaeontological than of anti- quarian research). I will first run briefly through such matters of detail as are necessary preliminaries to any discussion respecting the pyramids, following the line laid down in Sir Edmund Beckett's treatise on Building. I may remark that much which he there points out, and especially the theory which he advances respecting the measures of length used in the construction of the great pyramid, was not known to me when I wrote the papers above mentioned. It appears to me that he makes out a very strong case for his theory. I must frankly admit that he by no means entertains a similar opinion respecting my own views as to the purposes for which the pyramid was constructed. He can find nothing, he tells me, to suggest the idea that the builders of the pyramids had any astrological ideas in view ; and so far as I can judge, he would not admit that even astronomy entered into the plans of the pyramid architects otherwise than as an adjunct to the work of building. I believe, how- ever, that Sir E. Beckett's objections to the astrological interpretation of the pyramids, or rather to the association of the astrological theory with the tomb theory, have their origin rather in the idea that such a theory would be asso- ciated with my astrological interpretation of the origin of the Sabbath, than in any circumstances known respecting the pyramids or their builders. I have certainly found nothing in Sir E. Beckett's reasonings respecting his own theory (which I consider the most probable theory of pyramid dimensions yet advanced) opposed to my own views, but, THE PYRAMIDS OF GHIZEIL 14$ on the contrary, much which seems strongly to favour them. Whether the astrological theory has or has not much to be said in its favour is a point upon which I willingly leave others to decide. I think I shall be able here con- siderably to strengthen the evidence I formerly adduced to show that the pyramid's present features cannot well be accounted for on any other theory. In the first place, Sir E. Beckett starts with the statement, almost amounting in itself to an admission of the astro- nomical significance of the pyramid relations, that the great pyramid was built in the year 2170 B.C., by Cheops as Herodotus calls him, but Suphis or Shufu, as he is named in hieroglyphics painted on large stones over the king's chamber. This, says Beckett, was in the time of Peleg, ' ages before the Israelites were in Egypt, whom some persons have hastily guessed to have been employed in building the pyramids ' an argument effective indeed against Professor Smyth and those followers of his who see in the pyramid a sort of stone Bible, but scarcely as against those who believe no more in the 239 years of Peleg's life than in the nine hundred odd years of Methuselah's, or in the literal inter- pretation of the six days of creation. If we are to start with the theory that, in the year B.C. 2348, there were eight living persons in the world, and that, less than two centuries later, a monarch, ruling a nation large enough to provide tens of thousands of workers, erected the greatest mass of stonework ever raised on the face of this earth by man, we need not trouble ourselves to explain how and why the great pyramid was built. We might as well admit at once that the pyramid was built under* the direct personal superinten- dence of Uriel, the Archangel who has special charge over the astronomical relations of the solar system, The same whom John saw also in the sun ; who also explained earlier to an inquiring angel how, in the beginning, L I 4 6 FAMILIAR SCIENCE STUDIES. This ethereal quintessence of Heav'n Flew upward, spirited with various forms, That roll'd orbicular, and turn'd to stars Numberless, as thou seest, and how they move. One idea is not a whit more untenable than the other. Secondly, it is to be noted that according to some tra- ditions the second pyramid, though somewhat smaller than the first, and altogether inferior in design, was begun some- what earlier. I would invite special attention to this point. It is one of those perplexing details which are always best worth examining when we want to obtain a true theory. The second pyramid was certainly built during the reign of the builder of the first or great pyramid. It must have been built, then, with his sanction, for his brother, Chephren, according to Herodotus; Noun-shofo, or Suphis IL, accord- ing to the Egyptian records. Enormous quantities of stone, of the same quality as the stone used for the great pyramid, were conveyed to the site of the second pyramid, during the very time when the resources of the nation were being largely taxed to get the materials for the great pyramid conveyed to the place appointed for that structure. It would appear, then, that there was some strong in fact, some insuperable objection to the building of one great pyramid, larger by far than either the first or second, for both the brothers. Yet nothing has ever been learned respecting the views of the Egyptians about tombs (save only what is learned from the pyramids themselves, if we assume that they were only built as tombs) which would suggest that each king wanted a monstrous pyramid sepulchre for himself. If we could doubt that Cheops valued his brother and his family very highly, we should find convincing proof of the fact, in the circumstance that he allowed enormous sums to be expended on his brother's pyramid, and a great quantity of labour to be devoted to its erection, at the time when his own was in progress at still greater expense, and at the cost of still greater labour. But if he thus highly esteemed his brother, and, regarding him as THE PYRAMIDS OF GHIZEH. 147 the future ruler of Egypt, recognised in him the same almost sacred qualities which the people of Egypt taught their rulers to recognise in themselves, what was to prevent him from combining the moneys and the labours which were devoted to the two pyramids in the construction of a single larger pyramid, which could be made doubly secure, and more perfectly designed and executed ? Is anything what- ever known respecting either the Egyptians or any race of tomb-loving, or rather corpse-worshipping people, which would lead us to suppose that a number of costly separate tomb pyramids would have been preferred to a single, but far larger, pyramid-mausoleum, which should receive the bodies of all the members of the family, or at least of all those of the family who had ruled in turn over the land ? If we could imagine for a moment that Cheops would have objected to such an arrangement, is it not clear that when he died his successors would have taken possession of his pyramid, removing his body perhaps, or not allowing it to be interred there, if the sole or even the chief purpose for which a pyramid was erected was that it might serve as a gigantic tomb ? We may indeed note as a still more fatal objection to the theory that the chief purpose for which a pyramid was built was to serve as the builder's tomb, that it would have been little short of madness for Cheops to devote many years of his life, enormous sums of money, and the labour of myriads of his people, to the construction of a building which might and probably would be turned after his death to some purpose quite different from that for which he in- tended it. It is not to be supposed, and indeed history shows it certainly was not the case, that the dynasties which "ruled over Egypt were more secure from attack than those which ruled elsewhere in the East during those days. Cheops cannot have placed such implicit reliance on his brother Chephren's good faith as to feel sure that, after his own death, Chephren would complete the pyramid, place Cheops's body in it, and close up the entrance so securely 148 FAMILIAR SCIENCE STUDIES. that none could find the way into the chamber where the body was laid. Cheops could not even be certain that Chephren would survive him, or that his own son, Myceri- nus or Menkeres, would be able to carry out the purpose for which he (Cheops) had built the pyramid. Apart, then, from that feature of the tomb theory which seems so strangely to have escaped notice the utter wild- ness of the idea that even the most tomb-loving race would build tombs quite so monstrous as these we see that there are the strongest possible objections against the credibility of the merely tombic theory (to use a word coined, I imagine, by Professor Piazzi Smyth, and more convenient perhaps than defensible). It seems clear on the face of things that the pyramids must have been intended to serve some useful purpose during the lifetime of the builder. It is clear also (all, indeed, save the believers in the religion of the great pyramid, will admit this point) that each pyramid served some purpose useful to the builder of the pyramid, and to him only. Cheops's pyramid was of no use to Chephren, Chephren's of no use to Mycerinus, and so forth. Otherwise we might be sure, even if we adopted for a moment the exclusively tombic theory, that, though Chephren might have been so honest as not to borrow his brother's tomb when Chebps was departed, or Mycerinus so honest as not to despoil either his uncle or his father, yet among some of the builders of the pyramids such honesty would have been wanting. It is clear, however, from all the traditions which have reached us respecting the pyramids, that no anxiety was entertained by the builder of any pyra- mid on this score. Cheops seems to have been well assured that Chephren would respect his pyramid, and even (at great expense) complete it ; and so of all the rest. There must, then, have been some special reasons which rendered the pyramid of each king useless altogether to his successor. Nay, may we not go somewhat further, and, perceiving that Chephren's pyramid must have been built chiefly at his brother's cost, and nearly all of it during his brother's life- THE PYRAMIDS OF GHIZEH. 149 time, may we not assume that the particular purpose which Chephren's pyramid subserved to Chephren only, was nevertheless such a purpose as in some way advanced the interests of the dynasty? Nothing in the history of the dynasty implies that the relations among its members were very much more cordial than those usually prevailing among kings and their relatives. It would have implied singular generosity on Cheops's part, renewed by Chephren towards Mycerinus, and by Mycerinus towards Asychis, thus to have helped in the erection of mere tombs for their several heirs while these were still dependent upon them. But if the fortunes of the dynasty were in some way involved, or sup- posed to be involved, in these structures, the case would be entirely altered. It is a characteristic feature of my theory respecting the pyramids, though it certainly was not the point which suggested the theory (and, as the reader of my " Myths and Marvels " is aware, was not even touched upon in my original presentation of the theory), that it explains, not merely satisfactorily but fully, this particular circumstance, viz., that it was worth the reigning king's while to have special attention paid to the construction, not merely of his brother's pyramid, but also of his eldest son's large pyramid, of his three other sons' small pyramids, and of his six daughters' still smaller pyramids. There seems reason to believe that all these were put in hand, so to speak, nearly at the same time, though the great pyra- mid of Cheops, owing to the enormous scale on which the preliminary works were constructed, was probably not actually begun till some time after the others. Very probably the three small pyramids beside the third, the largest of which is the fourth pyramid or the pyramid of Asychis, were all commenced during the lifetime of Cheops. Thus the relative dimensions of the several pyramids, as shown in the accompanying map, Fig. 3, would correspond to the relative importance attached by Cheops to the fortunes always as associated with his of the various members of his own family, This, would explain, what has 150 FAMILIAR SCIENCE STUDIES. hitherto been thought perplexing, the singularly reduced scale on which the pyramid of Mycerinus is built, and the still further and most marked reduction in the case of the pyramid of Asychis. It is not at all likely that Mycerinus, if building a pyramid for himself, would have been content with a smaller pyramid than that of Cheops himself. On the contrary, all that we know of human nature, and espe- cially of the nature of the Egyptian kings, assures us that \ FIG. 3. each successive monarch would have endeavoured to sur- pass his predecessors. On the other hand, if Cheops assigned the proportions of a series of pyramids, one for each member of his family, he would naturally arrange them in order of magnitude as we see them in Fig. 3. To his brother and next heir, his right hand probably in the govern- ment of Egypt, he would assign a pyramid second only in dimensions to his own, though greatly inferior in quality. To his eldest son, young doubtless when the pyramids were THE PYRAMIDS OF GHIZEH. 151 begun, he would assign a much smaller pyramid (No. 3) ; but as this son was to succeed Chephren as king, Cheops would give him, like Chephren, a separate enclosure ; while to his younger sons and to his daughters he would assign pyramids not only smaller, but enclosed within the same area as his own. Space seems to have been left for Chephren's family, should he have any ; but it appears he had no children. To Asychis, his grandson, Cheops would assign a pyramid about as large as those of his own younger sons. It is noteworthy, by the way, that the linear dimen- sions of the pyramid of Asychis are less than those of the pyramid of Mycerinus, in the same degree that those are less than the linear dimensions of the pyramid of Cheops. Most certainly this distribution of the dimensions was not that which Asychis himself, or Mycerinus, would have selected. I would submit in passing that this explanation of the relative dimensions of the pyramids of Ghizeh is somewhat more natural than that given by the pyramid-religionists, who insist that the great pyramid was built under divine superintendence (or by divinely inspired architects), and not intended for a tomb at all, while all the other pyramids, being meant for tombs, were therefore inferior in size and construction. Not only is this explanation the only one ever attempted of this most significant peculiarity of the pyramid group singularly extravagant in itself, and unsatis- factory further as leaving Cheops, the first pyramid builder, without any pyramid for his tomb, but it gives no explana- tion whatever of the descent in scale from Chephren's pyramid to that of Mycerinus, and from this to the pyramid of Asychis. Again, however, I have to note that the circumstance here dwelt upon was not one of those which suggested my theory, nor was it noticed in the paper in which I first ad- vocated that theory. It is one of those pieces of evidence which is almost certain to be noticed in favour of a true theory sorne time after other evidence has caused such 152 FAMILIAR SCIENCE STUDIES. theory fo be adopted. But such things do not happen in the case of untrue theories, save by very rare accident It will presently be seen that the two characteristics of the pyramids, formerly regarded as perplexing, which find a natural and ready explanation in the astrological theory, are by no means the only ones of which the same may be said. Among points to which my attention has been specially directed by advocates of the exclusively tombic theory of the pyramids, one of the chief, one which, indeed, I was assured by several persons would convince me of the suffi- ciency of this theory, was what is called Lepsius's Law of Pyramid Building. It is thus referred to and described by Professor Piazzi Smyth : ' All the Egyptologists of our age, French, English, German, and American, have hailed the advent on their stage of time of the so-called "Lepsius's Law of Pyramid Building ; " they universally declaring that it satisfies absolutely all the observed or known phenomena. And it may do so for every known case of any Egyptian pyramid, except the great pyramid ; and there it explains nothing of what // chiefly consists in. Taking, however, the cases which it does apply to, viz., the profane Egyptian ex- amples, this alleged " law " pronounces that the sole object of any pyramid was to form a royal tomb subterranean, as a matter of course and that operations began by making an inclined descending passage leading down into the rock, and in cutting out an underground chamber at the end of it. The scheme, thus begun below, went on also growing above- ground, every year of the king's reign, by the placing there of a new heap or additional layer of building stones, and piling them, layer above layer, over a central square-based nucleus upon the levelled ground, virtually above the subter- ranean apartment ; and it was finally (that is, this superin- cumbent mass of masonry) finished off on that king's death by his successor, who deposited his predecessor's body em- balmed and in a grand sarcophagus in the underground chamber, stopping up the passage leading to it, cased in the rude converging sides of the building with bevelled casing THE PYRAMIDS OF GHIZEH. 153 stones, so as to give it a smooth pyramidal form, and left it in fact a finished Egyptian and Pharaonic pyramid to all posterity ; and no mean realisation either of prevailing ideas among soms early nations, of burying their monarchs sub montibus altis, in impressive quiet, immovable calm, and deep in the bosom of mother earth.' Although Lepsius states that he discovered this solution of the riddle of pyramidical construction, it was in part suggested earlier by James Wilde, and is thus described in the letterpress accompanying Frith's large photographs of Egypt : ' A rocky site was first chosen, and a space made smooth, except a slight eminence in the centre to form a peg upon which the structure should be fixed ' (which is absurd). ' Within the rock, and usually below the level of the future base, a sepulchral chamber was 'excavated, with a passage inclined downwards, leading to it from the north.' After describing the way in which the work proceeded, the ac- count goes on to say that ' in this manner it was possible for the building of a pyramid to occupy the lifetime of its founder, without there being any risk of his leaving it in- complete to any such degree as would afford a valid excuse for his successor neglecting to perform his very moderate part, of merely filling up the angles and smoothing off generally.' This, however, is not precisely the same as Lepsius's law, and is manifestly less complete and less satisfactory. But in the first place I am not at all disposed to admit that Lepsius's law, even though it explains the manner in which the pyramids may have been built, is either proved by any evidence cited in its favour, or in turn proves anything respecting the purpose of any of the pyramids. It agrees well with the theory that the pyramids, including, of course, the great one, served as tombs for the several persons to whom they belonged or were assigned. But no one thinks of questioning this, so far as all the pyramids, except the great one, are concerned ; and I apprehend that very few share Professor Smyth's faith that King Cheops never was buried, and was never meant to be buried, in the pyramid 154 FAMILIAR SCIENCE STUDIES, which bears his name. None of the difficulties of the exclusively tombic theory seem even touched by Lepsius's theory, whether it be accepted or rejected. The construc- tion of the pyramids by single layers year by year, if proved, and if it prove anything, shows that the use of the pyramids related chiefly to the life of those to whom the pyramids were assigned, not solely to their death and burial Lepsius's theory is partly based on a circumstance which no astronomer who attentively considers the matter can fail to interpret in one special manner, bearing very significantly on our ideas respecting the purpose for which the pyramids were constructed. In all the pyramids of Ghizeh there is a slant passage (in some there are two such passages) leading down into the rock, an under-ground chamber being cut at the end of the passage. Lepsius, ot course, like all who regard the astro- nomical relations fulfilled by the pyramids as of slight im- portance, pays no special attention to the circumstance that in every case the descending passage passes in a north and south direction at an angle always of about 26 degrees, and has its entrance always on the northern side. Fig. 4 shows the position of the descending passages in the four chief pyra- mids. But if it were not obvious in other ways that astro- nomical relations were regarded by the builders of the pyra- mids as of extreme importance, these slant passages would prove it. They show unmistakably, ( i) that the builders pro- posed to make the pyramids fulfil certain definite astro- nomical conditions ; and (2) the method in which the builders effected their purpose. I have shown in my last article on the Great Pyramid how an architect, proposing to set a building in a par- ticular latitude, might use either the sun, when due south, or those stars which circle close round the pole, for that purpose ; that the better the astronomers were in the days of the pyramid-builders, the more likely they were to prefer the latter, or stellar method, to the former, or solar method ; and that, if they adopted the solar method, the build' THE PYRAMIDS OF GHIZEH. '55 ing would be set too far north unless correction were made for the refraction of the atmosphere ; while if they adopted the stellar method, the building would be set too far south. Wherefore, as we find the centre of the great pyramid set somewhat south of the latitude 30 north which the builders clearly intended to have it occupy the error being about a mile and a quarter, while, if refraction were wholly neglected, it would have been about a mile and three- quarters we may infer that the astronomers who superintended the arrangements for fixing the latitude employed the stellar method ; that they were exceedingly skilful ob- servers, considering they had no telescopic meridian instruments ; and (with less certainty) that they made some correction for atmo- spheric refraction. I show also fully in that article that astronomers using the stellar method for that purpose would most certainly employ it to set the sides of the ' pyramid's ' square base facing as exactly as possible ( the four cardinal points. One method would certainly present itself, and only one would be at all suitable for this purpose. They would take their pole-star, what- ever it might be, and would note its direction when passing either just above or just below the pole, as of course it does in every sidereal day. The direction of the star at either of these epochs would be due north. But how could they mark this direction on their selected base ? 156 FAMILIAR SCIENCE STUDIES. They could in the first place set up a pointed upright, as A B in fig. 5, at the middle of the northern edge of the base, and another shorter one, c D, so that at one of the epochs, it would not matter which, an eye placed as at E would see the points c and E in the same straight line as the pole star s. Then the line D B would lie north and south. This would only be a first rough approximation, how- ever. The builders would require a much more satisfactory north and south line than D B. To obtain this they would bore a slant passage in the solid rock, as D c, which should FIG. 5. Showing how the builders of the pyramid probably obtained their base. point directly to the pole-star s when due north, starting their boring by reference to the rough north and south line D B, but guiding it as they went on, by noticing whether the pole-star, when due north, remained visible along the passage. But they would now have to make a selection between its passage above the pole and its passage below the pole. In using the uprights D and B, they could take either the upper or the lower passage ; but the underground boring could have but one direction, and they must choose whichever of the two passages of the star they preferred. We cannot doubt they would take the lower passage, not only as the more convenient passage for observation, but because the length of their boring D G would be less, for a THE PYRAMIDS OF GHIZEH. 157 given horizontal range FD, if the lower passage of the star .$ were taken, than it would be for the upper passage, when its direction would be as D G'. When they had bored far enough down to have a suffi- cient horizontal range F D (the longer this range, of course, the truer the north and south direction), they would still have to ascertain the true position of F, the point vertically above c. For this purpose they would get F first as truly as they could from the line D B prolonged, and would bore down from F vertically (guiding the boring, of course with a plumb-line), until they reached the space opened out at G. The boring F G might be of very small diameter. Noting where the plumb-line let down from F to G reached the floor of the space G, they would ascertain how far F lay to the east or to the west of its proper position over the centre of the floor of this space. Correcting the position of F accordingly, they would have F D the true north-and-south line. This method could give results of considerable accuracy ; and it is the only method in fact which could do so. When, therefore, we find that the base of the pyramid is oriented with singular accuracy, and secondly that just such a boring as D G exists beneath the base of the pyramid, running three hundred and fifty feet through the solid rock on ivJiich the pyramid is built, we cannot well refuse to believe that the slant passage was bored for this purpose, which it was so well fitted to subserve, and which has been so well sub- served in some way. Now, if this opinion is adopted, and for my own part I cannot see how it can well be questioned, we cannot possibly accept the opinion that the slant tunnel was bored for another purpose solely, or even chiefly, unless it can be shown that that other purpose in the first place was essential to the plans of the builders, in the second place could be sub- served in no other way so well, and in the third place was manifestly subserved in this way to the knowledge of those who made the slant borings. Now, it certainly is the case that, noting the actual position of this slant boring, we can 158 FAMILIAR SCIENCE STUDIES. form a shrewd guess at the date of the great pyramid's erec- tion. In the year 2170 B.C., and again (last before that) in the year 3350 B.C., and also for several years on either side of those dates, a certain bright star did look down that boring, or, more precisely, could be seen by any one who looked up that boring, when the star was just below the pole in its circuit round that point. The star was a very impor- tant one among the old constellations, though it has since considerably faded in lustre, being no other than the star Alpha of the constellation the Dragon, which formerly was the polar constellation. For hundreds of years before and after the dates 3350 and 2170 B.C., and during the entire interval between those dates, no other star would at all have suited the purposes of the builders of the pyramid ; so that we may be toleraby sure this was the star they employed. Therefore the boring, when first made, must have been directed towards this star. We conclude, then, with con- siderable confidence, that it was somewhere about one of the two dates 3350 B.C., and 2170 B.C., that the erection of the great pyramid was begun. And from the researches of Egyptologists it has become all but certain that the earlier of these dates is very near the correct epoch. But though the boring thus serves the purpose of dating the pyramid, it seems altogether unlikely that the builders of the pyramid intended to record the pyramid's age in this way. They could have done that, if they had wanted to, at once far more easily and far more exactly, by carving a suitable record in one of the inner chambers of the building. But nothing yet known about the pyramid suggests that its builder wanted to tell future ages anything whatever. So far from this, the pyramid was carefully planned to reveal nothing. Only when men had first destroyed the casing, next had found their way into the descending passage, and then had in the roughest and least skilful manner conceivable (even so, too, by an accident) discovered the great ascending gallery, were any of the secrets of this mighty tomb revealed for a tomb and nothing else it has been ever since Cheops died. THE PYRAMIDS OF GHIZEH. 159 To assert that all these events lay within the view of the architect who seemed so carefully to endeavour to render them impossible, is to ask that men should set their reason- ing faculties on one side when the pyramid is in question. And lastly, we have not a particle of evidence to show that the builders of the pyramid had any idea that the date of the building would be indicated by the position of the great slant passages. They may have noticed that the pole-star was slowly changing its position with respect to the true pole of the heavens ; and they may even have recognised the rate and direction in which the pole-star was thus moving. But it is utterly unlikely that they could have detected the fact that the pole of the heavens circles round the pole of the ecliptic in the mighty processional period of 25,920 years ; ' and unless they knew this, they would not know that the position of the slant passage would tell future genera- tions aught about the pyramid's date. On all these accounts, ( i ) because the builders probably did not care at all about our knowing anything on the subject, (2) because 1 If the architect of the great pyramid knew anything about the great processional period, then unless such knowledge was miraculously communicated the astronomers of the pyramid's time must have had evidence which could only have been obtained during many hundreds of years of exact observation, following of course on a long period during which comparatively imperfect astronomical methods were em- ployed. Their astronomy must therefore have had its origin long before the date commonly assigned to the Flood. In passing I may remark that in a paper on the pyramid by Abbe Moigno, that worthy but somewhat credulous ecclesiastic makes a remark which seems to show that the stability and perfection of the great pyramid, and there- fore the architectural skill acquired by the Egyptians in the year 2170 B.C. (a date he accepts), proves in some unexplained way the comparative youth of the human race. To most men it would seem that the more perfect men's work at any given date, the longer must have been the preceding interval during which men were acquiring the skill thus displayed. On the contrary, the pyramids, says Abbe Moigno, ' give the most solemn contradiction to those who would of set purpose throw back the origin of man to an indefinite remoteness.' It would have been well if he had explained how the pyramids do this. 160 FAMILIAR SCIENCE STUDIES. if they did they would not have adopted so clumsy a method, and (3) because there is no reason for believing, but every reason for doubting, that they knew the passage would tell future ages the date of the pyramid's erection, we must regard as utterly improbable, if not utterly untenable, the proposition that the builders had any such purpose in view in constructing the slant passage. I am therefore somewhat surprised to find Sir E. Beckett, who does not accept the wild ideas of the pyramid religionists, nevertheless dwelling, not on the manifest value of the slant passages to builders desiring to orient such an edifice as the great pyramid, but on the idea that those builders may have wanted to record a date for the benefit of future ages. After quoting a remark from Mr. Wackerbarth's amu- sing review of Smyth's book, to the effect that the hypothesis about the slant passage is liable to the objection that, the mouth of the passage being walled up, it is not easy to con- ceive how a star could be observed through it, Beckett says, ' Certainly not, after it was closed ; but what has that to do with the question whether the builders thought fit to indicate the date to anyone who might in after ages find the passage, by reference to the celestial dial, in which the pole of the earth travels round the pole of the ecliptic in 25,827 years, like the hand of a clock round the dial ? ' But in reality there is no more extravagant supposition among all those ideas of the pyramidalists (which Beckett justly regards as among the wildest illustrations of ' the province of the imagination in science ') than the notion that this motion of the pole of the earth was known to the builders of the pyramid, or that, knowing it, they adopted so preposterous a method of indicating the date of their labours. Let us return to the purposes which seem to have been actually present in the minds of the pyramid builders. Having duly laid down the north-and-south line F D, in fig. 5, and being thus ready to cut out from the nearly level face of the solid rock the corner sockets of the square base, they would have to choose what size they would give the THE PYRAMIDS OF GHIZEH. 161 base. This would be a question depending partly on the nature of the ground at their disposal, partly on the expense to which King Cheops was prepared to go. The question of expense probably did not influence him much ; but it re- quires only a brief inspection of the region at his disposal (in the required latitude, and on a firm rock basis) to see that the nature of the ground set definite limits to the base of the building he proposed to erect. As Piazzi Smyth re- marks, it is set close to the very verge of the elevated plateau, even dangerously near its edge. Assuming the centre of the base determined by the latitude observations outside, the limit of the size of the base was determined at once. And apart from that, the hill country directly to the south of the great pyramid would not have permitted any considerable extension in that direction, while on the east and west of its present position the plateau does not extend so far north as in the longitude actually occupied by the pyramid. These considerations probably had quite as much to do with the selection of the dimensions of the base as any that have been hitherto insisted upon. Sir E. Beckett says, after showing that the actual size of the base was in other respects a convenient one (in its numerical relation to pre- vious measures), the great pyramid 'must be some size,' but ' why Cheops wanted his pyramid to be about ' its actual size he does not profess to know. Yet, if the latitude of the centre of the base were really determined very carefully, it is clear that the nearest, and in this case the northern, verge of the rock plateau would limit the size of the base ; and we may say that the size selected was the largest which was available, subject to the conditions respecting latitude. True, the latitude is not correctly determined ; but we may fairly assume it was meant to be, and that the actual centre of the base was supposed by the builders to lie exactly in latitude 30 degrees north. However, we may admit that the dimensions adopted were such as the builders considered convenient also. I M 1 62 FAMILIAR SCIENCE STUDIES. fear Sir E. Beckett's explanation on this point, simple and commonplace though it is, is preferable to Professor Smyth's. If, by the way, the latter were right, not only in his views, but in the importance he attaches to them, it would be no mere fa$on de parler to say ' I fear ; ' for a rather unpleasant fate awaits all who ' shorten the cubit ' as Sir E. Beckett does. ' I will not attempt,' says Professor Smyth, ' to say what the ancient Egyptians would have thought ' of certain ' whose carriages/ it seems, ' try to stop the way of great pyramid research,' ' for I am horrified to remember the Pharaonic pictures of human souls sent back from heaven to earth, in the bodies of pigs, for far lighter offences than shortening the national cubit.' Sir E. Beckett has sought to shorten the pyramid cubit, with which Smyth is 'the sacred, Hebrew earth-commensurable, anti-Canite cubit,' a far heavier offence probably than merely ' shortening the national cubit.' But after all, it is unfortunately too true, that if the shorter cubit which Beckett holds to have been used by the pyramid builders was not so used, the pyramid does its best to suggest that it was ; and if Beckett and those who follow him (as I do in this respect) are wrong, the pyramid and not they must be blamed. For, apart from the trifling detail that the Hebrew cubit of 25 inches is entirely imaginary, ' neither this cubit, nor any multiple of it, is to be found in a single one of all Mr. Smyth's multitude of measurements, except two evidently accidental multiples of it in the dia- gonals of two of the four corner sockets in the rock ; which are not even square, and could never have been seen again after the pyramid was built, if the superstructure had not been broken up and stolen, which was probably the last thing that Cheops or his architect expected.' But of the other cubit, ' the pyramid and the famous marble " Coffer," in the king's chamber (which was doubtless also Cheops's coffin until his body was " resurrectionised " by the thieves who first broke into the pyramid), do contain clear indica- tions.' The cubit referred to is the working cubit of 2 of THE PYRAMIDS OF GHIZEH. 163 inches, or about a fiftieth of an inch less. For a person of average height, it is equal to about the distance from the elbow to the tip of the middle finger, plus a hand's-breadth, the former distance being the natural cubit (for a person of such height). The natural cubit is as nearly as possible half- a-yard, and most probably our yard measure is derived from this shorter cubit. The working cubit may be regarded as a long half- yard, the double working cubit or working Egyp- tian yard measure, so to speak, being 41^ inches long. The length of the base-circuit of the great pyramid may be most easily remembered by noticing that it contains as many working cubits as our mile contains yards, viz., 1,760; giving 440 cubits as the length of each of the four sides of the base. If Lincoln's Inn Fields were enlarged to a square having its sides equal to the greatest sides of the present Fields, the area of this, the largest 'square' in London, would be almost exactly equal to that of the pyramid's base or about 13^ acres. The front of Chelsea Hospital has almost the same length as a side of the pyramid's base, so also has the frontage of the British Museum, including the houses on either side to Charlotte Street and Montague Street. The average breadth of the Thames between Chelsea and London Bridge, or, in other words, the average span of the metropolitan bridges, is also not very different from the length of each side of the great pyramid's base. The length measures about 761 feet, or nearly 254 yards. Each side is in fact a furlong of 220 double cubits or Egyp- tian yards. The height of the pyramid is equal to seven-elevenths of the side of the base, or to 280 cubits, or about 484 feet. This is about 16 feet higher than the top of Strasburg Cathedral, 24 feet higher than St. Peter's at Rome, and is about 130 feet higher than our St. Paul's. These are all the dimensions of the pyramid's exterior I here propose to mention. Sir E. Beckett gives a number of others, some of considerable interest, but of course all de- rivable from the fact that the pyramid has a square base 440 164 FAMILIAR SCIENCE STUDIES. cubits in the side, and has a height of 280 cubits. I may notice, however, in passing, that I quite agree with him in thinking that the special mathematical relation which the pyramid builders intended to embody in the building was this, that the area of each of the four faces should be equal to a square having its sides equal to the height of the pyramid. Herodotus tells us that this was the condition which the builders adopted ; and this condition is fulfilled at least as closely as any of the other more or less fanciful relations which have been recognised by Taylor and his followers. But what special purpose had the architect in view, as he planned the addition of layer after layer of the pyramidal structure ? So far as the mere orienting of the faces of the pyramid was concerned, he had achieved his purpose so soon as he had obtained, by means of the inclined passage, the true direction of the north and south lines. But assuming that his purpose was to provide in some way for astronomical observation, a square base with sides facing the cardinal points would not be of much use. It would clearly give horizontal direction lines, north and south, east and west, north-east and south-west, and north-west and south-east. For if observers were set at the four corners, A ' B ' c ' D) as in fi S- 6 ' with suitable up- rights, where dots are shown at these corners, a line of sight from D'S upright to A'S would be directed towards the south, from the same upright to B'S would be directed towards the south- west, and from the same to c's would be directed towards the west Lines of sight from the other three uprights to each of the remaining ones would give the other directions named, or eight directions in all round the horizon. But such direction-lines are not very useful in astro- nomical observation, because the celestial bodies are not always or generally on the horizon. And no one who pays THE PYRAMIDS OF GHIZEH. 165 attention for any length of time, or with any degree of care, to the motions of the celestial bodies, will fail soon to recognise that east and west lines are of very little obser- vational use compared with north and south lines, whether taken horizontally or in a direction suitably elevated above the horizon. For whereas every star in the sky comes due south or north (unless it should pass exactly overhead) once in every circuit around the pole (without counting the sub- polar northings of those stars which never set), and at the same constant and regular intervals, the sun, moon, and planets also coming south at intervals only slightly varying (because of the motions of these bodies among the stars), the heavenly bodies do not come east and west at the same intervals. The sun does not come east or west at all, for instance, during the winter half of the year, while in the summer half he passes from due east to due west in a time which grows shorter and shorter as the length of the day in- creases. Without entering further into considerations which I have dealt with more fully in another place, it is manifest that any architect, proposing to erect an edifice for observing the heavenly bodies, would direct his attention specially to the meridian. He would require to observe bodies crossing different parts of the meridian. But he would recognise the fact that the southern half of the meridian was altogether more important than the northern ; for the sun and moon and all the planets cross the meridian towards the south. Again, those regions towards the south which are crossed by these bodies would be the most important of all. What the architect would do then would be this. He would so raise the building, layer by layer, as to leave a suitable narrow opening, directed north and south, and bearing on the part of the southern sky which the sun, moon, and planets traverse. Now, the grand gallery in the pyramid of Cheops fulfils precisely such a purpose as this. Before the upper part of the pyramid was added, the passage of the sun and moon and every one of the planets across the meridian, except 1 66 FAMILIAR SCIENCE STUDIES. perhaps Mercury (but I am not at all sure that Mercury need be excepted), could be observed through this remark- able slant gallery. Venus, of courge, could only be seen in the daytime when due south ; but we know that at her brightest she can be readily seen in the daytime when her place in the sky is known. And through a long narrow passage like the grand gallery of the pyramid of Cheops she could be seen when much nearer the sun's place in the sky. Of course, to observe the sun, moon, or a planet, the astro- nomer would only be so far down the tunnel as to see the planet crossing the top of the opening. If he went farther down he would lose the observation ; but the farther down he went without losing sight of the body, the more favour- able would be the conditions under which the observations would be made. Sometimes he could go to the very lowest part of the gallery. At midwinter, for instance, the sun could be observed from there, just crossing the top of the exceedingly small narrow slice of sky seen from that place. I am not, however, specially concerned here with the question of the manner in which astronomical observations would be made through the great ascending gallery of the great pyramid. That is a subject full of interest, but I have fully discussed it in the preceding essay. What I desire here specially to note is, that the gallery could only be used when the pyramid was incomplete. While as yet all the portion of the pyramid above the gallery was not erected, the heavenly bodies could be observed not only along the great gallery, but also from the level platform forming the upper surface of the pyramid in that stage of its construc- tion. But when the building began to be carried beyond that stage unless for a while a long strip in front of the gallery was left incomplete the chief use of the building for purposes of stellar observation must have come to an end. Not only have we no record that an open space was left in this way, and no trace in the building itself of any such peculiarity of construction, but it is tolerably manifest that no such space could have been safely left after the THE PYRAMIDS OF GHIZEH. 167 surrounding portions had been carried beyond a certain height. It is here that I find the strongest argument for the theory I have advanced respecting the purpose for which the pyramids were built. It is certain that, though these buildings were specially constructed for astronomical obser- vations of some sort, while the entire interior construction of the great pyramid adapted it specially for such a purpose, yet, only a short time after the great gallery and the other passages of this mighty structure had been completed, it was treated as no longer of any use or value for astronomical work. It was carried up beyond the platform where the priestly astronomers had made their observations, until the highest and smallest platform was added ; and then the casing stones were fitted on, which left the entire surface of the pyramid perfectly smooth and polished, not the minutest crack or crevice marring either the sloping sides, or the pavement which surrounded the pyramid's base. Now, I do not say that there is nothing surprising in what is known, and especially in the last-mentioned circum- stance, when the theory is admitted that the great pyramid was built by Suphis or Cheops in order that astronomical observations might be continued throughout his life, to de- termine his future, to ascertain what epochs were dangerous or propitious for him, and to note such unusual phenomena among the celestial bodies as seemed to bode him good or evil fortune. It does seem amazing, despite all we know of the fulness of faith reposed by men of old times in the fanciful doctrines of astrology, that any man, no matter how rich or powerful, should devote many years of his life, a large portion of his wealth, and the labours of many myriads of his subjects, to so chimerical a purpose. It is strange that a building erected for that purpose should not be capable of subserving a similar purpose for his successors on the throne of Egypt. Strange also that he should have been able to provide in some way for the completion of the building after his death, though that must have been a work 1 68 FAMILIAR SCIENCE STUDIES. of enormous labour, and very expensive, even though all the materials had been prepared during his own lifetime. But I do assert with considerable confidence that no other theory has been yet suggested (and almost every imaginable theory has been advocated) which gives the slight- est answer to these chief difficulties in the pyramid problem. The astrological theory, if accepted, gives indeed an answer which requires us to believe the kingly builder of the great pyramid, and, in less degree, those who with him or after him built the others, to have been utterly selfish, tyrannical, and superstitious or, in brief, utterly unwise. But unfortunately the study of human nature brings before us so many illustrations of the existence of such folly and superstition in as great or even greater degree, that we need not for such reasons reject the astrological theory. Of other theories it may be said that, while not one of them except the wild theory which attributes the great pyramid to divinely instructed architects, presents the builders more favourably, every one of these theories leaves the most striking features of the great pyramid entirely unexplained. Lastly, I would note that the pyramids when rightly viewed must be regarded, not as monuments which should excite our admiration, but as stupendous records of the length to which tyranny and selfishness, folly and superstition, lust of power and greed of wealth, will carry man. Regarded as works of skill, and as examples of what men may effect by combined and long-continued labour, they are indeed marvellous, and in a sense admirable. They will remain in all probability, and will be scarcely changed, when every other edifice at this day existing on the surface of the earth has either crumbled into dust or changed out of all know- ledge. The museums and libraries, the churches and cathe- drals, the observatories, the college buildings and other scholastic edifices of our time, are not for a moment to be compared with the great pyramid of Egypt in all that con- stitutes material importance, strength, or stability. But while the imperishable monuments of old Egypt are records of THE PYRAMIDS OF GHIZEH. 169 tyranny and selfishness, the less durable structures of our own age are, in the main, records of at least the desire to increase the knowledge, to advance the interests, and to ame- liorate the condition of the human race. No good whatever has resulted to man from all the labour, misery, and expense involved in raising those mighty structures which seem fitted to endure while the world itself shall last. They are and ever have been splendidly worthless. On the other hand, the less costly works of our own time, while their very construc- tion has involved good instead of misery to the lowlier classes, have increased the knowledge and the well-being of man- kind. The goodly seed of the earth, though perishable itself, germinates, fructifies, and bears other seed, which will in turn bring forth yet other and perchance even better fruits ; so the efforts of man to work good to his fellow man instead of evil, although they may lead to perishable material results, will yet germinate, and fructify, and bear seed, over an ever-widening field of time, even to untold generations. 170 FAMILIAR SCIENCE STUDIES. SUN-SPOTS AND FINANCIAL PANICS. I RECEIVE so many letters relating to the imagined troubles which the movements of the planets are to occasion during the next few years (chiefly through the intervention of the solar spots), that I think many may find interest in the most recent development of the sun-spot mania Professor Stanley Jevons's theory that there is a close and intimate connection between commercial crises and spots upon the sun. My object is not, I need hardly say, to advocate Jevons's theory. Nor do I propose merely to show how slight is the evidence on which the theory is based, and that, in some respects, it is even opposed to those views in whose support it was adduced. I write more with the view of dis- couraging that flow of unreasonable and altogether unscien- tific speculation with regard to sun-spots which has recently set in. About the year 1862, Professor Jevons prepared two statistical diagrams relating to monetary matters, the price of corn, &c. The study of these satisfied him that the com- mercial troubles of 1815, 1825, 1836-39, 1847, and 1857, ex- hibited a true but mysterious periodicity. There was no appearance of like periodicity, indeed, during the first fifteen years of the present century, when ' statistical numbers were thrown into confusion by the great wars, the suspension of specie payments, and the frequently extremely high prices of corn.' He admits, moreover, that the statistical diagram, so far as the eighteenth century is concerned, presents no appreciable trace of periodicity. SUN-SPOTS AND FINANCIAL PANICS. 171 In 1875, attracted by questions raised respecting solar influences, Professor Jevons discussed the data in Professor Thorold Rogers's ' Agriculture and Prices in England since 1259.' He then believed, he tells us somewhat naively, that ' he had discovered the solar period ' in the prices of corn and various agricultural commodities, and he accordingly read a paper to that effect at the British Association at Bristol. Subsequent inquiry, however, seemed to show that periods of three, five, seven, nine, or even thirteen years, would agree with Professor Rogers's data just as well as a period of eleven years ; in disgust at which result, Professor Jevons withdrew the paper from further publication. He still looks back, however, with some affection on that, his first essay towards ' finding the solar period' in terrestrial relations, and quotes now, with a certain complacency, a passage from the paper he had withdrawn in disgust from the proceedings of the British Association. ' Before concluding/ he says in this passage, ' I will throw out a surmise, which, though it is a mere surmise, seems worth making. It is now pretty generally allowed that the fluctuations of the money market, though often apparently due to exceptional and accidental events, such as wars, panics, and so forth, yet do exhibit a remarkable tendency to recur at intervals approximating to ten or eleven years. Thus, the principal commercial crises have happened in the years 1825, 1836-39, 1847, 1857, 1866, and I was almost adding 1879, so convinced do I feel that there will, within the next few years, be another great crisis. Now, if there should be, in or about the year 1879, a great collapse comparable with those of the years mentioned, there will have been five such occurrences in fifty-four years, giving almost exactly eleven years (10.8) as the average interval, which sufficiently approximates to n.i years, the supposed exact length of the sun-spot period, to warrant speculations as to their possible connection.' However, Professor Jevons, though he had done his best to follow the course laid down for such researches ' by those who are determined, above all things, that some terrestrial 172 FAMILIAR SCIENCE STUDIES. cycles shall be made to synchronise with the sun-spot cycle,' 1 had been thus far disappointed. 'I was embarrassed,' he says, ' by the fact that the commercial fluctuations could with difficulty be reconciled with a period of n.i years. If, indeed, we start from 1825 and add n.i years time after time, we get 1836.1, 1847.2, 1858.3, 1869.4, 1880.5, which shows a gradually increasing discrepancy from 1837, 1847, 1857, 1866, and now 1878, the true dates of the crises.' The true cycle-hunter, however, is seldom without an ex- planation of such discrepancies. ' I went so far,' he says, and again his naivete is charming, ' as to form the rather fanciful hypothesis that the commercial world might be a body so mentally constituted, as Mr. John Mill must hold, as to be capable of vibrating in a period of ten years, so that it would every now and then be thrown into oscillation by physical causes having a period of eleven years.' Un- fortunately for the scientific world, which could not have failed to profit greatly from the elucidation of so ingenious a theory, even though it had subsequently been found well to withdraw it, Professor Jevons became acquainted about this time with some inquiries by Mr. J. A. Broun, tending to show that the solar period is 10.45 years, not ir.i. This placed the matter in a very different light and removed all difficulties. ' Thus, if we take Mr. John Mill's " Synopsis of Commercial Panics in the Present Century," and rejecting 1866, as an instance of a premature panic' (this is very ingenious), 'count from 1815 to 1857, we find that four credit cycles occupy forty-two years, giving an average duration of 10.5 years, which is a remarkably close approxi- mation to Mr. Broun's solar period.' Encouraged by the pleasing aspect which the matter had 1 ' The tiling to hunt down, ' says one of these, ' is a cycle, and if that is not to be found in the temperate zones, then go to the frigid zones or to the torrid zone to look for it ; and if found, then above all things and in whatever manner ( !) lay hold of, study, and read it, and see what it means,' or make a meaning for it, if it has none, he should have added. SUN-SPOTS AND FINANCIAL PANICS. 173 now assumed, Professor Jevons determined to go further afield for evidence. ' It occurred to me at last/ he says, ' to look back into the previous century, where facts of a strongly confirmatory character at once presented them- selves. Not only was there a great panic in 1793, as Dr. Hyde Clarke remarked, but there were very distinct events of a similar nature in the years 1783, 1772-3, and 1763. About these dates there can be no question, for they may all be found clearly stated on pp. 627, 628, of the first volume of Mr. Macleod's unfinished " Dictionary of Political Economy." Mr. Macleod gives a concise, but I believe correct account of these events, and as he seems to enter- tain no theory of periodicity, his evidence is perfectly un- biassed.' It is true that neither Wolff's nor Broun's period can be strictly reconciled with the occurrence of four commercial crises, at intervals of exactly ten years ; for three times 1 1. 1 are 33.3, and three times 10.45 are 3 l -35> whereas the interval from 1763 to 1793 amounts only to 30. However we only have to regard the crisis of 1793 as a ' premature panic ' to remove this difficulty. Indeed with premature panics and delayed panics, overhasty sunspot crises and unduly retarded ones, we can get over even more serious difficulties. This ' beautiful coincidence,' as Professor Jevons called it, led him to look still farther backward, ' and to form the apparently wild notion that the great crisis, generally known as that of the South Sea Bubble, might not be an isolated and casual event, but only an early and remarkable manifes- tation of the commercial cycle.' The South Sea Bubble is usually assigned to the year 1720, and as that would be 43 years before 1763, we should have lof years, instead of 10^ years for the average interval, if three commercial crises occurred between 1720 and 1763. But this difficulty is merely superficial. ' It is perfectly well known to the his- torians of commerce,' says Professor Jevons, ' that the general collapse of trade, which profoundly affected all the more advanced European nations, especially the Dutch, 174 FAMILIAR SCIENCE STUDIES. French, and English, occurred in 1721. Now if we assume that there have been since 1721, up to 1857, thirteen com- mercial cycles, the average interval comes out 10.46 years. Or if we consider that we are in this very month (November, 1878), passing through a normal crisis, then the interval of 157 years, from 1721 to 1878, gives an average cycle of 10.466 years.' Before this could be accepted, however, three com- mercial panics had to be found to fill in the space between 1721 and 1763. Professor Jevons felt this keenly. He spent much time and labour during the summer of 1878, 'in a most tedious and discouraging search among the pam- phlets, magazines, and newspapers of the period, with a view to discover other decennial crises.' He seems to have done everything he could think of, short of advertising ' Wanted three crises, fitted to fill a crisisless gap in last century's commercial history ' but the results were not very satisfac- tory. ' I am free to confess/ he says, ' that in this search, I have been thoroughly biassed in favour of a theory, and that the evidence which I have so far found would have no weight if standing by itself. It is impossible, in this place, to state properly the facts which I possess I can only briefly mention what I hope to establish by future more thorough inquiry.' Even this, which has yet to be esta- blished, amounts to very little ; but that is the fault of the facts, not of Professor Jevons. In the first place it is remarkable, he thinks, that the South Sea Company, which failed in 1720-21, was founded in 1711, just ten years before, 'and that on the very page (312) of Mr. Fox Broun's " Romance of Trade," which men- tions this fact, the year 1701 also occurs in connection with speculation and stock-jobbing, as the promotion of companies was then called. The occurrence of a crisis in the years 1710-11-12, is indeed almost established by the list of bubble insurance companies formed in those years as col- lected by Mr. Cornelius Walford.' If the probability that a commercial crisis occurred in SUN-SPOTS AND FINANCIAL PANICS. 175 1710-12 (though the history of trade perversely omits to mention such a crisis,) is not considered sufficient, in com- pany even with the mention of 1701 as a year of stock -job- bing, to prove beyond all possibility of question, that com- mercial crises occurred in 1731, 1742, and 1752, let the hesitating student observe, that quite obviously ' about ten years after stock-jobbing had been crushed by the crisis of 1721, it reared its head aga.in.' It is remarked in the ' Gentleman's Magazine ' of 1 732 that ' stock -jobbing is grown almost epidemical. Fraud, corruption and iniquity in great companies as much require speedy and effectual remedies now as in 1720. The scarcity of money and stagnation of trade in all the distant parts of England, is a proof that too much of our current coin is got into the hands of a few persons.' Before 1734 matters had become still worse, for Mr. Walford says that ' gambling in stocks and funds had broken out with considerable fervour again during the few years preceding 1734. It was the first symptom of recovery from the events of 1720.' In 1734, accordingly, we find that an act was passed to check stock -jobbing. It might still seem, however, to some of those doubting spirits, whom no arguments can satisfy, that the occurrence in 1734, of ' the first symptoms of recovery from the events of 1720,' is not in itself proof positive of the occurence of a commercial crisis in 1732. They might, in their perversity, argue that the next commercial crisis, after that of 1720-21, would presumably have followed the recovery, 1734, from the effects of the South Sea collapse. To satisfy* these un- believers, Professor Jevons points out that, in 1732, a society called the 'Charitable Corporation for Relief of the In- dustrious Poor ' became bankrupt. Many people were ruined by the unexpected deficit thus discovered, and Parliament and the public were asked to assist the sufferers. The failure of a charitable corporation in 1732 is not per- haps absolutely demonstrative of the occurrence of a com- mercial crisis in 1732 ; but when considered in connection with the founding of the South Sea Company, in 1711, the 176 I- A MI LIAR SCIENCE STUDIES. occurrence of stock -jobbing in 1701, the revival in 1734 from the events of 1720-21, and especially with the circum- stance that Professor Jevons's theory absolutely requires a crisis in 1 732, it must in charity be accepted. It would indeed be exceedingly unkind to reject the evidence thus offered for a commercial panic in 1732, because none can be found to show that between 1732 and 1763 'anything approach- ing to a mania or crisis,' took place. ' My learned and obliging correspondents, at Amsterdam and Leyden,' says Professor Jevons, { disclaim any knowledge of such events in the trade of Holland at that time, and my own diagram, showing the monthly bankruptcies throughout the interval, displays a flatness of a thoroughly discouraging character.' This would dishearten perhaps any one but a believer in sun-spot influences. But the rule laid down by the high- priest of their order, to hold on resolutely to any cycle ' found or imagined, ' above all things and in luhatciier man- ner, to lay hold of such a cycle, despite all difficulties and every discouragement, is one which they follow with a zeal worthy of a more scientific and logical system of procedure. Though Professor Jevons could find no evidence whatever of. a crisis between the well-imagined one in 1732 and the real crisis in 1763, inquiry leads him to believe, he says, ' that yet there were remarkable variations in the activity of trade and the prices of some staple commodities, such as wool and tin, sufficient to connect the earlier with the later periods.' The evidence is not complete, and as it does not quite agree with the sun-spot theory, it is ' probably mis- leading.' Any one who can point out to Professor Jevons a series of prices of metals, or other commodities not merely agricultural, before 1782, will, he announces, confer a very great obligation upon him by doing so. However, though the theory absolutely requires a crisis in 1742 and another in 1752, or thereabouts, let us defer for the present any minuter inquiry on this point. ' I permit myself to assume,' says Professor Jevons, ' that there were, about the years 1742 and 1752, fluctuations of trade which SUN-SPOTS AND FINANCIAL PANICS. 177 connect the undoubted decennial series of 1711, 1721, and 1 732, with that commencing again in the most unquestionable manner in 1763.' There is something very pleasing in this. Our hero permits himself to assume that the strongest pos- sible evidence of steady commercial relations between 1732 and 1763 may be set on one side. He makes a series of un- doubted crises out of three dates : of these the first (1711) marking the time when one of the greatest commercial swin- dles of the last two centuries was started, indicates a season of undue confidence, instead of undue depression ; the second (1721) is not the true date of the event with which it is connected; and the third (1732) was not marked by any commercial event in the remotest degree resembling a general panic or crisis. Having achieved this noteworthy deed of derring-do running atilt against, and for the time being overthrowing, all the rules of logic (as if in a tourney a knight should overthrow the marshals, instead of his armed opponents) Professor Jevons is able triumphantly to declare that the whole series of decennial crises may be stated as follows: (1701?), 1711, 1721, 1731-32, (1742? 1752?), 1763, 1772-3, 1783, 1793, (1804-5), 1815, 1825, 1836-39, (1837, in the United States), 1847, ^57, 1866, 1878. A series of this sort, we are told, is not like a chain, as weak as its weakest part ; on the contrary, the strong parts add strength to the weak parts. In spite, therefore, of the doubtful existence of some of the crises, as marked in the list, ' / can entertain no doubt whatever ' (the italics are most emphatically mine), ' I can entertain no doubt whatever that the principal commercial crises do fall into a series having the average period of about 10.466 years. Moreover, the almost perfect coincidence of this period with Broun's esti- mate of the sun-spot period (10.45) * s by itself strong evi- dence that the phenomena are causally connected.' There is evidence of splendid courage in these statements ;*it is in this way that, according to the Scotch proverb, a man either ' makes a spoon or spoils a horn.' Before proceeding to consider the evidence by which the 178 FAMILIAR SCIENCE STUDIES. series of commercial crises is to be connected, or otherwise, with the series of sun-spot changes, let it be permitted to us to separate the actually recorded crises from those which Professor Jevons has either invented (as 1701, 1711, and 1732), or assumed (as 1742, 1752, and 1804-5). There remain the dates 1721, 1763, 1772-3, 1783, 1793, 1815, 1825, 1836-39, 1847, 1857, 1866 and 1878. The corresponding intervals (taking, when an interval instead of a date is given, the date midway between the two named), are as follows : 42 years, 9^ years, 10^ years, 10 years, 22 years, 10 years, \2.\ years, 9^ years, 10 years, 9 years, and 12 years. The evidence for the decennial period is not demonstrative, and the logical condition of the mind which, in presence of this evidence, ' can entertain no doubt whatever ' that the true average period is 10.466 years which, be it noted, is a period given to the thousandth part of a year, or to about 8| hours must be enviable to those who possess a much smaller capacity for conviction that is, a much greater capacity for doubt. But it may happen, perchance, that the irregularity of the recurrence of crises affords evidence in favour of a connec- tion between commercial panics and the sun-spot period. It is well known that the epochs when the sun is most spotted do not occur at regular intervals, either of n.i years, 10.45 ye ars , r an y other period. If the irregularities of the sun-spot period should be reflected, so to speak, in the irregularities of the panic period, the evidence would be even more satisfactory than if both periods were quite regular and they synchronised together. For in the latter case there would be only one coincidence, a coincidence which, though striking, might yet be due to chance ; in the other there would be many coincidences, the co-existence of which could not reasonably be regarded as merely for- tuitous. Only, at the outset it may be as well to determine before- hand what our conclusions ought to be, if no such resem- blance should be recognised between the irregularities of the two periods. We must not, perhaps, expect too close a SUN-SPOTS AND FINANCIAL PANICS. 179 resemblance. We may very well believe that while the nor- mal relationship between two connected sets of phenomena might result either in absolutely simultaneous oscillations, or, at least, in oscillations of perfectly equal period (so that whatever discrepancy might exist between the epochs of the respective maxima or minima should be constantly pre- served), yet that a multitude of more or less extraneous disturbing influences might prevent either form of synchro- nism from being actually observed. For instance, if we supposed that the absence of sun-spots is the cause of commercial depression, we might imagine that, at the time of fewest sun-spots, a commercial crisis would occur unless extraneous causes delayed it ; or we might imagine that, as a regular rule, the crisis would follow the time of fewest sun-spots by a given interval, as a year or two years ; yet we might very well understand that occasionally a crisis might be hastened by a few months, or even a year, or might be in equal degree delayed. Still there are limits to the amount of disturbance which we could thus account for without being forced to abandon altogether the theory that sun-spots influence trade, despite the antecedent proba- bility (which some consider so great) of a relationship of this kind. For instance, if we found commercial crises occurring in a year of maximum disturbance at one time, while at another they occurred in a year of minimum dis- turbance, at another, midway between a maximum and the next following minimum, at yet another midway between a minimum and the next following maximum, we should not feel absolutely forced to accept the theory that sun-spots somehow govern trade relations. Nay, I think a logically- minded person would feel that Jn the presence of such dis- crepancies nothing could establish the theory otherwise so extremely probable of the influence of sunspots on trade. Professor Jevons has not definitely indicated his own opin ions on this point. Perhaps, if he had, we should have found that he would allow wider latitude to the discrepancies which may exist, than one less attached to the sun-spot theory of trade would consider permissible. We have seen i8o FAMILIAR SCIENCE STUDIES. how readily he has been satisfied respecting crises which had to be either invented or assumed. 1 Perhaps a little further evidence on this point may be useful, as showing the extent to which that bias in favour of his theory, which he has so frankly admitted, seems really to have influenced him. We have seen that if crises fail to occur when his theory requires them, he readily constructs or assumes crises to fit into the vacant places. He is equally ready to deal with what others would regard as the equally fatal difficulty, that crises take place when, according to the decennial theory (a wider theory than the solar one, be it noticed), they should not have occurred. ' There is nothing in this theory,' he says, ' inconsistent with the fact that crises and panics arise from other than meteorological causes. There was a great politi- cal crisis in 1798, a great commercial collapse in 1810-11, (which will not fall into the decennial series) ; there was a stock-exchange panic in 1859 ; and the great American collapse of 1873-75. There have also been several minor disturbances in the money market, such as those of Febru- ary, 1 86 1, May and September, 1864, August, 1870, Nov- ember, 1873 ; but they are probably due to exceptional and disconnected reasons. Moreover, they have seldom, if 1 Professor Roscoe, in a lecture on ' Sun-spots and Commercial Crises ' (delivered, strangely enough, as one of a series of science lec- tures for the people), has raised Professor Jevons's assumed crisis a grade higher in the scale of probability. The dates, 1742, 1752, and 1804-5, when a crisis ought to have occurred, but did not, were given by Professor Roscoe as dates of doubtful crises, by which his audience understood that crises but of comparatively small extent occurred at those dates. Certainly the audience did not understand that, after long and careful search for the crises which should theoretically then have taken place, Professor Jevons had-failed to find any trace whatever of their occurrence. By the way, the audience at Manchester would not seem to have been very profoundly impressed by a conviction of the antecedent probability of the theory advocated by the lecturer. At first, Professor Roscoe's statement of the theory was received as a joke. 'Laughter,' 'laughter,' and ' renewed laughter, ' followed the enuncia- tion of the theory. Only when the evidence, carefully freed from what- ever might suggest doubt or difficulty, was brought forward, did the audience gradually become convinced that the lecturer was in earnest. SUN-SPOTS AND FINANCIAL PANICS. 181 ever, the intensity, profundity and wide extension of the true decennial crises.' In other words, if recognisable crises fail to occur when the decennial period requires them, yet we may assume that, at the proper time, some trade disturbances have taken place, only on so small a scale as to escape notice ; but if trade disturbances occur which even attract notice, at times not reconcilable with the decennial theory, then we may overlook them, because a true decennial crisis is intense, profound, and widely extended. It is a case of ' heads I win, tails you lose ' with the supporters of the decennial theory. Though even with this free-and-easy method of reasoning, the American crisis in 1873-75 might seem rather awkward to deal with. Americans, at any rate, are not very likely to accept the doctrine that that crisis was not intense, profound, and widely extended. I may remark in passing that, in jestingly advancing the theory which Professor Jevons has since adopted, I dealt also jestingly with this very difficulty in a way which seems to be at least as satisfactory as Professor Jevons's method of treating it. ' The last great monetary panic,' I wrote in 1877, 'occurred in 1866, at a time of minimum solar macu- lation. Have we here a decisive proof that the sun rules the money market, the bank rate of discount rising to a maximum as the sun-spots sink to a minimum, and vice versa ? The idea is strengthened,' I pointed out, ' by the fact that the American panic in 1873 occurred when spots were very numerous, and its effects have steadily subsided as the spots have diminished in number ; for this shows that the sun rules the money-market in America on a prin- ciple diametrically opposite to that on which he (manifestly) rules the money-market in England, precisely as the spots cause drought in Calcutta and plenteous rain-fall at Madras, wet south-westers and dry south-easters at Oxford, and wet south-easters and dry south-westers at St. Petersburg. Surely it would be unreasonable to refuse to recognise the weight of evidence which thus tells on both sides at once.' This was nonsense, and was meant to be taken as nonsense ; but it strikingly resembles some arguments which have been 182 FAMILIAR SCIENCE STUDIES urged, within the last hundred years too, respecting solar influences. Let us turn, however, to the actual records of sun-spots, and compare them with Professor Jevons's list of commercial crises. We have no better collection of evidence respecting sun- spots than that formed by Professor Wolff. Broun and Lament have called in question some of Wolff's conclu- sions, as will presently be more particularly noticed. But, in the main, Wolff's evidence remains unshaken. Very few astronomers we may even say no astronomers of repute have adopted the adverse views which have been thus expressed, and certainly none, even among those who have admitted the possible validity of such views on points of detail, entertain the least doubt respecting the general validity of the conclusions arrived at by Wolff. After carefully examining all the evidence afforded by observatory records, the note-books of private astronomers, and so forth, Wolff has deduced the following series of dates for the maxima and minima of solar disturbances since the year 1700 : Intervals in years. Dates of Maxima. Possible error in years. Intervals in years. Dates of Possi V lc Minima. : ycars I2.S 1705.0 2.0 I I.O 1712 o I.O IO.O I7I7-5 I.O IO.O 1723.0 I.O II. I727-5 I.O 12.0 1733-0 i-5 n-5 173^-5 i-5 10.7 1745-0 I.O ii-5 1750.0 I.O 10.8 1755-7 0.5 8-5 1761.5 0-5 9-3 1766.5 0.5 9-5 I77O.O I 0.5 9-o 1775-8 o-5 9.0 1779-5 -5 13-7 I 7 84.8 0-5 iS-5 1788.5 0.5 12. 1798.5 0-5 12.8 1804.0 o. i 12.7 1810.5 0-5 12.7 1816.8 o-5 10.6 1823.2 0.2 7-7 1829.5 0.5 10.2 1833.8 0.2 11.4 1837.2 o-5 12.2 1844.0 0.2 ii. 6 1848.6 0.5 10.9 ; 1856.2 O.2 10.6 1860.2 O 2 11.4 1867.1 O.I 1870.8 1878.5 SUN-SPOTS AND FINANCIAL PANICS. 183 The dates below the line are not in Wolff's list. It would be difficult, I conceive, for the most enthusi- astic believer in sun-spot influences to recognise any con- nection between the crises and the variations of solar macula- tion, whether Professor Jevons's list or the natural crises be considered. To quote from an article in the London ' Times,' which has been attributed to myself (correctly) : Taking 5} years as the average interval between the maximum and minimum sun-spot frequency, we should like to find every crisis occur- ring within a year or so on either side of the minimum ; though we should prefer, perhaps, to find the crisis always following the time of fewest sun-spots, as this would more directly show the depressing effect of a spotless sun. No crisis ought to occur within a year or so of maximum solar disturbance ; for that, it should seem, would be fatal to the suggested theory. Taking the commercial crises in order, and comparing them with the (approximately) known epochs of maximum and minimum spot frequency, we obtain the following results (we itali- cise numbers or results unfavourable to the theory) : The doubtful [I ought to have written 'assumed'] crisis of 1701 followed a spot minimum by three years ; the crisis ' (imagined) ' of 1711 preceded a minimum by one year; that of 1721 preceded a minimum by two years; 1731-32 ' (imagined crisis) ' preceded a minimum by one year ; 1742 ' (no crisis known) ' preceded a minimum by three years ; 1752 (no crisis) followed a maximum by two years ; 1763 followed a maximum by a year and a half; I77 2 ~73 came midivay between a maximum and a minimum; 1783 preceded a minimum by nearly two years ; 1793 came nearly mid- way between a maximum and a minimum ; 1804-05 ' (no known crisis) ' ' coincided with a maximum ; 1815 preceded a maximum by two years ; 1825 followed a minimum by two years ; 1836-39 inchided the year 1837, of maximum solar activity (that being the year, also, when a commercial panic occurred in the United States;') 1857 preceded a minimum by one year [this case was, by some inadvertence of mine, omitted from the ' Times ' article] ; 1 866 preceded a minimum by a year ; and 1878 follows a minimum by a year. Four favourable cases [it should have been five] out of seventeen [it should have been eighteen] can hardly be considered convincing. If we include cases lying within two years of a minimum, the favourable cases mount up to seven (eight) leaving ten unfavourable cases. I might have added, at this pointj that if a number of dates were scattered absolutely at random over the interval 1 84 FAMILIAR SCIENCE STUDIES. of 1701-1880, we should expect to find some such propor- tion between dates falling within two years on either side of a minimum and those not so falling. It must be remembered, I added in the 'Times' article, that a single decidedly unfavourable case, as in 1815 and 1837, 'does more to disprove such a theory than twenty favourable cases would do towards establishing it.' To the ' Times ' article Professor Jevons replied in a letter, which scarcely seemed to require an answer. At any rate, it left entirely undefended the weakest part of his theory. The agreement between the average period for commercial crises and Broun's estimate of the average sun-spot period was insisted upon afresh ; but the circum- stance that crises have occurred at every phase of the sun- spot wave at the maximum, at the minimum, soon after either of these phases, just before either and midway between maximum and minimum, both when spots are increasing and when they are diminishing in number was in no way accounted for. General doubts were thrown, indeed, on Wolff's accuracy ; but no special error was in- dicated in his interpretation of the evidence he had col- lected, and still less was any definite objection taken to Wolff's spot curve, regarded as a whole. Soon after, however in the ' Athenaeum ' Professor Jevons advanced a more definite defence of his theory. He first argued in favour of Broun's average period of 10.45 ye ars > and then commented unfavourably on some definite dates in Wolffs series. By the elaborate comparison of magnetic, auroral, and sun-spot data, he said, ' Mr. Broun appears to show con- clusively that the solar period is not n.i years, but about 10.45, this last estimate confirming the earlier determination of Dr. Lament.' It should be mentioned here that the magnetic and auroral data cannot be regarded as of them- selves proving anything respecting the sun-spot period ; they are as invalid in this respect as some of the evidence which Hansteen and others have derived from terrestrial SUN-SPOTS AND FINANCIAL PANICS. 185 relations respecting the solar rotation. The real fact is that, having shown clearly enough that the average magnetic and auroral period has (at any rate during the last century) been 10.45 years, Broun has endeavoured to invalidate the evidence obtained by Wolff for a sun-spot period of n.i years, simply because, if such a period is admitted, the theory of synchronism between magnetic and solar disturbances must of necessity be rejected. For this purpose, Broun has endeavoured to show that Wolff has overlooked a small maximum of sun-spots in 1797. The table given above shows very clearly that, if an extra maximum is to be thrown in anywhere, it must be between the maxima of 1788.5 and 1804.0, the interval between which is 15^ years. Broun has certainly not succeeded in demonstrating that 1797 was a year of many spots, nor could a small maximum then occurring be regarded as affecting the sun-spot curve more than the two small maxima which can be recognised in Wolff's picture of the sun-spot curve at about the years 1793 and 1795. Professor Jevons, however, complacently adopts, as proved, what Mr. Broun has surmised with very little probability. ' The fact is,' he says, ' that Dr. Wolff overlooked a small maximum in 1797, and was thus led to introduce into his curve an interval of seventeen years' (15^ only), ' an interval quite unexampled in any other part of the known solar history.' This again is incorrect : there was pre- cisely such an interval between the maxima of 1639.5 and 1655.0 as between those of 1788.5 and 1804.0; while the maximum of 1655.0 was followed by an interval of twenty years before another maximum occurred. We have on this point the definite information of Cassini, who, writing in 1671, when spots were beginning to re-appear, said : ' It is now nearly twenty years since astronomers have seen any con- siderable spots on the sun.' 'Mr. Broun shows, moreover,' proceeds Professor Jevons, 'that the n.i period fails to agree with all the earlier portions of Dr. Wolff's own data, which yield a period varying between 10.21 and 10.75 at tne utmost. This must relate to the earlier portion of what 1 86 FAMILIAR SCIENCE STUDIES. Wolff calls the modern series, viz., from 1750 onwards. It would be just as much or as little to the purpose to reply that the six intervals from the first maximum of the present century, 1804.0, to the last, which cannot be set earlier than 1870.6, have an average length of exactly 11.1 years. It is admitted that five or six periods do not afford sufficient evidence to determine the average, and for my own part, I may as well admit that I doubt the stability of the sun- spot period altogether, believing that in one century it may amount to fifteen or twenty years, and in another to seven or eight. But at least the observations of the present century and the mean period of n.i years resulting from them are open to no sort of question, whereas the very arguments on which Professor Jevons and Mr. Broun insist in opposing Wolff's conclusions would (if admitted) shake all faith in the evidence he adduces from Wolff's earlier dates of maxima and minima. The next point insisted on by Professor Jevons seems still less to the purpose, except as bearing on Wolff's general accuracy. ' Almost more serious,' he says, ' as regards the credibility of Dr. Wolff's results is the fact that Mr. Broun gives good reasons for believing that the year 1776 was a year of maximum sun-spots, whereas Dr. Wolff sets that very year down as one of minimum sun-spots.' The following are Broun's own words : ' There are no means of testing the earlier epochs of Dr. Wolff ; but no long period given by him will be satisfied by them. If I have already shown good grounds for substituting a maximum in 1776 for Dr. Wolff's minimum, a similar change in some of the epochs of the preceding century and a half may be quite possible.' ' Now, a highly scientific writer in the " Times," ' proceeds Professor Jevons, ' has condemned the theory of decennial crises, because the dates assigned will not agree with those of maximum and minimum sun-spots, taken, no doubt, accord- ing to Dr. Wolff's estimates ; and an eminent French statist has rejected the theory on the same ground. I think I am entitled, therefore, to point to the doubts which Mr. Broun's SUN-SPOTS AND FINANCIAL PANICS. 187 careful inquiries throw upon the accuracy of Dr. Wolff's relative numbers.' Now, a study of the curve of sun-spots will show how little Dr. Wolff's accuracy is, in reality, impugned by Mr. Broun's attack. We recognise in the curve, which, be it remembered, is Wolff's, a double minimum in the space between the year-ordinates for 1771 and 1781. One corre- sponds to the year 1773, the other to the last quarter of the year 1775. As the latter appeared from the evidence ex- amined by Wolff to be a more marked minimum, the former he regards as the true minimum for that particular wave of spots. But no one who knows anything about the varying aspects of the sun's disc during the two or three years which include the minimum, will wonder if the study of records, necessarily incomplete (for until Schwabe's time no one thought of keeping the sun constantly under survey), should have left the time of the actual minimum rather doubtful in one or two cases. The wonder is that Wolff should have found sufficient evidence to determine the true minimum in so many cases. This of itself would suffice to show how laborious must have been his researches. In the particular case about which Mr. Broun raises his question, it can be seen from Wolff's curve of spots that after an apparent mini- mum in 1773, spots began to appear, then grow fewer in number, till they reached a lower minimum in 1775, neither of these minima, however, being such as to correspond to an absolute spotlessness (which is represented by the level of the lowest minima in Wolff's curve). Then they increased rapidly in number, being greater in number in 1777 than they had been at any of the three preceding maxima. That in 1776, when the spots had already become very numerous, there should be records from which Mr. Broun could infer the existence of an actual maximum, is not at all surprising, though no astronomer accepts the inference ; nor if any did, would the inference at all carry with it the weight which Mr. Broun and Professor Jevons seem to recognise in it. Again, it is absolutely certain that there was a maximum i88 FAMILIAR SCIENCE STUDIES. in 1779; so that the supposed maximum of 1776 would involve one more wave, which, with the new wave intro- duced between 1790 and 1800, would give seventeen com- plete waves between the maxima of 1705 and 1870, an in- terval of less than one hundred and sixty-five years. This would make the average length of the sun-spot period 9.7 years, which would not at all suit the views of Mr. Broun and M. Lament. In passing, I may remark that in the article in the ' Times ' (I am obliged to identify myself with Professor Jevons's ' highly scientific writer,' simply because I wrote the article in question) I did not condemn the theory of commer- cial crises ; I expressed no opinion on that theory. What I indicated was simply that no possible connection can exist between that theory and the theory of sun-spots. As a matter of fact, I do not believe in the decennial theory of crises, though I perceive that in quite a number of cases commerce has oscillated through depression, revival and excitement to the next depression, in about that time. Nor again, do I believe in the sun-spot theory, though I perceive that during the last century or two the average sun-spot period has been about what Dr. Wolff indicates. But I have not attacked, and certainly I have not condemned, either of these theories. What I do insist upon very strongly, however, is, that the oscillations of commercial credit and the variations of the sun's condition as to maculation have, since the beginning of the last century, shown no approach to agreement. ' I will even go a step further/ adds Professor Jevons, ' and assert that in a scientific point of view it is a question- able proceeding to dress up a long series of relative numbers purporting to express the number of sun-spots occurring during the last century, with the precision of one place of decimals. As Mr. Broun had pointed out, there were no regular series of observations then, and results deduced from the occasional observations of different astronomers cannot be reduced into one consecutive series without a large exercise of discretion. As Mr. Broun has pointed out, Dr. SUN-SPOTS AND FINANCIAL PANICS. 189 Lament has criticised some of the epochs which Dr. Wolff considers certain (sicher\ and has shown that they depend on few observations. He remarks that old observers directed their attention chiefly to large sun-spots, so that Flaugergues (one of the principal observers during the period in question), saw the sun frequently without spots, when many were seen by other observers. The true scien- tific procedure would have been that which Professor Loomis has pursued in regard to auroras, namely, to place in a table all the reasonable observations, carefully dis- tinguishing those by different observers, so that there should be the least possible admixture of Dr. Wolff's own personal equations.' I have quoted this passage in full first, be- cause it presents the opinions of those adverse to Professor Wolff in this matter ; secondly, because the remarks about the difficulties of the subject (difficulties, that is, with which Professor Wolff has had to contend, and with which he has contended energetically and skilfully) are in the main just ; but thirdly and chiefly because it affords sound criterions by which to test Professor Jevons's method of procedure. If we should eschew one place of decimals in dealing with the results of observations counted by hundreds, what are we to think of three places of decimals deduced from a few dozen records of commercial matters ? If a sun-spot period derived from determinations of maxima and minima, every one of which is based on real observation, is untrustworthy, what opinion are we to form of a trade period based on crises of which five, or nearly a third of the whole number, are either imagined or assumed ? If, in fine, Dr. Wolff's method is unscientific, what name shall we find for that by which having derived a decennial period from admittedly unsatis- factory evidence, and having rejected the sun-spot period accepted by astronomers for one carefully concocted to fit another theory, Professor Jevons insists on the agreement of this fictitious crisis period and this incorrect sun-spot period, Avithout attempting to show that the admitted varia- tions of one agree with the admitted variations of the other? igo FAMILIAR SCIENCE STUDIES. For, after all, the strongest evidence against the theory that commercial crises depend on sun-spots, is given by those crises and sun-spot waves about which there is no sort of doubt or question the crises on the one hand, and the maxima and minima of sun-spots on the other, recorded during the present century. The study of the second half of the table given above will satisfy any unprejudiced person that this is the case ; from the crisis of 1804-5 (which never took place, but must be assumed to have taken place, to make up the series for the decennial theory of crises), to the crises of 1866 and 1878, we have crises occurring in every part of a sun-spot wave on the crest, on the valley, on the ascending slope, and on the descending slope. No theory of association can hold out against such obvious evidence of the absolute independence of the two orders of events. 1 1 The matter has been well summed up by a correspondent of the 'Athena-urn.' ' Professor Jevons,' he says, 'seems to attach great weight to the length of the average sun-spot period ; but if the average length of the period between commercial crises during a couple of cen- turies were shown to be identical with, or to differ but slightly from, the average period of sun-spots, this would be but a small step towards proving association between the two phenomena. The separate periods of minima must be shown to correspond with speculative crises, and the curve also must be proved to be of the same character. Professor Jevons does not appear to be aware that Dr. Wolff has in the forty- third volume of the ' ' Memoirs of the Astronomical Society, " given a list of the manuscripts and printed authorities from which he derives his data. Similar but fuller information is supplied by Dr. Wolff in the pages of his " Astronomische Mittheilungen." Dr. Wolff does not pretend to equal accuracy for all the periods, but there can be little doubt with regard to the sun-spot periods which have occurred during this century, and according to Professor Jevons, there seem to be serious discrepancies between these and the periods of commercial de- pression.' 191 COLD AND WET. DAY after day throughout May, June, and July, 1879, the same monotonous record continued 'The mean temperature has been considerably below the average.' Taking monthly means, we have to go back as far as October, 1878, for a month which was as warm as the average of former years. The cold of the winter months, though of course far more bitter, attracted less attention we may even say excited less apprehension than the cold which prevailed through May, June, and July. ' Accompanied by an unusually, though not quite unprecedentedly, heavy rainfall, the average rainfall for the whole year having been exceeded before the end of July, the low temperature, which actually has been unprecedented since trustworthy records of such matters have been kept, excited a feeling of anxiety, if not of alarm. Many are in- quiring whether some change may not have occurred by which the climate itself of this country, and, indeed, of the whole of Europe, has been modified. Perhaps the favourite theory in this direction is that the Gulf Stream has changed its course. But others take a still more melancholy view of matters, imagining that not Europe alone, but the whole earth, has experienced some dismal change. Either the sun has ceased to pour the due amount of heat upon the earth or the planets have combined to destroy our comfort, or else the whole of the solar system, in the course of its well known motion towards the constellation Hercules, has passed into some region where cosmical cold prevails, and suffers accordingly. It happens, unfortunately, that the 192 FAMILIAR SCIENCE STUDIES. dismal weather we have lately had has appeared to corre- spond in some degree with a series of gloomy vaticinations respecting the state of the earth during the years 1880-1885, as though our present troubles were ' the beginning of the end.' We learned from the Astronomer Royal for Scotland that in the building which he regards as a sort of stone Bible the 'Second Coming' is announced for the year 1882, with several prior years of discomfort, indicated by the ' im- pending south wall' of the great ascending gallery. The apocryphal prophecies of Mother Shipton indicate the year ' eighteen hundred and eighty-one/ as that in which, regard- less of rhyme, she considered that ' this our world to an end must come ; ' and as it happened that among the signs of the approaching end we were to have the seasons so con- founded as only to be known by the trees (a state of things which has certainly prevailed of late, when but for the fresh green foliage we might have judged from appearances that we were passing through a late autumn), many begin to think that, after all, there may be something in the old lady's predictions. But far more effective than any such prophecies, because less readily to be understood, have been the warnings of some American astrologer, who has announced that between 1880 and 1885 the perihelia of the four giant planets Jupiter, Saturn, Uranus, and Neptune would coincide (so the statement has reached us, it is not our fault if as so stated it should appear, as it does, sheer non- sense to the astronomer), wherefore obviously all the inhabi- tants of earth must during that time be exposed to the most grievous calamities, of which the bad weather we have ex- perienced affords merely a slight foretaste. And although these ideas are too absurd to be worth serious refutation, they find much wider acceptance than those imagine who suppose that in these days scientific facts are generally known, even though they may not be very generally under- stood. In speaking, indeed, of such ideas as absurd we are obliged to include the teachings of one who is deservedly regarded as a man of science ; albeit the exact measurements COLD AND WET. 193. and observations by which Professor Smyth lias determined the proportions of the Great Pyramid, must be carefully distinguished from the wild fancies which have led him to believe that the future of the world was prefigured in stone in that building 4,050 years ago. It may be well to consider how far the weather we have recently experienced can be regarded as abnormal (unusual it certainly has been), that those who take a rational view of such matters may form an opinion as to the prospect of approaching change, while the fanciful and superstitious may possibly find reason for believing that, after all, the beginning of the end may not yet have commenced. In the first place, we know from the imperfect records of olden times that long periods of cold and rainy weather have from time to time been experienced in this country and in Europe generally during past centuries. It is interesting to notice that the long-continued cold of the years 1593 and 1594 led many to form views as gloomy respecting the future as those which many ill-informed persons recently entertained. In the middle summer of the latter of those years Shakespeare wrote his Midsummer Nighfs Dream. He describes, in Titania's rebuke of Oberon, the bitter weather which had then prevailed for months in England : The winds, piping to us in vain, As in revenge, have suck'd up from the sea Contagious fogs ; which, falling in the land, Have every pelting river made so proud, That they have overborne their continents ; The ox hath therefore stretch'd his yoke in vain, The ploughman lost his sweat ; and the green corn Hath rotted ere his youth attain'd a beard ; The fold stands empty in the drowned field, And crows are fatted with the murrain flock ; The nine-men's morris is fill'd up with mud ; And the quaint mazes in the wanton green, For lack of tread are undistinguishable ; (which, substituting the agricultural show and our cricket o 194 FAMILIAR SCIENCE STUDIES. fields for nine-men's morris and the wanton green, accords closely enough with our recent experience) And through this distemperature we see The seasons alter ; hoary-headed frosts Fall in the fresh lap of the crimson rose ; And on old Hyerns' chin, and icy crown, An odorous chaplet of sweet summer buds Is, as in mockery, set ; the spring, the summer, The childing autumn, angry winter, change Their wonted liveries ; and the 'mazed world, By their increase, now knmvs not which is which, Nor is the interpretation of these troubles thereon advanced much wilder than are some of the theories now gravely urged and discussed. 'x'Vnd this same progeny of evil,' quoth Titania, Comes From our debate, from our dissension ; We are their parents and original. The fairies have quite as much to do with our present weather-troubles as the perihelia of Jupiter, Saturn, Uranus, and Neptune. But we have more exact evidence than poetical descrip tions such as these with which to compare our recent expe- rience. For 115 years we have a series of records of monthly mean temperatures in North Britain, and though it would not be safe to infer from such a series that throughout the whole of Great Britain the temperature had been below or above the average when it was below or above respec- tively on the shores of the Moray Firth and Firth of Forth, yet it may safely enough be assumed that if we had records as complete for any other spot in Great Britain, we should find similarly long periods of low or high temperature. From the records in question the following table has been formed, in which all periods of low temperature, lasting not less than five months, the mean temperature being COLD AND WET. 195 more than three degrees below the average, have been in- cluded : Date of Cold. Duration in months. Under mean temperature of the months. February-November, 1782 . January-August, 1799 10 7 =1.1 October-March, 1799-1800 6 -3-3 November- April, 1807-8 , 6 -3-5 March-August, 1812 . 6 -3-4 October-March, 1813-14 . 6 -3-6 November- August, 1815-16 10 -3-5 January- May, 1838 , , 5 -4.2 January-May, 1855 . , 5 -3-5 December- April, 1859-60 . 5 -3-o It is noteworthy that during the 18 years preceding the cold interval of 1782, the most intense and, with one excep- tion, the most protracted of the above series, there had been no instance of a temperature more than three degrees below the average and lasting so long as five months. Then came a period of 16 years without such a cold interval. So that the occurrence of long protracted and intense cold does not necessarily render it likely that such falls of temperature will for a while thereafter recur at short intervals. In the 1 6 years 1800-1816 there were no less than five instances of long-protracted cold ; but in the 63 years since 1816, only three such instances have been recorded besides the period of cold through which we passed in 1878-80. Whether this great difference between the last 64 years and the preceding 1 6 is due merely to accident or to causes affecting observa- tories situate near large cities is, as yet, not definitely made out. If the latter view be adopted, the cold of the eight months ending August 31, 1879 will appear the more ex- ceptional. That period of cold exceeded in intensity any of similar length of which we have authentic records. But the period wanted a month of the longest recorded in the above table. When we consider only cases in which the mean tem- perature of the month has not exceeded the average, we find 196 FAMILIAR SCIENCE STUDIES. yet longer periods of consecutive cold months. The longest of these (I am indebted for this information to an interesting paper in a recent number of Nature] is the period of 19 months from September 1798, to March, 1800, during which the mean temperature was 2.8 deg. below the average ; next in length comes a period of 17 months from September, 1859, to January, 1861, when the temperature was 2.2 deg. below the average ; thirdly, a period of 15 months, from February, 1782, to March, 1783, when the temperature fell 4.4 deg. below the average of those months. So that quite possibly since what has happened more than once already may happen again (without bringing with it the end of the world) such cold weather as that of 1879 ma y ^ ast f r a much longer time. It will, perhaps, hardly be thought necessary to explain that the cold and wet weather of the nine months ending August 31, 1879, was not brought about by planetary influ- ence. It came, indeed, too soon for those astrologers whose faith had been pinned on the perihelion passages between 1880 and 1 88 1, and it continued too long for those believers in cycles who promised or threatened drought in 1879. In passing, the perihelion predictions for the five years ending 1885, which have actually terrified some in a remarkable degree especially farmers, many of whom are almost as superstitious as sailors, probably because, like sailors, their well-being depends so much on the inconstant weather may be briefly dealt with. Jupiter, the nearest of the giant planets and far the largest (two-and-a-half times larger than all the rest together, with Venus, the Earth, Mars, Mercury, and the Moon thrown in as make- weights), passed his perihelion on September 5, 1880 ; but as he passes his perihelion once in every u 5-6th years, this can hardly be regarded as so exceptional a phenomenon that the end of the world must inevitably follow or be hastened by its occurrence. Saturn, which has been regularly passing his perihelion once every 29^ years (roughly) since the world began, if not for millions of years COLD AND WET. 197 before (according to the development theory), will not pass his perihelion before the autumn of 1885, by which time Jupiter will not be very far from aphelion. In other words, whatever mischief our theorists associate with Saturn's pas- sage of the part of his orbit nearest the Sun ought presuma- bly to be counteracted by Jupiter's approach to the part of his orbit farthest from the Sun. As for Uranus and Neptune which lie respectively twice and three times as far from the Sun as Saturn, while their combined mass is not a third of his, their perihelion passages can hardly produce very terrible results (somehow by the way astrology was as successfully prosecuted before these planets were discovered as now, when they must be considered in every horoscope). How- ever, as a matter of fact, they do pass their perihelia in 1882, at the convenient distances of about 1,700 and about 2,750 millions of miles respectively from our comparatively near neighbour the Sun. Lest this statement should encourage the notion that these two planets thus passing their perihelia in one and the same year (terrible coincidence) are very closely consorted to work mischief, let it be remarked that throughout the whole of the five years during which such terrible troubles are promised, the distance separating Uranus and Neptune will not be less than about 3,500 mil- lions of miles. The question whether recent inclement weather de- pends in any way on the Sun's condition with regard to spots is better worth discussing than the nonsense of the astrologers. We may remark in passing, however, that astrological absurdities have been to some degree encouraged by the enunciation of the doctrine that the planets in their courses influence the solar fluid envelopes and thus cause the number of spots to increase or to diminish a doctrine for which there seemed some evidence so long as the average solar spot period had not been accurately determined and might therefore be supposed to synchronise with the period of ii 5-6th years in which Jupiter completes his circuit. Now that the two periods are found to differ by three-quarters of 198 FAMILIAR SCIENCE STUDIES. a year at least, and if Mr. Broun's estimate is correct by about a year and five months, the theory of Jupiter's influence must be regarded as inadmissible, seeing that though for many years together sun-spots may be most numerous when Jupiter i near perihelion, for as many years together there- after they will be most numerous when he is near aphelion. However, the theory that sun-spots influence terrestrial phenomena does not, in reality, depend on the theory that the planets produce the sun-spots. If we inquire whether the cold and wet weather of 1879-80 was in any way associated with the paucity of sun-spots during those years, we find other and more important difficulties than those arising from the failure of the planetary theory of sun-spot pro- duction. In the first place, though Europe suffered from cold, America suffered rather from excessive heat, while in the southern hemisphere the average supply of heat was maintained without being anywhere in any noteworthy degree exceeded. But as the theory of solar influence on weather is not incompatible with a diversity of effects in different parts of the world nay, admits, or rather insists, upon the production of absolutely contrary effects in parts of one and the same country, we must inquire whether the other cases of long-continued cold cited above have coincided or not, like the present cold period, with a period of few sun-spots. The first and most remarkable of the intervals of cold tabulated above extended from February to November, 1782 ; the maximum of sun-spot frequency had been reached in about the middle of 1779, and the following minimum towards the end of 1784; thus the middle of the depression of temperature falling in the middle of 1782 followed a maximum by three years and preceded a minimum by nearly two years and a half. We may say roughly that the cold period fell midway between a maxi- mum and a minimum, in the decreasing phase of sun spots. The next cold interval ran from January to August, 1799, its middle, therefore, in May, 1799 ; thus following a mini- COLD AND WET. ! 99 mum of sun-spots in the middle of 1798 by about one year, and preceding a maximum at the beginning of 1804 by four years and a half. It fell then nearer a minimum than a maximum and in the increasing phase of sun-spots. The next cold interval, from October, 1799, to March, 1800, fell on the same slope of a sun wave, but not so near a minimum by half a year. The next, from November, 1807, to April, 1808, fell about midway between the sun-spot maximum of 1804.0 and the minimum of 1810.5, but rather nearer the minimum than the maximum and on the decreasing slope. The next March to August, 1812 occurred during the increasing stage of sun-spots, following a minimum by two years and preceding a maximum (1816.8) by rather more than four years. The cold interval from October, 1813, to March, 1814, fell on the same increasing slope, but as much nearer to the maximum as the former had been nearer to the minimum. Then came the long cold interval from November, 1815, to August, 1816. The middle of this interval fell in April, 1816, say 1816.3, or may be said to have coincided with the maximum of sun-spots in that year, set at 1816.8. The cold interval of January to May, 1838, followed almost as closely after a maximum of sun-spots (1837.2) as the cold interval of 1815-16 preceded one. That of January to May, 1855, preceded a minimum of sun-spots (1856.2) by about a year. That of December, 1859, to April, 1860, coincided exactly with the maximum of sun- spots in 1860-2. And lastly the present cold period follows only by a few months the minimum of sun-spots in 1878. We thus see that the most remarkable intervals of pro- tracted cold during the last 115 years have occurred in all parts of the sun-spot period indifferently at the maximum, at the minimum, midway between a maximum and the following minimum, midway between a minimum and the following maximum, soon after a maximum, soon after a minimum, shortly before a minimum, and lastly, shortly after a minimum. It will be rather difficult, then, to show that these cold periods depend directly or indirectly on the sun's 200 FAMILIAR SCIENCE STUDIES. condition with respect to spots, though when the bare announcement is made that the remarkable cold from which we have suffered in 1879-80 came after the sun had long been almost free from spots, many are ready to believe at once that the cold has been caused by the sun's spotless condition. On the whole, it may fairly be inferred that as yet, despite our meteorological observations and long-continued statistical researches, we are not able either to foretell seasons of cold or heat, of rain or draught, nor at present can any safe guess be made as to the duration of any cold interval which may be in progress. It may be mentioned in passing for the benefit of those who believe in weather prophecies, that the Almanack Mathieu, the favourite oracle of French farmers, promised exceedingly warm weather from the i gth to the 26th of July, 1879, during which interval, in reality, the temperature was considerably below the average. OUR WINTERS. WHEN frost and snow prevail, we hear a good deal about old-fashioned winters, seasonable Christmas weather, and so forth, the idea being generally prevalent that some 30 or 40 years ago our winters were much colder than they are now, and that, in particular, December was of yore a month of much frost and snow. Meteorological records give no support to these views, which appear to be based solely on imperfect recollection of bitter winters in the past, winters as exceptional then as such winters are now, but remembered as though they had occurred in successive years and for many years in succession. Forty years ago men spoke of old-fashioned winters much as many of us do now. The belief was just as prevalent then as now that some 30 or 40 years earlier the winters had been much more severe than at the then present time. It is true this does not of itself prove that no such change has occurred as many believe in ; for the winters 80 years ago might have been as much bitterer than the winters 40 years ago as these are supposed to have been bitterer than our present winters. But we should have to believe in a much greater change during the last 80 years than is assumed to have happened in the last 40 years. So that, as we have records of the winter weather 80 years ago, it becomes easier to put the prevalent superstition about the bitterness of past winters to the test. When this is done, we find nothing to suggest that the average winter weather 80 or 100 years ago was severer than that which we now ex- perience, 202 FAMILIAR SCIENCE STUDIES. Before considering some of the evidence relating to past winters, we may as well note that, so far as Christmas weather is concerned, there is a real foundation for the theory that there has been a change, though none whatever for the theory that winter weather has changed. The old-fashioned Christmas weather not the Christmas weather 30 or 40 years, but a century and a half ago was, in fact, the weather of a different part of the year. Christmas Day during the first half of last century, instead of occurring as now four or five days after the shortest day or winter solstice, fell more than a fortnight after that epoch. Now the coldest part of the year, on the average, falls about four weeks after the winter solstice ; so that we can very well understand that on the average of many years old Christmas Day and the old Christmas season would be colder than our present Christ- mas-tide. A study of the meteorological records of the last half century shows very clearly that such a difference exists between the Christmas weather of the New Style and that of the Old Style with its seasonal error of ten days. Thus, compare the weather of the last fortnight in December in which our present Christmas season falls with that of the first fortnight in January to which old Christmas-tide belonged. We find in 50 years seven in which the weather of the last fortnight in December was of a neutral character, mild and cold weather alternating in about equal proportions ; 27 in which the weather of that fortnight was mild, and in the remaining 16 only the weather was severe. On the con- trary, while there were eight years of neutral weather during the first fortnight in January, there were 15 only in which the weather of that fortnight was mild, the weather being severe in 27. We can understand, then, why December was depicted by the poets down to the time of the change of style as a colder month than we now find it. It belonged to a colder part of the year, just as Spenser's ' Mery Moneth of May ' be- longed to a warmer part of the year than our present May. Those who quote the accounts which have been handed down of bitter winters in past times have been apt to over- OUR WINTERS. 203 look the circumstance that those accounts nearly always tend to disprove, not to establish, the theory of change. Those records tell us of the exceeding seventy of cold which pre- vailed at such and such a time, but they also tell us that the cold was altogether exceptional. Sometimes even we find that while the maximum degree of cold recorded has fallen short of what has been experienced within the last 20 or 30 years, it is described as exceeding aught that even the oldest persons could remember. Gilbert White speaks of the cold in December, 1784, as very extraordinary ; but he mentions one degree below zero as the lowest temperature recorded out of doors in the shade. In January, 1855, a temperature of four degrees below zero was recorded in the neighbour- hood of London. One circumstance, indeed, which White mentions, would seem to show that cold such as we had in January, 1855, was regarded in his day as too improbable to be worth considering in making thermometers ; for he says that a thermometer by Martin, a well-known maker of scientific instruments, was graduated only down to four degrees above zero, so that the mercury sank quite below the brass guard of the bulb. Again, in describing the severe weather of January, 1776, when the Thames was frozen over, both above and below bridge, White tells us that during the four coldest nights the thermometer at South Lambeth fell to n, seven, six, and six (above zero), and at Selborne sank on one night exactly to zero ; but he adds that this was ' a most unusual degree of cold for the south of England.' It was the long continuance of the frost of 1776, not its intensity, which caused the effects to be so remarkable. The snow lay 26 days on the houses in the city, being all that time perfectly dry, so that the snow in the streets 'crumbled and trod dusty, and, turning gray, resembled bay salt.' The long continuance of the frost depended on the long- continued northerly winds. At any time we might have a similar experience.- We have been so far fortunate that for many years it has never chanced to blow continuously from northerly quarters for three or four 294 FAMILIAR SCIENCE STUDIES. weeks in January, the coldest month in the year. And we may safely conclude, from long experience that such a con- tinuance of northerly winds at that season is improbable. But there is no reason why it should not happen now as in 1776 and other past years. It was as little anticipated in the first week of 1776 as in the first week of 1879. Their experience was as ours has been. ' The old housekeepers living,' White tells us, ' did not remember ' a frost which had lasted (continuously) so long as that of January, 1776. Forty or fifty years ago those who believed that a great change had in the course of a generation or so affected winter weather in Great Britain were at a loss to explain the greater mildness of the season. In the United States and Canada, where a similar change was, quite erroneously, believed to have occurred, a cause was imagined in the clearing of forests and the consequent exposure of large tracts of land to the sun's rays. But in Great Britain and in Europe generally there had been no clearing away of many millions of acres of forest timber. So that, as a writer in 1837 admitted, 'If the climate of Great Britain has actually undergone a change, the cause, whatever it may be, must be of a different nature from that generally supposed to affect the climate of North America.' The imagined change in the last 40 years has been attributed to a cause which, perhaps, has some real effect on climatic relations, though certainly no such effect as has been attributed to it the enormous annual consumption of coal. It is possible that in manufacturing towns and in the larger cities, the mean temperature of the winter months may be slightly increased in this way ; though there is no valid evidence to show that this is the case, and any such increase must be very small. That the climate of the country should be influenced by the consumption of coal is altogether in- credible. Only a portion of the heat resulting from the use of coal in this country tends to warm the air, directly or in- directly. Most of it is or ought to be expended in generating various forms of force. But even if all the coals raised OUR WINTERS. 205 annually were used to increase the warmth of our air, the effect would be very slight by comparison with the heat received from the sun. The combustion of four times as many tons of coal as are annually raised in Great Britain would barely suffice to dry the Island after one day's heavy rainfall, if we could imagine it used in that way. If there had been, as some imagine, a change in the direction of the ocean currents which reach our shores, or in the temperature of the water which they bring to us from distant seas, we could understand that the climate of Great Britain should have been greatly changed. But all the evidence we have tends to show that the Gulf Stream, or the extension of the Gulf Stream to which we incorrectly give that name, occupies the same position and has the same charac- ter now as a century ago. And, in reality, not only is the mean temperature for each month the same now (or appa- rently so) as it was 50 or 100 years ago, but the prevalent weather of special months appears to have undergone no alter- ation other than that apparent alteration which has resulted from the change of style, an alteration which is observable only in comparing the weather of our present months with that ascribed to the same months by poets and others before the year 1752, when the change of style was effected. We have seen how marked a difference at present exists between the average weather of the last fortnight in December and that of the first fortnight in January, and how we can thus explain the contrast between the ordinary Christmastide weather of our time and that described by poets before the change of style. Many, however, believed that in this respect, at any rate, if not in the mean monthly temperature, there has been a marked change within a much shorter time. Forty or fifty years ago, they say, Christmas weather was nearly always frosty. Confronted by meteorological records which prove the reverse, they still believe that 80 or 90 years ago (when as yet no systematic meteorological records were kept) the old-fashioned Christmas weather prevailed in nine years out of ten. It may be of interest to inquire whether 206 FAMILIAR SCIENCE STUDIES. this really was the case or not. The answer comes in no doubtful terms. Gilbert White of Selborne has left a rough re- cord of the weather from the beginning of 1 768 to the end of 1 792. Of the 25 years thus recorded, we find that three ended with a fortnight of alternate rain and frost, in eight the last fortnight was frosty, and in the remaining 14 that fortnight was mild and rainy, mostly without frost, but in some of the 14 years a few slight frosts occurred. On the other hand, at that time, as now, the first fortnight in January was com- monly much colder than the last fortnight in December. The neutral cases were four ; in eight years the first fortnight in January was mild, and in the remaining 13 hard frost prevailed during that fortnight. 207 ABOUT LOTTERIES. IN an essay which appeared a few years since in the Cornhill Magazine, I considered among gambling superstitions some relating indirectly to such ventures as are made when tickets in lotteries are bought, a small certainty being exchanged for the small chance of a large profit. Whether it is that men are so well known to be inconsistent in such matters, that if any one points out the folly of gambling he may be regarded as almost certain to be a gambler himself, or whether the case is a merely casual coincidence, I do not know ; but certain it is that during the years which have elapsed since that essay appeared, I have received more invitations to purchase lottery-tickets and to take part in wildly speculative transactions than during any ten pre- ceding years of my life, Not only so, but in some cases invitations have been addressed to me to purchase tickets from persons claiming to be exceptionally lucky in selecting numbers. I have no doubt many of my readers have received such invitations, couched in terms implying that a very special favour was offered which must be quickly accepted lest it should be too late to gain the wealth thus generously proffered. But it struck me as being a singularly cool proceeding in my case, simply because much that I had written bore directly not only on the question whether such hopes as are held out in offers of the sort can possibly be well founded, but also on this other question, Can those who hold out such hopes be by any possibility honest men? Without definitely expressing any opinion on zoS FAMILIAR SCIENCE STUDIES. the second and more delicate of these questions, I pro- pose to consider here a few matters connected with lotteries, noting some of the systems on which they have been formed. Probably the reader will not find it very difficult to deter- mine what my answer would be to the question, if a cate- gorical reply were required from me. The simplest, and in many respects the best, form of lottery is that in which a number of articles are taken as prizes, their retail prices added together, and the total divided into some large number of parts, the same number of tickets being issued at the price thus indicated. Suppose, for instance, the prizes amount in value to 2oo/., then a thousand tickets might be sold at 45. each, or 4,000 at is. each, or a larger number at a correspondingly reduced price. In such a case the lottery is strictly fair, supposing the prizes in good saleable condition. The person who arranges the lottery gains neither more nor less than he would if he sold the articles separately. There may be a slight expense in arranging the lottery, but this is fully compensated by the quickness of the sale. The arrangement, I say, is fair ; but I do not say it is desirable, or even that it should be permissible. Advantage is taken of the love of gambling, innate in most men, to make a quick sale of goods which otherwise might have lain long on hand. Encouragement is given to a tendency which is inherently objectionable if not absolutely vicious. And so far as the convenience is concerned of those who collectively buy (in fact) the prizes, it manifestly cannot be so well suited as though those only had bought who really wanted the articles, each taking the special article he required. Those who buy tickets want to get more ihan their money's worth. Some of them, if not all, are believers in their own good luck, and expect to get more than they pay for. They are willing to get, in this way, something which very likely they do not want, something therefore which will be worth less to them in reality than the price for which it is justly enough valued in the list of prizes. ABOUT LOTTERIES. 209 Unfortunately those who arrange lotteries of this sort for mere trade purposes (they are not now allowed in this country, but abroad they are common enough, and English people are invited to take part in these foreign swindles) are not careful to estimate the price of each article justly. They put a fancy price on good articles, a full price on damaged articles, and throw in an extra sum for no articles at all. Many of them are not at all particular, if the sale of tickets is quick, about throwing in a few hundred more tickets than they had originally provided for, without in the least considering it necessary to add correspondingly to the list of prizes. But this is not all. How much those who arrange such lotteries really wrong the purchasers of tickets cannot be known. But we can learn how ready the ticket-buyers are to be wronged, when we note what they will allow. It seems absurd enough that they should let the manager of a lottery act entirely without check or control as to the number of tickets or the plan according to which these are drawn. But at least when a day is appointed for the drawing, and the prizes are publicly exhibited in the first instance, and as publicly distributed eventually, the ticket-buyers know that the lottery has been in some degree bond fide. What, how- ever, can we think of those who will pay for the right of drawing a ticket from a 'wheel-of- fortune,' without having the least means of determining what is marked on any of the tickets, or whether a single ticket is marked for a prize worth more than the price paid for a chance, or even worth as much ? Yet nothing is more common where such wheels are allowed, and nothing was more common when they were allowed here, than for a shopman to offer for a definite sum, which frequenters of the shop would readily pay, the chance of drawing a prize-ticket out of a wheel-of-fortune, though he merely assured them, without a particle of proof, that some of the tickets would give them prizes worth many times the price they paid. Even when there were such tickets, again, and some one had secured a prize (though the chances were that the prize-drawer was connected with p 210 FAMILIAR SCIENCE STUDIES. the business), people who had seen this would buy chances as though the removal of one good prize ticket had made no difference whatever in the value of a chance. They would actually be encouraged to buy chances by the very circumstance which should have deterred them. For if a good prize is drawn in such a case, the chances are that no good prize is left. Although lotteries of this sort are no longer allowed by law, yet are they still to some degree countenanced in con- nection with charity and the fine arts. Now, setting aside lotteries connected with the fine arts as singularly nondescript in character though it must not for a moment be supposed that we regard a taste for gambling with a love of the beau- tiful as forming an agreeable mixture we note that in lotteries started for charitable purposes there is usually no thought of gain on the part of those who originate the scheme. That is, they have no wish to gain money for themselves, though they may be very anxious to gain money for the special purpose they have in view. This wish may be, and indeed commonly proves to be, inconsistent with strict fairness towards the buyers of tickets. But as these are supposed to be also possessed with the same desire to ad- vance a charitable purpose that actuates the promoters of the scheme, it is not thought unfair to sell them 'their tickets rather dearly, or to increase the number of tickets beyond what the true value of the prizes would in strict justice permit. It is, however, to be noted that the assumption by which such procedure is supposed to be justified is far from being always accurate. It is certain that a large pro- portion of those who buy tickets in charitable lotteries take no interest whatever in the object for which such lotteries are started. If lotteries were generally allowed, and there- fore fairer lotteries could be formed than the charitable ones which are as unfair in reality as the dealings of lady stall- keepers at fancy bazaars the sale of tickets at charitable lotteries would be greatly reduced. It is only because those who are possessed by the gambling spirit can join no other ABOUT LOTTERIES, 211 lotteries that they join those started for charitable purposes. The managers of these lotteries know this very well, though they may not be ready to admit very publicly that they do. If pressed on the subject, they speak of spoiling the Egyptians, of the end justifying the means, and so forth. But, as a matter of fact, it remains true that these well-intentioned folk, often most devout and religious persons, do, in the pursuit of money for charitable purposes, pander to the selfishness and greed of the true gambler, encourage the growth of similar evil qualities in members of their own community, and set an evil example, moreover, by sys- tematically breaking the law of the country. It would be harsh, perhaps, to speak strongly against persons whose in- tentions are excellent, and who are in many cases utterly free from selfish aims ; but they cannot be acquitted from a charge of extreme folly, nor can it be denied that, be their purpose what it may, their deeds are evil in fact and evil in thtir consequences, It might be difficult to determine whether the good worked by the total sum gained from one of these charitable lotteries was a fair equivalent for the mis- chief wrought in getting it. But this total is not all gained by choosing an illegal method of getting the sum required. The actual gain is only some slight saving of trouble on the part of the promoters of the charitable scheme, and a further slight gain to the pockets of the special community in which the charity is or should be promoted. And it is certain that these slight gains by no means justify the use of an illegal and most mischievous way of obtaining money. It would be difficult to find any justification for the system, once the immorality of gambling is admitted, which might not equally well be urged for a scheme by which the proceeds (say) of one week's run of a common gaming-table should be devoted to the relief of the sick poor of some religious community. Nay, if charitable ends can at all justify immoral means, one might go further still, and allow money to be obtained for such purposes from the encouragement of still more objectionable vices. We might in fact recog- p 2 212 FAMILIAR SCIENCE STUDIES. nise quite a new meaning in the saying that ' Charity covers a multitude of sins.' I have said that a lottery in which all the prizes were goods such as might be sold, retail, at prices amounting to the total cost of all the tickets sold would be strictly fair. I do not know whether a lottery ever has been understood in that way. But certainly it seems conceivable that such a thing might have happened ; and in that case, despite the objections which, as we have shown, exist against such an arrangement, there would have been a perfectly fair lottery. Adam Smith, in his Wealth of Nations^ seems to have omitted the consideration of lotteries of this kind, when he said that ' the world neither ever saw, nor ever will see, a perfectly fair lottery, or one in which the whole gain com- pensated the whole loss ; because the undertaker could gain nothing by it.' Indeed, it has certainly happened in several cases that there have been lotteries in which the total price of the tickets fell short of the total value of the prizes these being presents made for a charitable purpose, and the tickets purposely sold at very low prices. It is well known, too, that in ancient Rome, where lotteries are said to have been invented, chances in lotteries were often, if not always, dis- tributed gratuitously. But assuredly Adam Smith is justified in his remark if it be regarded as relating solely to lotteries in which the prizes have been sums of money, and gain has been the sole object of the promoters. ' In the State lotteries/ as he justly says, ' the tickets are really not worth the price which is paid by the original subscribers,' though from his sequent remarks it appears that he had very imperfect information respecting some of the more monstrous cases of robbery (no other word meets the case) by promoters of some of these State swindles. The first idea in State lotteries seems to have been to adopt the simple arrangement by which a certain sum is paid for each of a given number of tickets, a series of prizes being provided less in total value than the sum thus obtained. ABOUl LOTTERIES. 213 It was soon found, however, that people are so easily gulled in matters of chance, that the State could safely assume a very disinterested attitude. Having provided prizes of definite value, and arranged the number of tickets, it simply offered these for sale to contractors. The profit to the State consisted in the excess of the sum which the con- tractors willingly offered above the just value (usually io/.) of each ticket. This sum varied with circumstances, but generally was about 6/. or 7/. per ticket beyond the proper price. That is, the contractors paid about i6/. or i7/. for tickets really worth io/. They were allowed to divide the tickets into shares, halves, quarters, eighths, and sixteenths. When a contractor sold a full ticket he usually got about from 2 1/. to 22/. for it ; but when he sold a ticket in shares his gain per ticket was considerably greater. The object in limiting the subdivision to one-sixteenth was to prevent labouring men from risking their earnings. It is hardly necessary to say, however, that the provision was constantly and easily evaded, or that the means used for evading the limitation only aggravated the evil. At illegal offices, commonly known as ' little goes,' any sum, however small, could be risked, and to cover the chance of detection and punishment these offices required greater profits than the legal lottery- offices. ' All the efforts of the police,' we read, ' were ineffectual for the suppression of these illegal pro- ceedings, and for many years a great and growing repugnance was manifested in Parliament to this method of raising any part of the public revenue. At length, in 1823, the last Act that was sanctioned by Parliament for the sale of lottery- tickets contained provisions for putting down all private lotteries, and for rendering illegal the sale, in this kingdom, of all tickets or shares of tickets in any foreign lottery,' which latter provision is to this day extensively evaded. The earliest English lottery on record is that of the year 1569, when 40,000 chances were sold at los. each, the prizes being articles of plate, and the profit used in the repair of certain harbours. The gambling spirit seems to have devel- 214 FAMILIAR SCIENCE STUDIES. oped greatly during the next century ; for, early in the reign of Queen Anne, it was found necessary to suppress private lotteries ' as public nuisances,' a description far better appli- cable (in more senses than one) to public lotteries. ' In the early period of the history of the National Debt/ says a writer (De Morgan, we believe) in the Penny Cyclopedia, ' it was usual to pay the prizes in the State lotteries in the form of terminable annuities. In 1694 a loan of a million was raised by the sale of lottery-tickets at io/. per ticket, the prizes in which were funded at the rate of 14 per cent, for sixteen years certain. In 1746 a loan of three millions was raised on 4 per cent, annuities, and a lottery of 50,000 tickets of io/. each ; and in the following year one million was raised by the sale of 100,000 tickets, the prizes in which were funded in perpetual annuities at the rate of 4 per cent. per annum. Probably the last occasion on which the taste for gambling was thus made use of occurred in 1780, when every subscriber of i,ooo/. towards a loan of twelve mil- lions, at 4 per cent, received a bonus of four lottery-tickets, the intrinsic value of each of which was io/.' About this time the spirit of gambling had been still more remarkably developed than in Anne's reign, despite the laws passed to suppress private lotteries. In 1778 an Act was passed by which every person keeping a lottery-office was obliged to take out a yearly license costing 5o/. This measure reduced the number of such offices from 400 to 51. In France the demoralisation of the people resulting from the immorality of the Government in encouraging by lotteries the gambling spirit, was greater even than in England. The fairest system for such lotteries as we have hitherto considered was that adopted in the Hamburg lotteries. The whole money for which tickets were sold was distributed in the form of prizes, except a deduction of io per cent, made from the amount of each prize at the time of pay- ment. Before pausing to consider the grossly unfair systems which have been, and still are, adopted in certain foreign ABOUT LOTTERIES. 215 lotteries, it may be well to notice that the immorality of lotteries was not recognised a century ago so clearly as it is now ; and therefore, in effect, those who arranged them were not so blameworthy as men are who, in our own time, arrange lotteries, whether openly or surreptitiously. Even so late as half a century ago an American lawyer, of high character, was not ashamed openly to defend lotteries in these terms. ' I am no friend,' he said, ' to lotteries, but I cannot admit that they are per se criminal or immoral when authorised by law. If they were nuisances, it was in the manner in which they were managed. In England, if not in France ' (how strange this sounds), 'there were lotteries annually instituted by Government, and it was considered a fair way to reach the pockets of misers and persons disposed to dissipate their funds. The American Congress of 1776 instituted a national lottery, and perhaps no body of men ever surpassed them in intelligence and virtue.' De Morgan, remarking on this expression of opinion, says, that it shows what a man of high character for integrity and knowledge thought of lotteries twenty years ago (he wrote in 1839). 'The opinions which he expressed were at that time/ continues 'De Morgan, ( shared, we venture to say, by a great num- ber.' The experience of those who arranged these earlier State lotteries showed that from men in general, especially the ignorant (forming the great bulk of the population who place such reliance on their luck), almost any price may be asked for the chance of making a large fortune at one lucky stroke. Albeit, it was seen that the nature of the fraud practised should preferably be such that not one man in a thousand would be able to point out where the wrong really lay. Again, it was perceived that if the prizes in a lottery were reduced too greatly in number but increased in size, the smallness of the chance of winning one of the few prizes left would become too obvious. A system was re- quired by which the number of prizes might seem unlimited and their possible value very great, while also there should 216 FAMILIAR SCIENCE STUDIES. be a possibility of the founders of the lottery not getting back all they ventured. So long as it was absolutely certain that, let the event be what it might, the managers of the lottery would gain, some might be deterred from risking their money by the simple statement of this fact. Moreover, under such conditions, it was always possible that at some time the wrath of losers (who would form a large part of the community if lottery operations were successful) might be roused in a dangerous way, unless it could be shown that the managers of public lotteries ran some chance, though it might be only a small chance, of losing, and even some chance of ruin as absolute as that which might be- fall individual gamblers. It was to meet such difficulties as these that lottery systems like that sometimes called the Geneva system were invented. This system we propose now to describe, as illus- trating these more speculative ventures, showing in particular how the buyers of chances were defrauded in the favourite methods of venturing. In the Geneva lottery there are ninety numbers. At each drawing five are taken. The simplest venture is made on a single number. A sum is hazarded on a named number, and if this number is one of the five drawn, the speculator receives fifteen times the value of his stake. Such a venture is called a simple drawing. It is easy to see that in the long run the lottery-keeper must gain by this system. The chance that the number selected out of ninety will appear among five numbers drawn, is the same that a selected number out of eighteen would appear at a single drawing. It is one chance in eighteen. Now if a person bought a single ticket out of eighteen, each costing (say) i/., his fair prize if he drew the winning ticket should be i8/. This is what he would have to pay to buy up all the eighteen tickets (so making sure of the prize). The position of the speculator who buys one number at i/., in the Geneva lottery, is precisely that of a purchaser of such a ticket, only that instead of a prize being i8/., if he wins, it is only 157. ABOUT LOTTERIES. 217 The lottery-keeper's position on a single venture is not pre- cisely that of one who should have sold eighteen tickets at i/. each for a lottery having one prize only ; for the latter would be certain to gain money if the prize were any sum short of i8/., whereas the Geneva lottery-keeper will lose on a single venture, supposing the winning number is drawn, though the prize is i5/. instead of i8/. But in the long run the Geneva lottery-keeper is certain to win at these odds. He is in the position of a man who continually wagers odds of 14 to i against the occurrence of an event the real odds against which are 1 7 to i. Or his position may be compared to that of a player who takes seventeen chances out of eighteen at (say) their just value, i/. each, or i7/. in all, his opponent taking the remaining chance at its value, i7., but instead of the total stakes, i8/., being left in the pool, the purchaser of the larger number abstracts 3/. from the pool at each venture. That men can be found to agree to such an arrangement as this shows that their confidence in their own good fortune makes them willing to pay, for the chance of getting fifteen times their stake, what they ought to pay for the chance of getting eighteen times its value. The amount of which they are in reality defrauded at each venture is easily calcu- lated. Suppose the speculator to venture i/. Now the actual value of one chance in eighteen of any prize is one- eighteenth of that prize, which in this case should therefore be i8/. If, then, the prize really played for has but fifteen- eighteenths of its true value, or is in this case i5/., the value of a single chance amounts only to one eighteenth of i5/., or to 1 6^. Sd. Thus at each venture of i/. the speculator is cheated out of 3^. 4, ,, 9, 14, 12 . . . .3 5 M .. 9, I4 12 . . . ,3 1 ,, ,, 9. 14, 12, 4, 5 . . ,5 8 9, 14, 12 . . . .3 3 n ,, 9, 14, 12, 4, 5, 8 . .6 7 ,i 9, M. 12, 8 . . .4 2 M 9 M, 12, 4, 5. 8, 3, 7, IS- 9 13 ,. it 14, 15 .... 2 10 ,, ,, 14, 12, 15, 13 . . .4 6 ,, 9, 14, 12, 8, 7, 15, 13, 10 . 8 11 14, 12, 15, 13 -4 Total displacement , . .52 Thus the total displacement is even, and the vacant line is also even : so that, if our suggested law is correct, the posi- tion should be a winning one. Let us now consider the effect of any change in the posi- tion of the blocks from the arrangement shown in Fig. n. What we want to ascertain is whether, when any such change has been made, by sliding without removing blocks, the position retains the characteristics which we have been led to regard as indicative of a winning position. It is clear that, whether we push the i or the 8 into the vacant place, the ' total displacement ' remains unchanged. If, however, we shift the 12 to the vacant position, the total displacement is altered ; for the numbers 4, 5, and i, which should precede 12, but did not in the original position, are now made to do so. The ' total displacement ' is reduced from 52 to 49, the vacant line from the second to the first. Thus, the law we are inquiring into still seems to hold good, for 282 FAMILIAR SCIENCE STUDIES. now both the total displacement and the vacant line are odd. So also it holds if, instead of pushing down the 12, we push up the 15. For in this case the numbers 3, 7, and 8, which should precede 15, and did precede 15 in the original posi- tion, are made to follow 15, the 'total displacement' being thus increased from 52, an even number, to 55, an odd num- ber, while the vacant line is also changed from even to odd. In all the cases thus far considered the total displacement has either been increased or diminished by three, when a block has been pushed up or down. But if after pushing 15 (Fig. u) up, we push 6 up, we only change the displacement (55) by one ;. for 6, which .had followed and should follow 2, is made to precede 2, increasing the total displacement by one, while [3 and 10, which had not followed 6 as they should, are made to do so, decreasing the total displacement by two, the actual reduction being therefore only one. Thus, after this change the total displacement is 54, an even number ; the vacant line is the fourth, or also even ; and the law we are considering seems to be fulfilled after this change as after the others. But we begin now to see that every vertical displacement of one block must increase or diminish the total displacement, either by the odd number three or by the odd number one. An upward displacement puts a number before three others which had been after those numbers. Now, either the dis- placed number is greater than all those three or greater than two of them, and less than one, or greater than one of them only and less than two, or less than all three of them. In the first case, the total displacement is increased by three ; in the second, it is increased by two and reduced by one, or increased on the whole by one; in the third it is increased by one and reduced by two, or reduced on the whole by one ; in the fourth case, the total displacement is reduced by three. And obviously, pushing down a block must exactly reverse these effects in the respective cases considered ; either re- ducing the total displacement by three or by one, or increasing it by one or by three. THE FIFTEEN PUZZLE. 283 Since, then, each vertical change increases or diminishes the total displacement by an odd number (3 or i), successive changes of this sort cause the total displacement to be alter- nately odd and even. They also, of course, cause the vacant line to be alternately odd or even. So that, if the total dis- placement and the vacant line are both odd or both even for any given position, they are both even or both odd after a vertical displacement, both odd or both even after the next vertical displacement, both even or both odd after the next ; and so on continually, that is (since horizontal displacements produce no change at all in them), they remain always alike, both even or both odd, whatever changes are made. On the other hand, it is equally clear that if for any given posi- tion the 'total displacement' is odd and the vacant line even, the former will be even and the latter odd after a vertical displacement ; one odd, the other even, after the next vertical displacement ; and so on continually ; that is, (since horizontal displacements produce no change at all in them), they remain always unlike one odd, the other even what- ever changes are made. Since, then, in the won position the total displacement (o) is even, and the vacant line (4th) is also even, in every position deducible from the won position or reducible to the won position, the total displacement and the vacant line are either both even or both odd. And therefore no posi- tion in which the total displacement is even and the vacant line odd, or vice versa, can possibly be a winning po- sition. We have established a law which at any rate proves the hopelessness of attempting to pass from the position shown in Fig. 12, or from any position I2> deducible from or reducible to this arrangement, to the won position shown in Fig. 6. For in Fig. 12, the displacement is one or odd, and the vacant line even. This, with many, will be regarded as a sufficient analysis of the Fifteen Puzzle, 284 FAMILIAR SCIENCE STUDIES. since every one who has ever tried it knows well that we can always reduce any given position in a few minutes, either to the position shown in Fig. 6 (the won position), or to that shown in Fig. 12, which may conveniently be called the lost position. But in reality something more is required for the com- plete analysis of the puzzle. We have proved that from none of the multitudinous positions (one-half of the total number) in which the total displacement is odd and the vacant line even, or vice versa, can any position be obtained in which the total displacement and the vacant line are either both even or both odd ; also, that from not one of the' multitudinous positions of the latter kind (say the winning kind) can one of the former kind (say the losing kind) be obtained. But we have not yet proved that from any posi- tion of the winning sort any other position of the winning sort, including the won position, can be obtained ; or that from any position of the losing sort any other position of the same sort, including the lost position. We cannot possibly prove either of these relations ex- perimentally, for the simple reason that there are more than ten millions of millions of positions of the winning sort, and as many of the losing sort. 1 1 There are in each position fifteen occupied squares and one square unoccupied, which square we may always suppose to be occupied by the number 16. The total possible number of arrangements, there- fore, is the same as the number of permutations of 16 things (all appearing in each arrangement, which is, indeed, understood usually by mathematicians when they use the word permutation as distinguished from combination). This number, it is well known, is that obtained by multiplying together the number, i, 2, 3, 4, &c., up to 16, or 20,922,789,888,000. Of these, one-half, or 10,461,394.944,000, are winning and as many are losing positions. I venture to quote here, in passing, some remarks which I made in my article on the Fifteen Puzzle in the Australasian remarks not, of course, intended to be taken an grand serieiix, but which were unfor- tunately so taken by a few whom I must consider rather dull-brained readers. ' Professor Piazzi Smythe, and other believers in the Great Pyramid, may find in the above numbers proof positive that the archi- THE FIFTEEN PUZZLE. 285 Yet it is not difficult to prove that from any winning position any other winning position, and from any losing any other losing position, may be obtained. The demonstration may be arranged as follows : When we take a square of four small squares only, and have three numbered blocks (say i, 2, 3) and one vacant square, we can shift these round from any given position into twelve positions, as thus : ist 2nd 3rd 4th FIG. 13. These are only half the possible positions of the numbers i, 2, 3, in a square of four quarter-squares. The other half will be obtained by starting from the position and carrying the vacant square round in the way above shown, for the series of 12 positions from the initial position. In this, the simplest case, we see that starting from any given position, half the possible arrangements of three numbers in a square of four square spaces, one vacant, tects of that building at once anticipated the celebrity of the Great Boss Puzzle, and were acquainted with the distance of the star Alpha Centauri, the nearest of all the stars. The proof runs thus : The base of the pyramid is square, like the Fifteen Puzzle box, and has four sides, suggesting manifestly the division of each side into four equal 286 FAMILIAR SCIENCE STUDIES. can be obtained, and half only ; but if the sequence of the numbers (going round the square) be altered from i, 2, 3 to i, 3, 2, or vice versa, 1 all the remaining positions can be obtained. The movements by which such posi- tions are obtained may be regarded as a turning movement around the central point of the square ; and in this case there is but one point around which such turning movement can be made. Moreover, notice that it matters nothing which way the turning takes place. The successive posi- tions shown in Fig. 13 form a complete re-entering series, and according as we consider this series in the order there shown, or in the reverse order, the turning is supposed to have taken place in the same direction as the hands of a watch or in the reverse direction. Now, it is to be noticed that in the complete puzzle, or in a similar puzzle with a smaller or greater number of parts, and, by cross lines through these, the division of the square into sixteen squares. But the pyramid has only one apex ; hence is at once suggested the removal of one of the sixteen squares, leaving the magic Fifteen. Then the Fifteen Problem admits of 20,922,789,888,000 distinct positions. Now, all the best measurements of the distance of Alpha Centauri indicate rather more than 20 billions of miles. Un- questionably the true distance must be just 20,922,789,888,000 miles; and this the pyramid architects manifestly knew. But they could not have learned this by any observations possible in their time. Hence we have further evidence of supernaturally imparted knowledge. Quod crat demonstrandum? 1 There are only two possible arrangements, i, 2, 3, i, 2, 3, i, 2, 3, &c., and i, 3, 2, I, 3, 2, I, 3, 2, &c., so far as sequence round the square is concerned. Further, in each arrangement the numbers run in numerical order, either in one direction or in another. It was from failing to notice this law in the sequence of three numbers that Hum- boldt was led to imagine that there is some significance in the cir- cumstance that the three promontories terminating the continents of America, Africa, and Australia, in the southern seas, approach suc- cessively nearer to the South Pole. As there are only three, they could not but do so, either as we take them in order from east to west, or else as we take them in order from west to east. The point is con- sidered more at length in my essay on equal-surface projections of the globe in 'Essays on Astronomy.' THE FIFTEEN PUZZLE. 287 rectangles (as a 9 square, or a 25 square, or a 3 by 4 rect- angle, or a 5 by 6 rectangle, and so forth), every point of intersection of the cross lines forming the squares is a centre round which, by bringing the vacant square next to any such point, the three blocks left around it can be turned, as in the above case we turned the numbers i, 2, 3. But we can also turn the numbers round any line between such points of intersection. Thus, in the won pos-ition of Fig. 6, the blocks 15, 14, 10, n, 12, can be turned round the line between the blocks 11 and 15, retaining the same sequence round the rectangle of six squares in which these blocks and the vacant square lie ; and similarly with any other such line between two squares. Again, the blocks 15, 14, 13, 9, 10, n, and 12 in the same figure can be turned round the line between the blocks 14, n, and 14, 15. Next, the blocks round any one of the middle squares can be moved round such squares (after the vacant square has been brought next to it). Thus the blocks 15, 14, 10, 6, 7, 8, and 12, Fig. 6 can be moved round the block n. So the blocks round any adjacent pair of the blocks now occupied by the number, 6, 7, 10, and n, in Fig. 6, can be turned round that pair (as, 12, 8, 7, 6, 5, 9, 13, 14, 15 round the pair 10, n). And lastly, the border squares can be turned round the central set of four squares occupied in Fig. 6 by the numbers 6, 7, 10, II. In all, in the complete puzzle, there are thirty-six kinds of turning motion, namely : round nine points of intersec- tion, round twelve lines between squares, round six lines between pairs of squares, round four squares, round four pairs of squares, and round one square of four square. In what follows, I propose, for the convenience of descrip- tion and explanation, to regard rotations such as are above described as always taking place in one direction, viz. in the direction contrary to that in which the hands of a watch move (this being what mathematicians call the positive direction of rotation); and when I speak of rotation round a rectangle or square of blocks, whether the whole set or 288 FAMILIAR SCIENCE STUDIES. part of a set shown in a figure, I mean that the border squares in that rectangle are to be rotated round ; also when I speak of rotation by so many squares I mean that the vacant square is to be carried round in the fonvard direction of rotation so many squares. At first sight it might appear, in studying Fig. 13, that the vacant square was carried the other way round and, indeed, this is the case if we con- sider the blocks as moved separately. But in what follows we suppose, unless the contrary is specified, that the set of blocks to be rotated are carried round together. For in- stance, we consider there has been a rotation of one square in moving from position i to position 4, of another square in moving to position 7, of another in moving to position 10, and of a fourth in moving onwards to the original posi- tion i. So much premised, I proceed to show, step by step, that in rectangles and squares six, eight, nine, twelve, and finally of sixteen blocks, we can always pass from any position to another of the same kind. In Fig. 14 we have the won position for five blocks in a A six-block rectangle. Let it be required to get any three blocks in given order in the upper row, which is equivalent to getting any given or possible arrangement of the five blocks. The two blocks which f 1 "R F i are to be where 2 and 3 are now must either be next to each other (in order of sequence round the rectangle) or not. If they are not, bring the one which is to occupy square 3 to that square by rota- ting round rectangle A B, then the corner vacant in figure will be occupied with some other block than the one required to be in square 2. Rotate round A C till this block comes to square 2. Now bring these two squares by rotation round A B to the right-hand column ; and rotate the other round A C till the one which is to be in square i is in square 2. Then a forward rotation by one square round A B brings the three numbers into the required position. If the THE FIFTEEN' PUZZLE. 289 two numbers to occupy squares 2 and 3 were originally adjacent and in wrong order, we must separate them by rotating round AB till either the top or bottom row are occupied by the two numbers and a vacant square between them, into which vacant square we put the middle block of the bottom or top row, as the case may be. After this the above method can be applied. So that in every case the top row, or any three squares in sequence round AB, may be occupied by any three blocks we please in any order. We cannot do more that this, for only two blocks remain, and it may be shown for such a rectangle as A B, precisely as for the original puzzle, that one-half the possible arrange- ments, though interchangeable inter se, are not interchange- able with arrangements belonging to the other half. 1 Next take the case of a rectangle of eight squares, as A B, Fig. 1 5, where the won position for such a rectangle is shown. What we have to do in this case is to get a given set of five blocks in assigned order, into the squares i, 2, 3, 4, and 5. First, as in the last case, we get the two blocks which are to occupy the squares 3 and 4 into these squares, and by rotating backwards round C B, we bring them into the right-hand column. The remaining blocks of the five belong to the last case, since they are in a rectangle (A D) of six squares. We bring them into proper sequence, but in the squares i, 2, 3 (instead of 5, i, 2, which they are eventually to occupy). Then all the five blocks are in proper sequence, and a rotation of one square round A B brings them into the proper squares i, 2, 3, 4, 5. Next take a square of nine squares, as A B, where the won position for such a square is shown. What we have to show 1 The total displacement and the vacant line in all positions reducible to that shown in fig. 14 are either both even or both odd ; in all other positions one is even, the other odd. U 290 PAMILIAR SCIENCE STUDIES. F FIG. 16. in this case is that a given set of six blocks can be brought, in a given order, into the squares i, 2, 3, 4, 5 and 6. Now, of the blocks to occupy squares i, 2, 3, two, at least, must be in one or other of the rectangles C B, D B. According as two such are in C B or B D, bring them to position, 2, 3, or 4, 7, in their right order of sequence as around A B. In A c eacn case, shift them by rotating them round 5 to the position 3, 6, and the va- cant square to the corner B. Then, if the third block is at 2, 5, or 8, the case be- longs to that first dealt with, the three blocks to be placed being in a rectangle (C B) "of six squares, one vacant Bring them in right sequence (as around 5) to the squares 2, 3, 6, and by a rotation of one square to the position i, 2, 3. If, however, the third block is at i or at 4, shift the block in 5, 8, bringing 8 to the corner B, and then A E is a six-squared rectangle containing the three given blocks and one vacant square, and the three blocks can be brought in the required order to the squares i, 2, 3. Lastly, if the third block is at 7, rotate 3, 6, and the vacant square round C B to the positions 8, 5, 2, and again the three given blocks are in a six-squared rectangle (A F), and can be brought to the required order in squares 7, 4, i, and thence rotated round A B to squares i, 2, 3. These are all possible cases ; and as, after thus correctly filling the squares i, 2, 3, the re- maining five blocks are in a six-square rectangle D B, we can arrange them in any order we please except as regards the two which, in the final position, occupy squares 7 and 8. Next take a rectangle of four squares by three as A B, Fig. 17, where the won position for such a Here we have to show that a given set A C I 2 3 4 5 6 7 8 9 IO ii F B FIG. 17. rectangle is shown. of nine blocks can be brought, in a given order, into the squares of i, 2, 3, 4, 5,6, 7, 8, and 9. It will be most con- 'I HE FIFTEEN PUZZLE. 291 venient in this case to begin by getting into the squares i, 5, 9, the proper blocks for those squares. (It will be seen at once from what follows, that if the rectangle were three squares broad and four high, instead of three high and four broad, we should begin by the top row of three, the same method applying in all other respects to each case.) Now, of the three blocks for the left-hand column, two must be either in the square C B or in the rectangle D B. In the former case they can be brought at once to the squares 4, 8, in the latter they can be brought to 5, 9, and rotated round A Bto the squares 4, 8. Let the vacant square be then brought to the corner B, if not already there. Then, if the third block of the three is in the square C B, the last case enables us at once to bring the three in the right sequence to the squares 2, 3, 4, whence they can be rotated round A B to the required squares i, 5, 9. If the third block is at i or 5, shift the blocks 6, 10, and n (n to corner square). This frees the square 5, and the second case enables us to bring the three blocks to squares i, 2, 3, in the rectangle A E, whence we rotate them to i, 5, 9. If the third block is at 9, rotate 4, 8, and the vacant square to the positions n, 7, 3, and then the three blocks are in a square of nine squares (A F), and can be brought at once in the required order to Ihe squares i, 5, 9. Then the rest of the rectangle, namely, the square C B, can be arranged, as shown in the last case, so that all the blocks, except those for the squares 10, n, are in assigned positions. Note, also, that in this case we might have begun by getting into the right position the four blocks intended to occupy the squares i, 2, 3, 4. Thus, having first got the blocks for the squares 2, 3, 4, into the squares 9, 5, i, in the way already shown for any three blocks, we bring to the square 10 the block intended for square i, doing this by rotation around C B or C F, as the case may require, without touching the blocks in i, 5, 9 ; then rotation around A B brings the four blocks into the required squares, i, 2, 3, 4, in the assigned order. u 2 292 FAMILIAR SCIENCE STUDIES. Lastly, we reach the case of the Fifteen Puzzle itself shown in the won position in Fig. 6, and again in Fig. 18. We have to show that a given set of 13 of these blocks can be brought to the squares i, 2, 3, 4, 5, 6, 7, 8, 9, 10, n, 12, 13, in an assigned order. Here the reasoning is of precisely the same kind as in the two preceding paragraphs. Three of the four blocks meant for squares 1, 2, 3, 4, must be either in the rectangle C B or in the rectangle D B. In either case we can bring them (directly in one case, by rotation around D B in the other) to the squares 4. 8, 12. If the remaining block is in the oblong C F. we get the four into right order, down the right hand column of the oblong C B by the last case, and rotate to the required squares i, 2, 3, 4. If the fourth block is in one of the squares i, 5, 9, rotate the blocks in n, 15 (bringing the one in 15 to corner B), and then the four blocks lie in the oblong A E, and can be brought to the squares i, 2, 3, 4, as in last case. Lastly, if the fourth block is at 13, push down the blocks in 4, 8, 12, rotate those in 7, 3, bringing the one in 3 to corner square 4, and then the four blocks are in the oblong I) B, and can be brought into the lowest row in the required order, as in the last case, and thence rotated to the squares i, 2, 3, 4. After this, the rest of the square, namely, the oblong D B, can be arranged, as shown in the last case, so that all the blocks, except those in the squares 14, 15, are in assigned positions. I might here go on to show that in any square or oblong whatever, no matter how great the number of blocks in the length and breadth, all except the last two can be brought into any assigned order. To do this, all that would be necessary would be to show that, if in an oblong or square of given numbers of blocks in length and breadth the blocks can so be THE FIFTEEN PUZZLE. 293 arranged, they can also be arranged in an oblong or square having one more row added either to its length or breadth. For then, having already shown that we can so arrange an oblong of two by three, an oblong of two by four, a square of three by three, an oblong of three by four, and a square of four by four, it follows that we can similarly arrange an oblong of three by five and of four by five, a square of five by five : and so on, without limit. But I leave this as an exercise for the reader, noting only that the method is precisely similar to that by which the last case above dealt with was obtained from the last but one, that from the preceding, and so forth. In a paper which appeared in the Australasian for August 21, 1880, I have proved the above relations, and also the general case, in another way, not quite so simple but more concise ; showing that from any given position a certain number of positions must always be obtainable, and that number being (with the given position) exactly one-half of the total number of possible arrangements, must include all the cases of its own kind, that is, either winning or losing as the case may be. I have there also established the following rules for distinguishing winning from losing positions in an oblong or rectangle of any number of squares in the length and breadth. First, if the number both of horizontal and vertical rows be even (as in the Fifteen Puzzle), the won position, in which the blocks succeed each other in numerical sequence, follow- ing the lines as in reading, and leaving the last square vacant, can be obtained from any position in which the ' total dis- placement ' and the number of the partly vacant square are either both even or both odd ; but if the ' total displacement ' is even and the number of the partly vacant line odd, or vice versa, the won position cannot be obtained. Secondly, if the number of horizontal rows be odd, and the number of vertical rows even, then the won position can be obtained if the ' total displacement ' is even and the 294 FAMILIAR SCIENCE STUDIES. number of the partly vacant line odd, or vice versa. But if the ' total displacement ' and the number of the incomplete line are either both odd or both even, the won position cannot be obtained. Thirdly and Fourthly. If the number of vertical rows be odd, then, whether the number of horizontal lines be (iii) even or (iv) odd, the won position can be obtained if the ' total displacement ' is even, and cannot be obtained if the ' total displacement ' is odd. These four laws include all possible cases. Let me add in conclusion, that the total number of possible arrangements in a square of ten blocks- in the side is so great, that if we imagine each case represented by a tiny globe one millionth of an inch in diameter, and these globes gathered in the form of a great sphere, the extent of that sphere would be greater than that of the entire region of space over which the mightiest telescope yet made by man extends his survey, though, from the remotest star reached by such a telescope, light, with its stupendous velocity of 187,000 miles a second, takes thousands of years in reaching this earth. It may be noticed, in conclusion, that the above study of the ways of solving the puzzle for six-block and eight- block rectangles will be found to indicate the proper way of dealing with the only cases of difficulty which ever arise in dealing with the Fifteen Puzzle. I wrote the whole of this paper, for instance, without having before me any actual set of blocks, simply drawing mental pictures of the various cases before writing the paragraphs respectively relating to them. Yet, on the first trial with the actual puzzle, I found that four or five minutes sufficed to resolve any position into the final (won or lost) position of its own kind ; and after half-an-hour's practice (based on the principles above ex- plained) I found the solutions averaged only two minutes. 295 ETNA. THERE is a marked contrast between the circumstances of the eruption of Etna in the summer of 1879, an d those of the last preceding eruption. For many years the great South European volcanic system had shown but few signs of disturbance, and those only slight. Vesuvius had occa- sionally threatened an outbreak. The crater of that moun- tain had filled several times to the brim, and had once or twice overflowed ; but there had been no great eruption of Vesuvius. Etna had been almost entirely quiescent for the preceding ten years. The other less important outlets of the South European volcanic system had been equally free from disturbance. It was otherwise when in November 1868 Etna burst into eruption. During thirteen months the volcanic system of Southern Europe had been disturbed by subterranean movements. Scarcely a single portion of the wide area included under that name had been free from occasional shocks of earthquake. There had been shocks at Con- stantinople, at Bucharest, at Malta, and at Gibraltar. Mount Vesuvius, the most active though not in all respects the most important of the outlets by which that system finds relief, had been in a state of activity during the whole of the preceding year, and three several times in actual eruption. But it had seemed as though Vesuvius owing perhaps to changes which had taken place in its subterranean ducts and conduits had been unable to give complete relief to the forces then at work beneath the southern parts of 296 FAMILIAR SCIENCE STUDIES. Europe. Whenever Vesuvius had been quiescent for a while during 1868, earthquakes occurring at far distant places not only showed the connection which exists between the action of Vesuvius and the condition of regions far remote from Vesuvius, but that the great Neapolitan outlet was not able to relieve as usual the remote parts of that wide volcanic region. Even in England and Ireland there were earthquakes, at times corresponding significantly with the temporary quiescence of Vesuvius. In fact, scarcely ten days had passed after the occurrence of an earthquake which alarmed the inhabitants of Western Europe, before a great eruption of Vesuvius began. A vast cone was thrown up, from which the imprisoned fires burst forth in rivers of molten lava ; and round the base of this cone other smaller ones formed themselves which added their efforts to that of the central crater and wrought more mischief than in any eruption of Vesuvius since that of 1797. But, enormous as was the quantity of lava which those cones poured forth, it would seem that Vesuvius was still unable to give perfect relief to the imprisoned gases and fluids which had long disturbed the South of Europe. All that Vesuvius could do had been done ; the smaller cones had discharged the lava which communicated directly with them, and had then sunk to rest ; the great cone alone con- tinued but with diminished energy to pour forth masses of burning rock and streams of liquid lava. That the im- prisoned subterranean fires had not fully found relief was shown by the occurrence of an earthquake at Bucharest, late on the evening of November 27, which was only a day after the partial cessation of the eruption of Vesuvius. Pro- bably the masses of liquid fire which had been flowing towards Vesuvius had collected beneath the whole of that wide district which underlies Etna, Stromboli, and the Neapolitan vents. Be this as it may, it is certain that but a few hours after the occurrence of the earthquake in Walla- chia, Mount Etna began to show signs of activity, and by the evening of November 28, 1868, was in violent eruption. ETNA. 297 When we consider these circumstances in connection with the recognised fact that Etna is an outlet of the same volcanic system, we can hardly be surprised that the ineffec- tual efforts of Vesuvius should have been followed by an eruption of the great Sicilian volcano. We can imagine that the lakes of fire which : underlie the Neapolitan vent should have been inundated, so to speak, by the continual inrush of fresh matter, and that thus an overflow should have taken place into the vast caverns beneath the dome of Etna which had been partially cleared when the Sicilian mountain was in eruption in 1865. During a whole year some such process had probably been going on, until at length the forces which had been silently gathering them- selves were able to overcome the resistance of the matter which stopped up the outlets of Etna, and the mountain was forced into violent and remarkably sudden action. Unlike Vesuvius, Etna has always, within historic times, been recognised as an active volcano. Uiodorus Siculus speaks of an eruption which took place before the Trojan war, and was so terrible in character as to drive away the Sicani who had peopled a neighbouring district. We learn also from Thucydides that in the sixth year of the Pelopon- nesian war a lava-stream destroyed the suburbs of Catania. This eruption, says the historian, was the third which had taken place since the island had been colonised by the Greeks. Classical readers will scarcely need to be reminded of Pindar's graphic description of the eruption which took place fifty years before the one referred to by Thucydides. Although the poet only alludes to the mountain in passing, he has yet succeeded in presenting with a few skilful strokes the solemn grandeur of ancient Etna, the scene of the struggles of the buried giant Typhceus. He portrays the snowy mountain as ' the pillar of the heavens, the nurse of eternal snows, hiding within deep caverns the fountains of unapproachable fire ; by day a column of eddying smoke, by night a bright and ruddy flame ; while masses of burning rock roll ever with loud uproar into the sea.' 298 FAMILIAR SCIENCE STUDIES. The cone of Etna rises to more than twice the height of Mount Vesuvius. Of old, indeed, the Sicilians assigned to their mountain a height not falling very far short of that of the grandest of the Alpine mountains. But in 1815, Captain (the late Admiral) Smyth ascertained by a careful series of trigonometrical observations that the true height of the mountain is 10,874 feet. The Catanians were indignant that a young, and at that time undistinguished, Englishman should have ventured to deprive their mountain of nearly 2,000 feet of the height which had been assigned to it by their own observer Recupero, and they refused to accept the new measurement. Nine years later, however, Sir John Herschel from barometrical observations estimated the mountain's height at 10,872^ feet. The close agreement between the two results was spoken of by Herschel Lyell tells us as a ' happy accident ; ' but, as Dr. Wollaston re- marked, ' it was one of those accidents which would not have happened to two fools.' The figure of Etna is a somewhat flattened cone, which would be very symmetrical were it not that on the eastern side it is broken by a deep valley called the Val del Bove, which runs nearly to the summit of the mountain, and descending half-way down its banks is connected with a second and narrower valley, called the Val di Colonna. The cone is divided into three regions called the desert, the woody, and the fertile regions. The first of these is a waste of lava and scoriae, from the centre of which uprises the great cone. The woody region encircles the desert land to a width of six or seven miles. Over this region oaks, pines, and chestnut-trees grow luxuriantly ; while here and there are to be seen groves of cork and beech. Surrounding the woody region is a delightful and well-cultivated country lying upon the outskirts of the mountain and forming the fertile region. This part of Etna is well inhabited, and thickly covered with olives, vines, and fruit-trees. One of the most singular peculiarities of the mountain is the preva- lence over its flanks of a multitude of minor cones, nearly ETNA. 299 a hundred of which are to be seen in various parts of the woody and fertile regions. Of these, Sir Charles Lyell remarks, that ' although they appear but trifling irregularities when viewed from a distance as subordinate parts of so imposing and colossal a mountain, they would, nevertheless, be deemed hills of considerable magnitude in almost any other region.' It has been calculated that the circumference of the cone is fully eighty-seven English miles ; but that the whole district over which the lava extends has nearly twice that circuit. Of the earlier eruptions of Mount Etna we have not received very full or satisfactory records. It is related that in 1537 the principal cone, which had been 320 feet high, was swallowed up within the hollow depths of the mountain. And again, in 1693, during the course of an earthquake which shook the whole of Sicily and destroyed no fewer than 60,000 persons, the mountain lost a large portion of its height, insomuch that, according to Boccone, it could not be seen from several parts of the Valdemone whence it had before been clearly visible. Minor cones upon the flanks of the mountain were diminished in height during other outbursts in a different manner. Thus in the great eruption of 1444, Monte Peluso was reduced to two-thirds of its former height, by a vast lava-stream which encircled it on every side. Yet, though another current has recently taken the same course, the height of this minor mountain is still three or four hundred feet. There is also, says Sir Charles Lyell, 'a cone called Monte Nucilla, near Nicolosi, round the base of which successive currents have flowed, and showers of ashes have fallen, since the time of history, till at last, during an eruption in 1536, the surrounding plain was so raised, that the top of the cone alone was left pro- jecting above the general level.' But the first eruption of which we have complete and authentic records is the one which occurred in the year 1669. An earthquake had taken place by which Nicolosi, a 300 FAMILIAR SCIENCE STUDIES. town situated about twenty miles from the summit of Etna, was levelled to the ground. Near the site of the destroyed town two gulfs opened soon after, and from these gulfs such enormous quantities of sand and scoriae were thrown out that a mountain having a double peak was formed in less than four months. But, remarkable as was the evidence thus afforded of the energy of the volcanic action which was at work beneath the flames of the mountain, a yet more striking event presently attracted the attention of the alarmed inhabitants of the neighbouring country. On a sudden, and with a crash which resounded for miles around, a fissure, twelve miles in length, opened along the flanks of the dis- turbed mountain. The fissure extended nearly to the summit of Etna. It was very deep how deep is unknown but only six feet in width. Along its whole length there was emitted a most vivid light. Then, after a brief interval, five similar fissures opened one after another, emitting enormous volumes of smoke, and giving vent to bellowing sounds which could be heard at a distance of more than forty miles. At length the eruption commenced in earnest. The volume of lava which was poured forth was greater than any that has ever been known to flow from the mountain during historical times. According to the estimate of Ferrara, no less than 140 millions of cubic yards of lava were poured down the sides of the mountain. The current, after melt- ing down the foundations of a hill called Mompiliere, over- flowed no fewer than fourteen towns and villages, some of which had as many as three thousand and four thousand in- habitants. Alarmed at the progress of the sea of lava which threatened to overwhelm their city, the Catanians upreared a rampart of enormous strength and sixty feet in height. So stoutly was this bulwark established that the lava was unable to break it or to burn it down. The molten sea gradually accumulated, until at length it rose above the summit of the rampart, from which it poured in a fiery cascade, and de- stroyed the nearer part of the city. ' The wall was not ETNA. 301 thrown down, however,' says Sir Charles Lyell, 'but was discovered long afterwards by excavations made in the rock by the Prince of Biscari so that the traveller may now see the solid lava curling over the top of the rampart as if still in the very act of falling. The current had performed a course of fifteen miles before it entered the sea/ where it was still six hundred yards broad and forty feet deep. It covered some territories in the environs of Catania, which had never before been visited by the lavas of Etna. While moving on, its surface was in general a mass of solid rock ; and its mode of advancing, as is usual with lava-streams, was by the occasional fissuring of the solid walls. A gentle- man of Catania, named Pappalardo, desiring to secure the city from the approach of the threatening torrent, went out with a party of fifty men whom he had dressed in skins to protect them from the heat, and armed with iron crows and hooks. They broke open one of the solid walls which flanked the current near Belpasso, and immediately forth issued a rivulet of melted matter which took the direction of Paterno ; but the inhabitants of that town, being alarmed for their safety, took up arms and put a stop to further operations.' In the eruption of 1755 a singular circumstance oc- curred. From the Val del Bove, usually dry and arid, there flowed a tremendous volume of water forming a stream two miles broad, and in some places 34 feet deep. It flowed in the first part of its course at the rate of two miles in three minutes. It is said to have been salt, and many supposed it had been in some way drawn from the sea, since its volume exceeded that of all the snow on the mountain. It has, however, since been found that vast reservoirs of snow and ice are accumulated in different parts of the mountain beneath the lava. The snow was melted by the heat of the rising lava, and was made salt by vaporous exhalations. Of the singular solidity of the walls of an advancing lava-stream, Recupero has related a remarkable instance. During the eruption of 1766, he and his guide had ascended 302 FAMILIAR SCIENCE STUDIES. one of those minor cones which lie, as we have said, on the flanks of the mountain, and from the summit of this hill they watched with feelings of awe the slow advance of a fiery river two miles and a half in breadth. Suddenly they saw a fissure opening in the solid walls which encircled the front of the current of lava ; and then, from out this fissure, two streams of lava leapt forth and ran rapidly towards the hill on which the observers were standing. They had just time to make their escape, when, turning round, they saw the hill surrounded by the burning lava. Fifteen minutes later the foundations of the hill had been melted down, and the whole mass floated away upon the lava, with which it pre- sently became completely incorporated. It would be a mistake, however, to suppose that such an occurrence as the one we have just related is often observed. On the contrary, it seems that when burning lava comes into contact with rocky matter, the latter is usually very little affected. It is only when fresh portions of incandescent lava are successively brought into contact with fusible rocks that these can be completely melted. Sir Charles Lyell quotes a remarkable story in illustration of the small effects which are produced by lava when there is not a continual supply of fresh material in an incandescent state. ' On the site of Mompiliere, one of the towns overflowed in the great eruption of 1669, an excavation was made in 1704 ; and by immense labour the workmen reached, at the depth of 35 feet, the gate of the principal church, where there were three statues held in high veneration. One of these, together with a bell, some money, and other articles, was extracted in a good state of preservation from beneath a great arch formed by the lava.' This will seem the more extraordinary when it is remembered that eight years after the eruption the lava was still so hot at Catania, that it was impossible to hold the hand in some of the fissures. Among the most remarkable of the eruptions of Etna which have taken place in recent times are those of 1811 and 1819. ETNA. 303 In 1 8 1 1, according to Gemmelaro, the great crater gave vent, at first, to a series of tremendous detonations, from which it was judged that the dome of the mountain had become completely filled with molten lava, which was seek- ing to escape. At length a violent shock was experienced, and from what followed it would seem that by this shock the whole internal framework of the mountain had been rent open. For, first a stream of lava began to pour out from a gap in the cone not far from the summit. Then another stream burst out at an opening directly under the first, and at some distance from it. Then a third opening appeared, still lower down ; then a fourth, and so on, until no less than seven openings had been formed in succession, all lying in the same vertical plane. From the way in which these openings appeared, and the peculiarity that each stream of lava had ceased to flow before the next lower one burst forth, it is supposed that the internal framework of the mountain had been rent open gradually, from the sum- mit downwards, so as to suffer the internal column of lava to subside to a lower and lower level, by escaping through the successive vents. This, at least, is the opinion which Sc'rope has expressed on the subject, in his treatise on ' Volcanoes.' The eruption of 1819 was in some respects even more remarkable. I have already mentioned the Val del Bove, which breaks in upon the dome of Etna upon the eastern side. In the eruption of 1819 the whole of this great valley was covered by a sea of burning lava. Three large caverns had opened not far from the fissures, out of which the lava had flowed in 1811 ; and from these, flames, smoke, red-hot cinders, and sand were flung out with singular impetuosity. Presently another cavern opened lower down, but still no lava flowed from the mountain. At length a fifth opening formed, yet lower, and from this a torrent of lava poured out, which spread over the whole width of the Val del Bove, and flowed no less than four miles in the first two days. This torrent of lava was soon after enlarged by the acces- sion of enormous streams of burning matter flowing from 304 FAMILIAR SCIENCE STUDIES. the three caverns which had formed in the first instance. The river of lava at length reached the head of the Colonna Valley, where there is a vast and almost vertical precipice, over which the lava streamed in a cataract of fire. But there was a peculiarity about the falling lava which gave to the scene a strange and awful character. As the burning cascade rushed down, it became hardened through the cool- ing effects due to its contact with the rocky face of the pre- cipice. Thus, the matter which had flowed over the head of the valley like a river of fire fell at the foot of the pre- cipice in the form of solid masses of rock. The crash with which the falling crags struck the bottom of the valley is described as inconceivably awful. At first, indeed, the Catanians feared that a new eruption had burst out in that part of the mountain, since the air was filled with clouds of dust, produced by the abrasion of the face of the precipice as the hardened masses swept over it. The length of time during which the lava of 1819 con- tinued to flow down the slopes of the great valleys is well worth noticing. Mr. Scrope saw the current advancing at the rate of a yard per hour nine months after the occur- rence of the eruption. The mode of its advance was re- markable. As the mass slowly pushed its way onward, the lower portions were arrested by the resistance of the ground, and thus the upper part would first protrude itself, and then, being unsupported, would fall over. The fallen mass would then in its turn be covered by a mass of more liquid lava, which poured over it from above. And thus ' the current had all the appearance of a huge heap of rough and large cinders rolling over and over upon itself by the effect of an extremely slow propulsion from behind. The contraction of the crust as it solidified, and the friction of the scoriform cakes against one another, produced a crackling sound. Within the crevices a dull red heat might be seen by night, and vapour issuing in considerable quantity was visible by day.' The circumstance that Etna uprears its head high above the limit of perpetual snow has a remarkable bearing on the ETNA. 305 characteristics of this volcano. The peculiarity is touched on by Pindar in the words already quoted, in which he speaks of- Etna as 'the nurse of everlasting frost concealing within deep caverns the fountains of unapproachable fire.' It will be readily conceived that the action of molten lava upon the enormous masses of snow, which lie upon the upper part of the mountain, must be calculated to produce under special circumstances the most remarkable and, unfortunately, the most disastrous effects. It does not always happen that fire and ice are thus brought into danger- ous contact. But records are not wanting of catastrophes produced in this way. In 1755, for example, a tremendous flood was occasioned by the flow of the two streams of lava from the highest crater. The whole mountain was at the time (March 2nd) covered with snow, and the torrent of lava formed by the union of the two streams was no less than three miles in width. It will be readily conceived that the flow f such a mass of molten fire as this over the accumu- lated snows of the past winter produced the most disastrous effects. ' A frightful inundation resulted,' says Sir Charles Lyell, ' which devastated the sides of the mountain for eight miles in length, and afterwards covered the lower flanks of Etna (where they were less steep), together with the plains near the sea, with great deposits of sand, scoriae, and blocks of lava.' In connection with this part of the subject I may mention the singular and apparently paradoxical circumstance that, in 1828, a large mass of ice was found, which had been pre- served for many years from melting by the fact that a current of red-hot lava had flowed over it. We might doubt the occurrence of so strange an event, were it not that the fact is vouched for by Sir Charles Lyell, who visited the spot where the ice had been discovered. He thus relates the circum- stances of the discovery : 'The extraordinary heat expe- rienced in the South of Europe, during the summer and autumn of 1828, caused the supplies of snow and ice which had been preserved in the spring of that year for the use of 306 FAMILIAR SCIENCE STUDIES. Catania, and the adjoining parts of Sicily, and the island of Malta, to fail entirely. Great distress was consequently felt for want of a commodity regarded in those countries as one of the necessaries of life rather than an article of luxury, and the abundance of which contributes in some of the larger cities to the salubrity of the water and the general health of the community. The magistrates of Catania applied to Signer Gemmelaro, in the hope that his local knowledge of Etna might enable him to point out some crevice or natural grotto on the mountain where drift snow was still preserved. Nor were they disappointed ; for he had long suspected that a small mass of perennial ice at the foot of the highest cone was part of a large continuous glacier covered by a lava-current. Having procured a large body of workmen, he quarried into this ice, and proved the superposition of the lava for several hundred yards, so as completely to satisfy himself that nothing but the subsequent flowing of the .lava over the ice could account for the position of the glacier ' (in other words, the ice had not accumulated in a cavern of moderate extent accidentally formed beneath overhanging lava masses ). ' Unfortunately for the geologist,' adds Lyell, ' the ice was so extremely hard, and the excava- tion so expensive, that there is no probability of the opera- tions being renewed.' This strange phenomenon is explained, in all likelihood, by the fact that the drift of snow over which the lava flowed had become covered with a layer of volcanic sand before the descent of the molten matter. The effect of sand in resist- ing the passage of heat is well known. Nasmyth the in- ventor of the steam-hammer illustrated this property in a re- markable manner, by pouring eight tons of molten iron into a cauldron one -fourth of an inch thick, lined with a layer of sand and clay somewhat more than half an inch thick. When the fused metal had been twenty minutes in the cauldron the outside was still so cool that the palm of the hand could be applied to it without inconvenience. And lava consolidates so quickly that there must soon have been ETNA. 307 formed over the snow a solid covering, strong enough to resist the effects of the fresh molten matter which was con- tinually streaming over it. In this way we may readily con- ceive, as Sir Charles Lyell has remarked, that a. glacier 10.000 feet above the sea level would endure as long as the snows of Mont Blanc, unless heated by volcanic heat from below. It is worthy of notice that in the Antarctic seas there is an island called Deception Island, which is almost entirely composed, according to the authority of Lieut. Kendall, of alternate layers of ice and volcanic ashes. One of the most perplexing subjects to geologists is the existence of so remarkable a valley as the Val del Bove, breaking the contour of the dome of Etna nearly to the summit. It must be remembered that there are few subjects which have been more carefully examined than the question of the formation of valleys and ravines. The primary agent recognised by geologists is the action of subterranean forces in upheaving and depressing the land. In this way, doubt- less, all the principal valleys have been formed. But fluviatile influences have also to be considered : and a valley which exists upon the flank of a mountain may, in nearly every instance, be ascribed to the action of running water. In the case of the Val del Bove, however, we are forced to come to a different conclusion. If this valley had been formed by the action of running water in some long-past era of the mountain's history, the chasm would have deepened as it approached the base. On the contrary, the precipices which bound the Val del Bove are loftiest at the upper ex- tremity, and gradually diminish in height as we approach the lower regions of the mountain. Nor can we imagine that the valley has been formed by a landslip. The dimensions of the depression are altogether too great for such an explanation to be available. And, passing over this circumstance, we are met by the consider- ation that, if the land which once filled this valley had x 2 3 o8 FAMILIAR SCIENCE STUDIES. 1 slipped ' (in the ordinary sense of the term), we should see the traces of the movement, and be able to detect the exist- ence of the removed mass. Not only is there no evidence of a motion of this sort, but the slightest examination of the valley at once disposes of the supposition that such a motion can at any time have taken place. It remains only that we suppose the valley to have been caused by the bodily subsidence of the whole mass which had formerly filled up what is now wanting to the dome- shaped figure of the mountain. And the subsidence must have taken place in a sudden manner, not necessarily in a single shock, but certainly not by a slow process of sinking. For the mass which has sunk is sharply separated from the rest, so that the precipitous walls of the valley exhibit the structure of the mountain's frame, to a depth of from 3,000 to 4,000 feet below the summit of the cone. In other words, a portion of the crust has been separated from the rest and has then sunk bodily down, leaving the remainder un- changed. When we consider the dimensions of the valley, such an event becomes very startling. ' The Val del Bove,' says Lyell, ' is a vast amphitheatre, four or five miles in diameter, surrounded by nearly vertical precipices.' One might almost be prepared to doubt that such a valley as this could be formed in the manner described, were it not that within recent times we have had evidence of the occurrence of similar events. During a violent earthquake and volcanic eruption which took place in Java in 1822, the face of the mountain Galongoon was totally changed, 'its summits broken down, and one side, which had been covered with trees, became an enormous gulf in the form of a semicircle. This cavity was about midway between the summit and the plain, and surrounded by steep rocks.' Yet more remark- able was the great subsidence which took place in the year 1772 on Papendayang, the largest volcano in the island of Java. On that occasion, ' an extent of ground fifteen miles in length and six in breadth, covered by no less than forty ETNA. 309 villages, was engulfed, and the cone of the mountain lost 4,000 feet of its height.' There is nothing unreasonable, therefore, in supposing that some such event may have resulted in the formation of the strange valley which mars the dome-shaped figure of Mount Etna, although no such events have been witnessed in the neighbourhood in recent times. One singular feature of the valley remains to be men- tioned. The vertical face of the precipices which bound it are broken by what, at a distant view, appear to be dark buttresses, strangely diversified in figure, and of tremendous altitude. On a closer inspection, however, these strange objects are seen to be composed of lava jutting out through the face of the cliffs. Being composed of harder materials than the cliffs, they waste away less rapidly, and thus it is that they are seen to stand out like buttresses. Now, we would invite the close attention of the reader to this part of our subject, because, as it seems to us, it illustrates in a sin- gularly interesting manner the mode in which volcanic cones are affected during eruption. We have seen that in the eruption of i8n there was evidence of a perpendicular rent having taken place in the internal framework of Etna, and in 1669 a fissure was formed which extended right through the outer crust. In one case lava was forced through the rent, and burst out at the side of the mountain. In the other, the brilliant light which was emitted indicated the presence of molten lava deep down in the fissure. Now, when we combine these circumstances with the dykes seen in the Val del Bove, and with the similar appearances seen round the ancient crater of Vesuvius, we can come, as it appears to me, to but one conclusion. Before and during an eruption, the lava which is seeking for exit must be forced with such tremendous energy against the internal framework of the mountain's dome, as to fracture and rend the crust, either in one or two enormous fissures, or in a multitude of smaller ones. It does not follow that all or any of the fissures would be visible, because the outer 310 FAMILIAR SCIENCE STUDIES. surfaces of the crust may not be rent. Into the fissures thus formed the lava is forced by the pressure from below, and, there solidifying, the crust of the dome remains as strong, after the liquid lava has sunk to its usual level, as it was before the eruption. When we see dykes situated as in the Val del Bove, we learn that the fissures caused by the pressure of the lava extend far down the flanks of a volcanic mountain. That they are numerous is evidenced by the fact that those seen in the Val del Bove amount, according to Sir Charles Lyell, to ' thousands in number.' And perhaps we may understand from such considera- tions as these the manner in which the Val del Bove itself was formed. For a wide strip of country between two great fissures might be so waved and shaken by the action of the sea of molten lava beneath as to be fractured cross-wise ; and then, on the subsidence of the lava, the whole mass below the fracture would sink down bodily. We gain an extended conception of the energy of the forces which arc at work during volcanic eruptions, when we see that they thus have power to rend the whole framework of a moun- tain. Among recent eruptions of Mount Etna, one of the most singular was that of the year 1852, which began so suddenly that a party of Englishmen, who were ascending the mountain, and had nearly reached the foot of the highest cone, were only able to escape with great difficulty. The eruption which had commenced so abruptly did not cease with corresponding rapidity, but continued with but few slight intermissions, for fully nine months. The eruption in progress as I write has not yet attained any remarkable degree of energy, though possibly before these lines appear, another story may have to be told. In the last week of May a fissure opened on the north side of the mountain, ' and thence volumes of smoke and flame were seen to issue from it. From the crater itself, a great cloud of black ashes has been poured forth, rendering the mountain invisible and obscuring the rays of the sun ' (by ETNA. 311 which the writer must surely mean obstructing their passage), ' even at a distance of many miles. These ashes have been carried far and wide, and have even covered the ground as far away as Reggio, on the adjacent coast of Calabria. Three new craters .have opened in the direction of Randazzo, on the north side of the mountain, and the lava is running rapidly towards the town of Francavilla, where great alarm is felt, though that town is situated beyond the river Alcantara, and on the very outskirts ot the region usually threatened by eruptions. On the opposite side of the mountain, Palermo and the adjacent villa of Santa Maria di Licodia are reported to be greatly alarmed.' But at present the direction of the disturbance is towards the north, and the chief danger lies therefore also in that direction. The new craters, and the fissure with which the eruption began, lie all on the northern side of the mountain. 'The stream of lava, which is estimated to be 70 metres' (about 75 yards) ' in width, is flowing in a direction some- where between Francavilla and Randazzo, and seems to have reached the high road which encircles the mountain, and connects the latter town with the villages Linguaglosso and Piedimonte. These villages are inshrouded in a canopy of ashes, and almost total darkness prevails in them. None of the ordinary concomitants of a great eruption seem to be absent. Balls of fire, or what are taken for such, are hurled into the air from the new craters and fissuies, and, having reached a great height, they burst with a loud crash. Reports like the rolling of artillery are heard in the night, while night and day alike the stream of lava flows stealthily and irresistibly on, until by the latest accounts it has reached to within a few miles of Linguaglossa.' Whether the eruption now in progress will attain the dimensions of the more remarkable of those which have preceded it, remains to be seen. As the last took place ten years ago, and was considerable, though following one which has occurred but three-and-a-half years earlier, it seems not unlikely that the present may be an important eruption. 312 FAMILIAR SCIENCE STUDIES. What we know already respecting it, tends to confirm the belief of Sir Charles Lyell, that, if the earth's internal fires are diminishing in intensity, the diminution takes place very slowly. A process of change may be going on which will re- sult one day in the cessation of all subterranean movements. But the rate at which such a process is going on is so slow at present as to be imperceptible. We cannot point to a time within the historical era, or even within that far wider range of duration which is covered by geological records, at which the earth's internal forces were decidedly superior in energy to those at present in action. Nor is this to be re- garded as of evil import, but altogether the reverse. The work achieved by subterranean action, destructive though its immediate effects may often appear, is absolutely neces- sary to the welfare and happiness of the human race. It is to the reproductive energy of the earth's internal forces that we are indebted for the existence of continents and islands on which warm-blooded animals can live. ' Had the primeval world been constructed as it now exists,' says Sir John Herschel, ' time enough has elapsed, and force enough directed to that end has been in activity, to have long ago destroyed every vestige of land.' So that, raising our thoughts from present interests to the future fortunes of the human race, we may agree with Sir Charles Lyell that the most promising evidence of the permanence of the present order of things consists in the fact that the energy of sub- terranean movements is always uniform, when considered with reference to the whole of the earth's globe. WEATHER FORECASTS. A FEW years ago attention was called to the circumstance that whereas, in the United States, daily weather forecasts appeared whereof rather more than four-fifths were correct, our English weather reports were limited to announcements of the weather which had prevailed the day before, except in a few cases where storms or transient disturbances were pre- dicted with a fair share of success. At that time it seemed to be the general opinion of British meteorologists that such weather warnings as were then and are still issued in America could not be given in this country. Mr. Scott, the director of the Meteorological Office, said only four years ago that the results attained in the United States ' furnished no prece- dent for us,' because ' the area covered by the telegraphic system there is so much larger than in Western Europe, irrespective of the fact ' that ' the system is military and provided on a most liberal scale with funds.' Since that time a system of daily weather forecasting has been arranged, which has been almost as successful as the American system, notwithstanding the serious difficulties with which the meteorologists of Western Europe have to contend. Our meteorologists have learned to recognise certain rules of the weather, which, though not invariable, are yet fulfilled in a large proportion of cases. They have learned to indicate the weather phenomena at any given time in such a way that these rules can be applied quickly and correctly correctly, it will be understood, in this sense, that the result- indicated is correctly described as the most probable though the 314 FAMILIAR SCIENCE STUDIES. forecast accordingly made may not be fulfilled by the event. Those little maps which appeared in The Times and other newspapers for many months before forecasts began to be made illustrate well the general principle on which weather predictions for the British Isles or for Western Europe, depend. Compare even the simplest of these charts with a table of meteorological statistics for fifty or sixty stations, and the value of the graphic method is at once recognised. The clearest head could not, after hours of study, deduce any law from the most complete and elaborate table of meteorological statistics. But it is by no means difficult to construct a chart from such a table, and the chart shows at a glance the state of the weather for the whole region over which meteorological stations are distributed. We see the lines of equal barometrical pressure (that is, of equal atmospheric density), the regions of low pressure around which the winds usually blow (as the wind-arrows show in cyclonic circulations), the areas of high pressure, or anti-cyclones as they are called, and we learn whether the general pressure over the whole region is above or below the average ; the direction and force of the winds are indicated simply and clearly ; the temperatures are shown ; and we see also where rain is falling, so learning whether the area of low pressure is, as usual, wet, and, if so, in what degree, or whether it is simply cloudy, and the nature of the clouds prevailing there and elsewhere. A single map thus teaches a good deal. But yet more is learned when the map for a given time is compared with the series of preceding maps. For we thus learn in what way the areas of low barometric pressure are travelling whether, as usual, from a southerly or westerly to a northerly or easterly point, or (as occasionally happens) from a northerly or easterly to a southerly or westerly point. We note whether as they travel they are gathering or losing moisture ; whether the wind is increasing or diminishing in force at given distances from the cyclone centre ; whether the curves of equal barometric pressure are drawing closer (which indicates sharp pressure gradients or WEATHER FORECASTS. 315 rapid change of pressure) or drawing apart (which indicates that pressure is becoming more equable). We note, also, how temperature is changing with the progress of the area or areas of low or of high pressure, whether the skies are clear- ing, or darkening, and so forth. From such indications the probable progress of weather changes during the next few hours can be inferred, with more or less confidence, accord- ing as the changes over the region of observation have been steady or the reverse during the preceding hours or days. In some cases it becomes possible to forecast with tolerable confidence the progress of the weather during more than twenty-four hours ; in others, though forecasts may be issued very little reliance can be placed upon them, simply because the circumstances of the preceding changes indicate that the atmosphere is in an exceptionally variable condition. It is to be noticed, also, that when the skies are generally overcast the chances of correct prediction are considerably diminished for this reason, simply that the upper air-currents, which have a most important influence in producing weather changes, cannot at such times be studied, our only means of determining their direction and rate consisting in the observation of the movements taking place in the higher cloud-regions. It is also a great assistance to the meteoro- logist to know the nature of the higher clouds above different parts of the region where observations are made, for some of the most important weather changes depend principally on the temperature of the upper air-currents, and this can only be inferred from the appearance of the clouds which travel or are formed in those higher regions. So many of our weather changes travel, from S.W. to N.E., or from some southerly or westerly towards some northerly or easterly point, that the prediction of weather changes in the British Isles is rendered much more difficult than it would be if there were a number of available stations towards the south-west instead of a wide extent of ocean, from which only imperfect meteorological information can reach us. Even in the most frequented seas ships are 316 FAMILIAR SCIENCE STUDIES. widely enough scattered. Not one in a hundred can give any information to meteorologists which can be of use in predicting weather, because most ships are not sailing for ports near enough for any meteorological information to reach them in good time for use in forecasts. In fact, Mr. Scott remarks, that even as regards the climatology of the sea we can get only imperfect information. ' The endeavour to give a correct account of the climate of any district of the sea presents,' he says, ' much the same prospect of suc- cess as we should have, were we set to determine the climate of the different parts of France, from observations made by English tourists in their railway journeys through the length and breadth of the land.' But, if this is the case as regards climate, how much more hopeless must be the attempt to get weather indications from sea regions. We might form a fair idea of the climate of a district of France by combining together the reports of a great number of railway tourists, because time would help us. But time would be against us in the attempt to learn from such reports what weather changes, if any, were travelling towards us from France. Before the reports of a sufficient number of travellers could be received and analysed, the weather changes would have come and gone, and the reports would have become useless. In fact, when we consider that the prediction of weather has only been rendered possible (as all meteorologists admit) by the facilities of communication afforded by the electric telegraph, and that it is impossible to communicate telegraphi- cally with ships at sea (unless a ship chances to be laying a submarine cable) we perceive that the presence of a wide expanse of ocean on that side of a land region, from which most weather changes travel, must render satisfactory prediction exceedingly difficult. In fact it is impossible, usually, to make satisfactory forecasts for the western parts of Ireland. In the United States also, it is noticed that the predictions for the eastern and northern States are on the whole more correct than those for the western and southern States. WE A THE K FORECASTS. 317 We may here consider those American predictions of European weather which have been made during the last few years with a fair degree of success. The first storm predicted by the New York Herald arrived as threatened, though not quite in the way expected, for instead of arriving from the south-west it came from the north. After that, other telegrams were received, which for the most part were justified by the event, though they have nearly all been characterised by the same defects they have been too vague as to time, and they have given no means of determi- ning in what direction the gale, when it arrived, would blow. There are those, indeed, who deny that any storms have really crossed the Atlantic as predicted, and consider the apparent fulfilment of some among the predictions of the New York Herald as merely accidental. Still, there can be little doubt that the predictions are made in all good faith, and are based on real evidence as to the condition of the Atlantic. It would be interesting to know how these forecasts are arrived at. As General Strachan has remarked, ' Our American friends are not very willing to " show their hands," as the saying is.' However, we may surmise how it is done. They have active agents who make extracts of the logs of all the steamers directly they arrive in New York, and by means of these extracts they can follow up all the storms which occur in our parallels. Thus it may often happen that information of storms is obtained by the Herald before they have had time to reach Western Europe. The Herald at once flashes the news by tele- graph. We get the telegram surely and speedily, and the storm, if it does not vanish in due time, shortly afterwards. It is singular and illustrates strikingly the way in which storms travel usually from the south-west (though the wind may first begin to blow from other quarters) that we should thus receive news from America brought thither by ships sailing towards the south-west or meet- ing the storm. No ship sailing towards Europe ever brings news of an approaching storm, for the storm 3 i8 FAMILIAR SCIENCE STUDIES. reaches us first. It will be observed, too, how completely the prediction of weather depends on telegraphic communi- cation. If we are ever to have effective weather reports from the Atlantic, it can only be by arranging some system of communication like that by which, during the voyages of cable-laying ships, we have had hourly news of their progress and of the weather prevailing in the parts they are traversing. But we can see no hope at present of any such system being devised ; certainly, none could be arranged with our present means of submarine communication. The American storm- warnings, though sometimes fulfilled, are not altogether satisfactory. As we have said, some meteorologists doubt whether storms ever have traversed the Atlantic from America to Europe ; and Professor Loomis, the American meteorologist, has shown that only a small proportion of the storms which reach Western Europe from the Atlantic can be identified with the disturbances which had previously been recognised either in America or in the western parts of the North Atlantic. It must be admitted that the prediction of weather changes is making progress. A^eady it has falsified Arago's well-known saying, ' Jamais, quels que puissent etre les progres des sciences, les savants soucieux de leur reputation ne se hasarderont a predire les temps,' and has passed beyond the range indicated by. Leverrier, who considered that science could not hope for more in this direction than the recognition of the progress of a storm and the issue of useful storm-signals. But there still remains room for further progress, and good reason to believe that further progress will be achieved. Not only are our meteorologists learning to recognise more and more clearly the laws according to which atmospheric movements and changes of condition proceed, and so deriving more and more satisfac- tory information from the observations already made, but they are extending the range of observation, and they are establishing stations in regions whence effective information can be obtained instead of merely increasing the number of WEATHER FORECASTS. 319 stations in regions already occupied. They also recog- nise now more clearly than of yore the necessity of care in selecting stations for weather-study, as distinguished from climatology where the conditions are such that the indications are general, not peculiar to the place. ' Geo- graphical position and freedom from conditions which will affect the character of the observations, especially of wind, are here,' says the Director of the Meteorological Office, ' of paramount importance. If an opportunity occurs of obtaining a report from a new station which will give us earlier and surer intimation of coming changes of weather, we reject ruthlessly offers of observations from the most ably-served observatory in the district,' meaning in the district already occupied. What we specially want at present, however, for satisfactory weather prediction, is the establish- ment of stations at a distance, so that rapidly- approach ing weather changes may be recognised before they are actually upon us. In this connection we may call special attention to the proposal of Count Wilczekand Lieutenant Weyprecht, that a system of observatories should be established at suitable points around the polar regions. They indicate, as suitable parts of the northern hemisphere, the north coasts of Spitzbergen and of Novaya Zemlya, the neighbourhood of the North Cape, the Mouth of the Lena, New Siberia, Point Barrow, on the North East of Behring Strait, the west coast of Greenland and the east coast of Greenland in about 75 deg. north latitude. For the southern polar region they name the neighbourhood of Cape Horn, Kerguelen, or Macdonald Islands, and some one of the groups south of the Auckland Islands. Mr. Scott points out that one good station on Spitzbergen or Jan Mayen would be worth as much as ten in Western Europe, and therefore it can readily be understood that if the far-seeing scheme of Wilczek and Weyprecht were carried out, a great advance would before long be noted in the accuracy of weather forecasts, and possibly a considerable increase in the range of time over which our meteorologists could extend their predictions. 320 FAMILIAR SCIENCE STUDIES, The possibility of foretelling weather for two days as satisfac- torily as we can now make forecasts for one day, would give far more than twofold value to the system of prediction. We have hitherto said nothing on a subject which at the present time is attracting more serious attention than the daily forecasting of weather the possibility, namely, of anticipating the probable character of approaching seasons. Unfor- tunately, we have but too good reason for saying little on this subject, since there is little to be said, and nothing that can be regarded as promising. We have lately passed through (or rather we are now passing through) an altogether exceptional period of cold and wet weather. If there ever has been an occasion when approaching weather should have afforded some evidence of its character it would seem to have been in the autumn of 1878, yet there was no circumstance in the weather prevailing from Midsummer, 1878, until the beginning of November, which suggested the approach of one of the longest and altogether the bitterest spells of cold weather ever experienced in Western Europe. So of the recent heavy and long-continued rainfalls, and of those experienced in 1872, in the autumn of 1875, an d last year. Not a sign was noted by meteorologists of the approach of those plagues of water. Some have told us that there are weather cycles corresponding with the sun-spot period; but not the slightest connection can be traced between the sun-spot changes and either our temperature or ur rainfall. The heavy rainfall of 1875 occurred when spots were numerous, the deluges of 1878 and of the present year when spots were few or absent altogether. The long continued cold of the year 1879 occurred when spots have been few, but among the series of long cold spells (some even longer than the one now in progress has yet lasted) some of the most remark- able have occurred when spots were most numerous, others when, as in 1879, spots were few, and others in almost every part of the sun-spot cycle. Nor can we form any opinion as to the probable duration of WEATHER FORECASTS. 321 any spell of cold or of wet weather. We may say now what was said by Mr. Scott four years ago, but unfortunately we may now say it with far more point, ' as to the prediction of weather ' for a long time in advance, ' it has riot been shown to be feasible to forecast weather even for one short week, except on the principle, which affords us scanty con- solation, that weather when once established takes a long time to change.' . . . ' This does not mean that the chances are in favour of the weather never changing, but are only against its changing on a definite day, and increase with the length of time the existing weather has lasted.' 322 FAMILIAR SCIENCE STUDIES. SOME STRANGELY FULFILLED DREAMS. So far as can be judged by ordinary methods of interpreta- tion, it would seem that in the days when the history of Joseph was written, and again in the time of Daniel, no doubt was entertained respecting the supernatural origin of all dreams. Joseph's brothers, according to the narrative, took it for granted that Joseph's dreams indicated something which was to happen in the future. Whether they questioned the validity of his own interpretation is not altogether clear. They hated him after his first dream, and envied him we are told, after his second ; which shows they feared he might be right in his interpretation ; but, on the other hand, they conspired together to slay him, which suggests that they entertained some doubts on the subject. In fact, we are expressly told that when they conspired against him, they said, ' Behold, this dreamer cometh ; come now therefore, and let us slay him,' and so forth, ' and we shall see what will become of his dreams.' Jacob, moreover, though he had ' observed ' Joseph's ' saying ' about the dream (after rebuking him for telling the story), seems to have taken Joseph's death for granted : 'Joseph is without doubt rent in pieces.' Possibly in those days, even as now, dreams were noticed when they were fulfilled, and forgotten when, as it seemed, they remained unfulfilled. In like manner, when the butler and baker of Pharaoh dreamed each man his dream in one night, they were sad (that is, serious) the morning after : for they could not SOME STRANGELY FULFILLED DREAMS. 323 understand what the dreams meant. But Joseph said, ' Do not interpretations belong to God ? ' Doubtless this was the accepted belief in the days when the history of Joseph was written. It is singular that the butler, though he forgot Joseph till Pharaoh's dreams reminded him of his fellow- prisoner, seems to have associated the power of interpreting the two dreams with the power of bringing about the events supposed to be portended by the dreams. ' It came to pass, as he interpreted to us, so it was ; me he restored unto mine office, him he hanged.' It is just thus that, in our own time, persons who believe in the claims of fortune-tellers to predict the future, commonly believe also that fortune-tellers can to some degree control the future also. Pharaoh's dreams were rather more fortunate to Joseph than either his own or those of the chief butler and baker. (It is noteworthy how the dreams of the story run in pairs.) In fact, one might be led to surmise that he inherited something of the ingenuity shown by his father's mother referring to an arrangement, a year or two before Joseph entered the world, in which his mother showed to no great advantage, according to modern ideas. Be this as it may, it was certainly a clever thought of Joseph to sug- gest that the unfavourable weather he had predicted might be provided against by appointing a man discreet and wise to look after the interests of Egypt. Whom was Pharaoh likely to appoint but the person who had predicted the seven bad harvests ? Even so, in these our own times, another Joseph told the British Pharaoh who lately ruled over India that years of famine in India can be predicted, and their effects prevented by appointing a man discreet and wise to look after the interests of India. And it is curious enough that this modern Joseph seems to have turned his thoughts to his ancient namesake, putting forward the idea that the seven good years and the seven bad years were years of many sun-spots, followed by years of few sun-spots. Nay, so strangely do these coincidences sometimes run on all-fours, that the younger Joseph has adopted the idea that 324 FAMILIAR SCIENCE STUDIES. the pyramids of Egypt (which were once thought to be Joseph's store-houses) were ' astronomical instruments.' Now, it is certain, though this he has not noticed, that before the upper half (in height) of the great pyramid was set on, the great ascending gallery might have been used all the year round for observing the sun at noon ; and that by using a dark screen at its uppermost or southern extremity, and admitting the sun's light only through a small opening in this curtain, a large and well-defined image of the sun could have been obtained without any telescope, an image showing any large spots which might be present on the sun's disc. It would be a pleasant theory (and all the better suited for association with the sun-spot-weather theory, in having no valid evidence in its favour) to suggest that Joseph really ascertained the approach of good and bad harvests by solar observations. His advice was that the fifth part of the land of Egypt should be taken up that is, stored up in the seven plenteous years : but the Astronomer-Royal for Scotland assures us that the numbers five and seven are symbolised repeatedly in the great pyramid. Could anything clearer be desired ? But although I have been allowing fancy to lead me far away from facts, I think it may safely be inferred from the story of Pharaoh's dreams that the prediction of good and bad harvests was one of the qualities which the Pharaohs chiefly valued in their wise men, whether magi or astro- logers. The story of Nebuchadnezzar's dream is still more sin- gular. I suppose the usual service expected by the kings of Babylon from their soothsayers included the interpretation of all dreams which had left a strong impression on the king's mind dreams like the night visions of Eliphaz the Temanite, bringing fear and trembling, making all the bones to shake. It does not seem to have entered into the ordinary course of their duties to tell the king first what he had dreamed (when he had forgotten), and afterwards what the dream might signify. Indeed, though it is not a very un- SOME STRANGELY FULFILLED DREAMS. 325 common occurrence to forget a dream, yet a dream which has been forgotten does not generally leave a very strong impression, and therefore would not require interpretation. It happened otherwise with Nebuchadnezzar. His spirit was troubled, and his sleep broke from him, because of his dream, but what he had dreamt he could not remember. His action hereupon was somewhat crazy : but we must re- member there was madness in his blood. He told the Chaldseans, that ' if they would not make known to him his dream and the interpretation thereof, they should be cut in pieces, and their houses made a dunghill.' This was pre- cisely the way, one would imagine, to cause them to invent a dream for him (he could not have detected the truth very well), and to have devised a suitable interpretation, pleasing in the king's eyes which to persons of their ingenuity should not have been very difficult. 1 However, we must not further consider these more ancient dreams, but turn at once to the examination of some of those remarkable dreams of modern times which have been regarded as showing that dreams are really sent in some cases as forewarnings, or at any rate as foreshadowings of real events. I propose to consider these narratives with special reference to the theory that dreams which seem to be fulfilled are fulfilled only by accident : so many dreams occurring and so many events, that it would in fact be stranger that no such fulfilments should be recognised than that some among them should seem exceedingly striking. There is one dream story which can hardly be explained by the coincidence theory, if true in all its particulars. It is related by Dr. Abercrombie as deserving of belief, though 1 A great deal in the art of dream-interpretation for the rich and powerful must obviously have depended on ingenuity in making things pleasant. Thus, when an Eastern potentate dreamt that all his teeth fell out, and was told that he was to lose all his relatives, he slew the indiscreet interpreter; but when another and a cleverer interpreter told him the dream promised long life, and that he would survive all his relatives, he made the man who thus pleasantly interpreted the omen many rich and handsome presents. 326 FAMILIAR SCIENCE STUDIES. I must confess that for my own part I cannot but think the actual facts must have undergone considerable modification before the story reached its present form. Certainly the case does not illustrate the occurrence of dreams, as a warning, effective or otherwise according to circumstances, for the dream happened simultaneously with the event to which it was supposed to relate. The story runs as follows (Dr. Abercrombie gives the story in a somewhat, but not essentially, different form) : On the night of May n, 1812, Mr. Williams, of Scorrior House, near Redruth, in Cornwall, woke his wife, and in great agitation told her of a strange dream he had just had. He dreamt he was in the lobby of the House of Commons, and saw a man shoot with a pistol a gentleman who had just entered the lobby, who was said to be the Chancellor. His wife told him not to trouble himself about the dream, but to go to sleep again. He followed her advice, but pre- sently woke her again, saying he had dreamt the same dream. Yet a third time was the dream repeated ; after which he was so disturbed that, despite his wife's entreaties that he would trouble himself no more about the House of Commons, but try to sleep quietly, he got up and dressed himself. This was between one and two o'clock in the morning. At breakfast, Mr. Williams could talk of nothing but the dream; and early the same morning he went to Falmouth, where he told the dream to all of his acquaint- ance whom he met. Next day, Mr. Tucker, of Trematon Castle, accompanied by his wife, a daughter of Mr. Williams, went to Scorrior House on a visit. Mr. Williams told Mr. Tucker the circumstances of his dream. Mr. Tucker remarked that it could only be in a dream that the Chan- cellor would be found in the lobby of the House of Com- mons. Mr. Tucker asked what sort of man the Chancellor seemed to be, and Mr. Williams minutely described the man who was murdered in his dream. Mr. Tucker replied, ' Your description is not at all that of the Chancellor, but is very exactly that of Mr. Perceval, the Chancellor of the SOME STRANGELY FULFILLED DREAMS. 327 Exchequer.' He asked if Mr. Williams had ever seen Mr. Perceval, and Mr. Williams replied that he had never seen him or had any communication of any sort with him ; and further, that he had never been in the House of Commons in his life. At this moment they heard the -sound of a horse galloping to the door of the house ; immediately after a son of Mr. Williams entered the room, and said that he had galloped from Truro, having seen a gentleman there who had come by that evening's mail from town, who had been in the lobby of the House of Commons on the evening of the nth, when a man called Bellingham had shot Mr. Perceval. After the astonishment which this intelligence created had a little subsided, Mr, Williams described most minutely the appearance and dress of the man whom he had seen in his dream fire the pistol at the Chancellor, as also the appearance and dress of the Chancellor. About six weeks after, Mr. Williams, having business in town, went in company with a friend to the House of Commons, where, as has been already observed, he had never before been. Immediately that he came to the steps of the entrance of the lobby, he said, ' This place is as distinctly within my recol- lection, in my dream, as any room in my own house,' and he made the same observation when he entered the lobby. He then pointed out the exact spot where Bellingham stood when he fired, and also that which Mr. Perceval had reached when he was struck by the ball, where he fell. The dress both of Mr. Perceval and Bellingham agreed with the description given by Mr. Williams, even to the most minute particulars. So runs the story. Of course, like the 'well-authenti- cated ' ghost stories, this one is confirmed by a number of particulars which are open to no other disadvantage than that of depending, like the rest of the story, on the narrator himself. It would be utterly absurd to base any theory respecting dreams on a story of this sort. The fact that on the night in question Mr. Williams dreamt about a murder in the House of Commons depends on his o\vn assertion 328 FAMILIAR SCIENCE STUDIES. and his wife's confirmation. The details of the dream, the description of Perceval and Bellingham, Mr. Williams' ignorance respecting Mr. Perceval's appearance and the arrangement of the rooms in the House of Commons, these and a number of other matters essential to the significance of the story, depend on ' trustworthy witnesses,' whose evidence has in point of fact never been taken. All these points are like the details which appear in the papers the first few days after the occurrence of some ' tragic event.' They may be true or not, but they are apt to undergo considerable alteration when the witnesses are actually examined. If \ve accepted the story precisely as it stands, we should be led to some rather startling results. In the first place, the coincidences are too numerous to be explained as merely accidental. Mr. Williams, or any other among the millions who slept and dreamt on the night of the murder, might be readily enough believed to have had a startling dream about the murder of some member of Parliament high in office. Nor could the triple repetition of such a dream be surprising ; for a dream which has produced a great effect on the mind is apt to be repeated. But that the event itself of Perceval's murder should be represented precisely as it occurred to a man who did not know Perceval or Bellingham from Adam, involves a multiplicity of rela- tions which could not conceivably be all fulfilled simul- taneously. We should have to admit, if we accepted the story as it stands, that there was something, I will not say supernatural or preternatural, but outside the range of known natural laws, in the dreams of Mr. Williams of Scorrior House. Now, the case does not fall under precisely the same category as those numerous stories told of the appearance of persons, at the moment of their death, to friends or re- latives at a distance. In the first place, most of these stories are themselves open to grave doubt. The persons who relate them are by their own account of highly sensitive and readily excitable temperament, and we do not look for perfectly un- SOME STRANGELY FULFILLED DREAMS. 329 coloured narratives from such persons. But even if we accept the general theory that under certain conditions the mind of a dying person may affect in some way the mind of a person at a distance who is in some way in sympathy with the moribund, we can hardly extend the theory to in- clude strangers. It may rot be utterly incredible, perhaps, that some physical mode of communication exists by wh ; ch one brain may receive the same impressions which affect another though I must confess I cannot see my own way to believe anything of the sort. But we can hardly imagine that the brain of a sleeping person in no way connected with a dying man could be affected by such brain-waves. Every story of the kind, truthful or otherwise, has described an impression produced on some dear friend or relative ; so that we should be justified in thinking (if we believe these stories at all) that brain-waves are especially intended for the benefit of close friends or near of kin. It would be a new and startling thing if any man might have a vision of any other person who chanced to be dying ; and considering that not a minute passes without several deaths, while there are some 1,500 millions of living persons, scarcely a day might be expected to pass without some one or other of the multitudinous deaths of the day finding some one or other brain among the 1,500 millions in the proper frame for receiving the visionary communication by the brain-wave method. Nor is it easy to imagine a religiously supernatural inter- pretation of the story. The dream was certainly not sent as a warning, for when Williams dreamt his dream, Perceval was either being murdered, or was already dead. The event could produce no beneficial influence on mankind generally, or on the English people specially, or the Cornish folk still more specially. The number of persons who could be certain that Mr. Williams was telling the truth (always on our present assumption that this was the case) were very few in fact, only Mr. and Mrs. Williams, Mr. Tucker, and perhaps one or two friends who remembered that the details 330 FAMILIAR SCIENCE STUDIES. of the murder were communicated before the news could have reached Mr. Williams. One does not readily see how Williams himself was to be beneficially influenced by his remarkable experience. Most of those who heard the story would sit in the seat of the scornful, and receive no benefit but harm. The idea generally entertained, and most pro- bably by Williams as well as the rest, would be simply this, that if it was worth while to let a miraculous vision of Perceval's murder appear to anyone, it would have been well to have let the vision appear before the event, and to some one not living quite so far from town. Not, indeed, that the warning might save Perceval ; for in reality it is a bull of the broadest sort to imagine that a true vision of a murder can .prevent the murder. But a warning dream might serve useful purpose without preventing the event it indicated. If a man dreamt that he was to die in a week, and believed the dream, he would have no hope from the advice of his doctor, or from any other precautions he might make against death ; yet he would usefully employ the week in arranging his affairs. But it could be of no earthly use to Perceval, or anyone else, that a vision of his death should appear in triplicate to some one down in Cornwall on the very night when the tragedy occurred in London. I imagine that the true explanation of the story is some- what on this wise ; Williams probably had three startling dreams about a murder ; told them to his wife in the way related, and on the following morning to several friends. News presently came of the murder of Perceval on the night when Williams had had these dreams ; and gradually he associated the events of his dreams with the circumstances of the murder. When six weeks later he visited the scene of the murder, he mistook his recollection of things told him about Perceval, the lobby of the House of Commons, &c., for the recollection of things seen in his dreams. The story actually related probably assumed form and substance after Williams's visit to London. In perfect good faith, he, his SOME STRANGELY FULFILLED DREAMS. 331 wife, and his friends may have given to the story the form it finally assumed. Of course, the explanation is rendered a little easier if we suppose Mi. Williams and his wife were not unwilling to colour their story a little. If a phonograph could have received the first account of the dream as im- parted to Mrs. Williams on the night of May 1 1, I fancy the instrument might have repeated a tale somewhat unlike that which adorns the 'Royal Book of Dreams/ and Dr. Abercrombie's treatise on the Intellectual Powers. But without any intentional untruthfulness a story of this kind is apt to undergo very noteworthy modifications. Dr. Abercrombie himself vouches for the truth of the two following stories, that is to say, he vouches for his belief in both stories : ' A Scotch clergyman who lived near Edinburgh dreamt one night, while on a visit in that town, that he saw a fire, and one of his children in the midst of it. On awaking, he instantly got up and returned home with the greatest speed. He found his house on fire, and was just in time to assist one of his children who in the alarm had been left in a place of danger.' The second story runs as follows : Two sisters had been for some days attending a sick brother, and one of them had borrowed a watch from a friend, her own being under repair. The sisters were sleeping together in a room communicating with that of their brother, when the elder awoke in a state of great agitation, and roused the other to tell her that she had had a frightful dream. ' I dreamt,' she said, ' that Mary's watch stopped, and that when I told you of the circumstance you replied, " Much worse than that has happened ; for 's breath has stopped also," ' naming their sick brother. The watch, however, was found to be going correctly, and the brother was sleeping quietly. The dream recurred the next night ; and on the following morning, one of the sisters having occasion to seal a note, went to get the watch from a writing-desk in which she had deposited it, when she found it had stopped. She rushed into her brother's room in alarm, remembering the dream, and found that he had been suddenly seized with a fit of suffocation, 332 FAMILIAR SCIENCE STUDIES. and had expired (Abercrombie, 'Intellectual Powers,' pp. 289, 302.) With regard to the first of these stories, I would remark that we find in it what is not always to be found in stories of dream warnings, a reason and use in the dream, assuming always that the story is true and that the dream really was sent as a warning. It is possible, of course, that the story was embellished by the Scotch clergyman who related it to Abercrombie. If the story be true in all its details, it re- mains possible that the agreement between the dream and the event was a mere coincidence. On the first point, I shall say only that some men, and even some clergymen, have been quite capable of improving a story of this sort, with the desire perhaps of impressing on their hearer the anxious care which Providence takes in their special behalf. On the second point, it should be always remembered that among the many millions of strange dreams which might be fulfilled, some few are certain to be fulfilled, and it is of these dreams that we hear, not of those, though they are millions of times more numerous, which are not fulfilled. If, how- ever, we accept the story precisely as related, and believe that the fulfilment of the dream was not accidental, we have at least a reasonable case of dream warning. We cannot, indeed, perceive why in this case Providence should inter- fere when so many similar cases happen without interference of any sort. And to the logical mind the idea will certainly suggest itself that if special interpositions of Providence can occur in such cases, they might be expected to be greatly more numerous than they are. But considering the case apart from others, we cannot cavil at the action of Providence in this case. The danger, however, of approval in such cases will be manifest if we consider that by parity of rea- soning we ought to be dissatisfied when lamentable events happen which dream warnings might have prevented. With regard to the second of the above stories I venture to express entire want of faith. The action of the sister, who, finding the watch had stopped, rushed in alarm into SOME STRANGELY FULFILLED DREAMS. 333 her brother's room, showed that she was weak-minded and superstitious ; and we cannot expect exact statements of facts from weak-minded and superstitious persons. If the story were accepted as related, the case would differ altogether from the former. We can understand that Providence might interfere to warn a father of his child's danger in time to save the child ; but we can not reasonably believe that a double dream should be specially sent to indicate that when a cer- tain watch had stopped a certain man would be found dead. If the events happened as told the coincidence was strange, but that is all. It seems to me altogether more probable, how- ever, that the story was inexactly related to Dr. Abercrombie. I have said that cases in which dreams are not fulfilled are usually forgotten. Occasionally, however, such dreams are preserved on account of some peculiarity in the circum- stances. The following case, related by Abercrombie, is almost as singular as if the dream warning had been fulfilled by the event. A young man who was at an academy a hun- dred miles from home, dreamt that he went to his father's house in the night, tried the front door, but found it locked ; got in by a back door, and finding nobody out of bed, went directly to the bedroom of his parents. He then said to his mother, whom he found awake, ' Mother, I am going a long journey, and am come to bid you good-bye.' On this she answered, in much agitation, ' Oh, dear son, thou art dead ! ' He instantly awoke, and thought no more of his dream, until a few days after he received a letter from his father, inquiring very anxiously after his health, in conse- quence of a frightful dream his mother had had on the same night in which the dream now mentioned occurred to him. She dreamt that she heard some one attempt to open the front door, then go to the back door, and at last come into her bedroom. She then saw it was her son, who came to the side of her bed, and said, ' Mother, I am going a long journey, and I am come to bid you good-bye,' on which she exclaimed, ' Oh, dear son, thou art dead ! ' But nothing unusual happened to either of the parties. 334 FAMILIAR SCIENCE STUDIES. This case, if correctly related by the young man, would afford some evidence in favour of the theory that mind can act on mind at a distance. But we have to trust wholly in the veracity of the unknown young man ; and it is barely possible that after reading his mother's letter he invented the account of his own dream. Or the story may have been told years after the event, and the facts related may have differed very widely from what actually happened. We know that memory often plays strange tricks in such cases. At any rate, there was in this case no forewarning of any event, unless we suppose that the dream was sent to mother and son simultaneously, to prevent the son from undertaking a long journey at that time assuming further that, if he had undertaken such a journey, he would have died upon the way. But anyone who could take this view of the matter would believe anything. This unfulfilled dream, the circumstances of which, if accurately known, might probably be readily explained, reminds me of a dream or vision related by Dickens in a letter to Forster, and of the explanation which Dickens suggested in relation to it. The original narrative is so charming that I shall make no apology for quoting it without change or abridgment. ' Let me tell you,' he wrote from Genoa on September 30, 1843, *f a curious dream I had last Monday night, and of the fragments of reality I can collect which helped to make it up. I have had a return of rheumatism in my back and knotted round my waist like a girdle of pain, and had lain awake nearly all that night under the infliction, when I fell asleep and dreamed this dream. Observe that throughout I was as real, animated, and full of passion as Macready (God bless him !) in the last scene of Macbeth. In an indistinct place, which was quite sublime in its indistinctness, I was visited by a spirit. I could not make out the face, nor do I recollect that I desired to do so. It wore a blue drapery, as the Madonna might wear in a picture by Raphael ; and bore no resemblance to anyone I have ever seen except in stature. I think (but I SOME STRANGELY FULFILLED DREAMS. 335 am not sure) that I recognised the voice. Anyway, I knew it was poor Mary's spirit. I was not at all afraid, but in a great delight, so that I wept very much, and stretching out my arms to it called it ' dear.' At this I thought it recoiled ; and I felt immediately that, not being of my gross nature, I ought not to have addressed it so familiarly. ' Forgive me ! ' I said, ' we poor living creatures are only able to ex- press ourselves by looks and words. I have used the word most natural to our affections ; and you know my heart.' It was so full of compassion and sorrow for me which I knew spiritually, for, as I have said, I did not perceive its emotions by its face that it cut me to the heart ; and I said, sobbing, ' Oh ! give me some token that you have really visited me ! ' ' Form a wish,' it said. I thought, reasoning with myself, if I form a selfish wish it will vanish, so I hastily discarded such hopes and anxieties of my own as came into my mind, and said, ' Mrs. Hogarth is surrounded with great distresses ' observe, I never thought of saying ' your mother,' as to a mortal creature 'will you extricate her?' 'Yes. 5 'And her extrication is to be a certainty to me that this has really happened ? ' ' Yes.' ' But answer me one other question,' I said, in an agony of entreaty lest it should leave me : ' What is the true religion ? ' As it paused a moment with- out replying, I said ' Good God ! ' in such an agony of haste, lest it should go away, ' you think, as I do, that the form of religion does not so greatly matter, if we try to do good ? or,' I said, observing that it still hesitated, and was moved with the greatest compassion for me, ' perhaps the Roman Catholic is the best? perhaps it makes one think of God oftener, and believe in Him more steadily ? ' ' For you,' said the spirit, full of such heavenly tenderness for me that I felt as if my heart would break ' for you, it is the best ! ' Then I awoke with the tears running down my face, and myself in exactly the condition of the dream. It was just dawn. I called up Kate, and repeated it three or four times over, that I might not unconsciously make it plainer or stranger afterwards. It was exactly this, free from all 336 FAMILIAR SCIENCE STUDIES. hurry, nonsense, or confusion whatever. Now, the strings I can gather up leading to this were three. The first you know forms the main subject of my former letter. The second was, that there is a great altar in our bedroom, at which some family who once inhabited this palace had mass performed in old time ; and I had observed within myself, before going to bed, that there was a mark in the wall above the sanctuary, where a religious picture used to be ; and I had wondered within myself what the subject might have been, and what the face was like. Thirdly, I had been listening to the convent bells (which ring at intervals in the night), and so had thought, no doubt, of Roman Catholic services. And yet for all this, put the case of that wish being fulfilled by any agency in which I had no hand, and I wonder whether I should regard it as a dream, or an actual vision.' The promise of the dream-spirit was not fulfilled in this respect If it had chanced that some agency other than Dickens's own had, at that time, relieved Mrs. Hogarth from her anxieties, we can hardly doubt that he would have regarded the vision as real. He was, indeed, rather prone to recognise something beyond the natural in events which, to say the least, admitted of a quite natural interpretation. The story of his dream, I may remark in passing, is interesting as showing how the thoughts of the dreamer's own mind are in a dream assigned to the visionary persons created also in reality out of the dreamer's mind. The spirit in Dickens's dream expressed precisely his own views about religion, and hesitated precisely where (as he elsewhere tells us) he himself hesitated. But where, in his own mind, he thought only that the Roman Catholic religion might be the best for him, the vision said simply that it was so. Had the dream promise been fulfilled, Dickens would prob- ably have followed the supposed teaching of the dream- spirit Or even if no test had been suggested to his mind in the dream, and the spirit had seemed to speak only of religion, he would probably have concluded that for him the Roman Church was the best. He would have felt, as SOME STR ANGEL Y FULFILLED DREAMS. 337 Eliphaz the Temanite did, that this thing was secretly brought to him. It is indeed singular how closely in some respects the dream of Eliphaz the Temanite resembled that which Charles Dickens the Englishman dreamed, three or four thousand years later. ' In thoughts from the visions of the night,' says Eliphaz, 'when deep sleep falleth upon men. Fear came upon me, and trembling, which made all my bones to shake. Then a spirit passed before my face, the hair of my flesh stood up. It stood still, but I could not discern the form thereof : an image was before mine eyes, there was silence, a> 'id I heard a voice, saying, Shall mortal man be more just than God ? shall a man be more pure than his maker ? ' Fear possessed Eliphaz, instead of the delight which filled the heart of Dickens in the supposed presence of the departed dear one. But, like Dickens, the Temanite could hear a voice only, not discerning the form of the vision \ and again, to him as to Dickens, the supposed vision repeated only what was in the dreamer's own mind. Twenty years later Dickens had a dream which was ful- filled, at least to his own satisfaction. ' Here,' he wrote on May 30, 1863, 'is a curious case at first hand. On Thursday night last week, being at the office here,' in London, ' I dreamed that I saw a lady in a red shawl with her back towards me, whom I supposed to be E. On . her turning round I found that I didn't know her, and she said, " I am Miss Napier." All the time I was dressing next morning I thought, "What a preposterous thing to have so very distinct a dream about nothing ! And why Miss Napier ? for I never heard of any Miss Napier." That same Friday night I read. After the reading came into my retiring-room Mary Boyle and her brother, and the lady in the red shawl, whom they present as ' Miss Napier." These are all the circum- stances exactly told.' This was probably a case of uncon- scious cerebration. Dickens had no doubt really seen the lady, and been told that she was Miss Napier, when his attention was occupied with other matters. There would be nothing unusual in his dreaming about a person whom he 338 FAMILIAR SCIENCE STUDIES. had thus seen without noticing. Of course it was an odd coincidence that the lady of whom he had thus dreamed should be introduced to him soon after possibly the very day after. But such coincidences are not infrequent. To suppose that Dickens had been specially warned in a dream about so unimportant a matter as his introduction to Miss Napier would be absurd ; for, fulfilled or unfilled, the dream was, as Dickens himself described it, a very distinct dream about nothing. Far different in this respect was the strange dream which President Lincoln had the night before he was shot. If the story was truly told by Mr. Stanton to Dickens, the case is one of the most curious on record. Dickens told it thus in a letter to John Forster : ' On the afternoon of the day on which the President was shot, there was a cabinet council, at which he presided. Mr. Stanton, being at the time commander-in-chief of the Northern troops that were con- centrated about here, arrived rather late. Indeed, they were waiting for him, and on his entering the room, the President broke off in something he was saying, and re- marked, " Let us proceed to business, gentlemen." Mr. Stanton then noticed with surprise that the President sat with an air of dignity in his chair, instead of lolling about in the most ungainly attitudes, as his invariable custom was; and that instead of telling irrelevant and questionable stories, he was grave, and calm, and quite a different man. Mr. Stanton, on leaving the council with the Attorney-General, said to him, " That is the most satisfactory cabinet meeting I have attended for many a long day. What an extraordinary change in Mr. Lincoln ! " The Attorney-General replied, " We all saw it before you came in. While we were waiting for you, he said, with his chin down on his breast, ' Gentle- men, something very extraordinary is going to happen, and that very soon.' To which the Attorney-General had observed, 'Something good, sir, I hope?' when the President answered very gravely, ' I don't know I don't know. But it will happen, and shortly, too.' As they were all impressed SOME STRANGELY FULFILLED DREAMS. 339 by his manner, the Attorney-General took him up again. ' Have you received any information, sir, not yet disclosed to us ? ' ' No,' answered the President, ' but I have had a dream. And I have now had the same dream three times. Once on the night preceding the battle of Bull Run. Once on the night preceding such another ' (naming a battle also not favourable to the North). His chin sank on his breast again, and he sat reflecting. ' Might one ask the nature of this dream, sir?' said the Attorney-General. ' Well,' replied the President without lifting his head or changing his atti- tude, ' I am on a great broad rolling river and I am in a boat and I drift ! and I drift ! but this is not business,' suddenly raising his face, and looking round the table as Mr. Stanton entered ' let us proceed to business, gentle- men.' " Mr. Stanton and the Attorney-General said, as they walked on together, it would be curious to notice whether anything ensued on this, and they agreed to notice. He was shot that night.' Here the dream itself was not remark- able ; it was such a one as might readily be dreamed by a man from the Western States who had been often on broad rolling rivers. Nor was its recurrence remarkable. The noteworthy point was the occurrence of this dream three several times, and (as may be presumed from the effect which the dream produced on its third recurrence) those three times only, on the night preceding a great mis- fortune for the cause of the North. However, there is nothing in the story which cannot be attributed to merely casual coincidence, though the coincidence was sufficiently curious. As three years had elapsed from the time of Lincoln's death when Stanton told Dickens the story, it is possible that the account may have been incorrect in some details. It is, indeed, in this way that probably most of the more wonderful dream stories are to be explained. The tricks played by the memory in such matters would be perfectly amazing if they were not so familiar. For instance, Dr. Carpenter states that a lady had frequently asserted that 340 FAMILIAR SCIENCE STUDIES. she had seen a table move at the command of a medium when no one was near it. At length someone had sufficient hardihood to challenge this assertion made, it will be un- derstood, in perfectly good raith ; and to satisfy the doubter of its truth, the lady turned to a note-book in which she had described the circumstances of the event at the time of its occurrence. There she found it stated, not as her memory had falsely told her, that no one was near the table, but that the hands of six persons were touching it ! It is possible that in the following recent and certainly most remarkable case of a fulfilled dream, the exact circum- stances, had they been recorded, would have been found to be not precisely those which the narrator believed them to be. In the Daily Telegraph some months ago, in an obituary notice of General Richard Taylor, son of a former President of the United States (General Zachary Taylor), and one of the Southern generals during the Civil War, the following curious narrative was related : ' On the morning of the day when the City and Suburban Handicap was won by " Aldrich," a little-fancied outsider, it so chanced that General Taylor travelled down to Epsom in company with Lord Vivian, and heard from him that it was his intention to back Lord Rosebery's horse, because he had dreamt that he saw the primrose and rose-hoops borne to victory in the race which they were on their road to witness. Acting upon this hint, General Taylor took 1,000 to 30 about "Aldrich," and was not a little elated at the success of what he justly called "a -leap in the dark." But for the accident which caused " Lemnos," another much-backed candidate for the race, to fall at Tattenham Corner, there is little probability that the dream of Lord Vivian would have found the interpretation upon which General Taylor counted. ' The story probably came from one who had heard the actual circumstances as related by Lord Vivian himself at the time of their occurrence. The narrator's recollection of what he had heard, and Lord Vivian's recollection of the event itself, may both have been to some degree defective. SOME STRANGELY FULFILLED DREAMS. 341 That one or other was in fault is manifest when we compare with the above account Lord Vivian's own statement a day or two later. He wrote as follows to the editor of the Daily Telegraph : ' In your " leader " on General Taylor, in this day's paper, you introduce an anecdote relative to a dream of mine. The facts are these : I did dream, on the morning of the race forthe City and Suburban Handicap, that I had fallen asleep in the weighing-room of the stand of Epsom, prior to that race, and that after it had been run I was awakened by a gentleman the owner of another horse in the race --who informed me that "The Teacher" had won. Of this horse, so far as my recollections serve me, I had never before heard. On reaching Victoria Station, the first per- son I saw was the gentleman who had appeared to me in my dream, and I mentioned it to him, observing that I could not find any horse so named in the race. He replied, " There is a horse now called ' Aldrich,' which was previously called ' The Teacher.' " The dream so vividly impressed me that I declared my intention of backing " Aldrich " for ioo/., and was in course of doing this, when I was questioned by his owner as to "why I backed this horse." I replied, " Because I had dreamt he had won the race." To this I was answered, " As against your dream, I will tell you this fact : I tried the horse last week with a hurdle-jumper, and he was beaten a distance ") I afterwards learnt that the trial horse was " Lowlander " !). I thanked my informant, and discontinued backing " Aldrich." General Taylor, who had overheard what passed, asked me if I did not intend back- ing the horse again for myself, to win him i,ooo/. by him. This I did by taking for him 1,000 to 30 about " Aldrich." Such is the true account of my dream, and of General Taylor's profit from it.' The difference between this account and that in the Daily Telegraph may not seem intrinsically important ; but it is noteworthy as indicating the probability that in other details there may have been changes (unintentional, of course). 342 FAMILIAR SCIENCE STUDIES. The Spectator made the following remarks (very much to the point, I think,) on this case : ' Lord Vivian's letter adds very much to the inexplicable element in the story. In the shape in which the Daily Tele- graph originally put it, there was nothing at all in the dream but what it was quite reasonable for anyone to explain as a somewhat remarkable coincidence between a dream of the event and the event as it actually resulted, the best offered being, however, a practical proof that the dream, as alleged, had occurred, and had greatly influenced the mind of the dreamer and one of his companions before the prediction was fulfilled. But Lord Vivian's testimony that, instead of dreaming of " Aldrich " as the winner, the friend seen in his dream had mentioned a horse whose name was utterly un- known to him at least, unknown to him in his waking state and of whose running he had no knowledge, and that the name so dreamed of proved to have been the former name of a horse actually in the race, supplies a very excellent reason why he should have been sufficiently struck by his dream to intend acting upon it, until he was discouraged by hearing of the horse's defeat by a hurdle-jumper, and why General Richard Taylor insisted that if Lord Vivian did not bet on " Aldrich " on his own account, he should still bet on him on behalf of General Richard Taylor. In truth, Lord Vivian has supplied the only really striking feature in the story. Everybody would be disposed to explain it at once as a case of coincidence, but for the bit of fresh knowledge apparently supplied in the dream, and verified in fact before the chief prediction of the dream had been tested. Now, here we have exceedingly good evidence, not only of a suc- cessful prediction of an unlikely event for that is nothing, and occurs every day but of its prediction after a fashion which appears to have been beyond the scope of the dreamer's power. That he should have dreamt of the winning of the race by a horse of name quite unknown to him would of course have been nothing. But that after such a dream a friend should have been able to point out a horse actually SOME STRANGELY FULFILLED DREAMS. 343 running in the race, to which the unknown name had actually belonged, was clearly a practical verification of the informing character of the dream, and makes the coincidence if coincidence it were of the complete fulfilment of all the important predictions of the dream, one far more extraordi- nary than the fulfilment of any simple anticipation. Is there any explanation possible of the really curious part of the story, the discernment that a horse which had been called " The Teacher " was to run in the race, although Lord Vivian could not recall ever having heard of such a horse, without recourse to hypothesis of an unverified and as yet purely conjectural kind?' The writer of the article in the Spectator proceeds to offer such an explanation : ' Supposing Lord Vivian to have really had something to do with the horse called " The Teacher," and to have been told in a moment of almost complete inattention that it had been rechristened " Aldrich," it is barely possible we do not say it is at all likely that this association may have revived in sleep, without presenting any of the appearance of a memory. In his waking hours, his mind may have dwelt on Lord Rosebery as a coming power on the Turf, and that may have turned his attention to the name of Lord Rosebery's horse. This name may, in sleep, have revived the half-obliterated association of old days, and the name of " The Teacher " may have come back. And then the imposing character of this name may have sug- gested a dream in which the dreamer was solemnly told that " The Teacher " had won the race. Such, we say, is a pos- sible, though not at all probable, explanation of this strange dream, supposing it related with perfect accuracy. Certain it is, that our memories are often so much transformed in our sleeping state, that they hardly comport themselves as memories at all, but rather as brand-new experiences, when they are really due to the laws of association, though of association so completely stripped of all its most familiar elements as to look stranger than a totally new impression.' Of course this explanation, even if accepted, gives no 344 FAMILIAR SCIENCE STUDIES. account of the fulfilment of the dream despite the heavy antecedent probability against 'Aldrich' winning. Unless we set this down to mere coincidence, we should either have to believe that Lord Vivian was specially favoured with a vision by which if only he were clever enough to avail himself of the information he might win much money on a horse-race (a somewhat questionable proceeding if he were assured that the information were trustworthy, and a somewhat foolish pro- ceeding if he were not), or else we must suppose that, in his sleep, information which he had once had (but had forgotten) about the horse's qualities showed him what in his waking hours he could not have ascertained, that the horse really had a better chance than bettors imagined. Possibly persons who bet on horse-races give their minds (or what they re- gard as such) so entirely to that absorbing though not very ennobling pursuit, that they often dream about horses win- ning races. As their name is legion, and their dreams \\ould therefore be multitudinous, the wonder rather is, per- haps, that we do not oftener hear of seemingly remarkable fulfilments of such dreams, than that one or two cases of the kind should be recorded. Certainly there is little in this case to encourage special faith in dreams about racing. However ready the believer in dreams may be to regard dream warnings as supernatural, he can hardly regard infor- mation about horse-races as communicated from above. If they came from the contrary direction, it would be unsafe to accept them with blind confidence, remembering to whom the parentage of falsehood has been, on excellent authority, attributed. 345 SUSPENDED ANIMATION. SOME time since an article appeared in the Times, quoted from the Brisbane Courier (an Australian paper of good credit), stating that one Signer Rotura had devised a plan by which animals might be congealed for weeks or months without being actually deprived of life, so that they might be shipped from Australia for English ports as dead meat, yet on their arrival here be restored to full life and activity. Many regarded this account as intended to be received seriously, though a few days later an article appeared, the opening words of which implied that only persons from the north of the Tweed should have taken the article au grand serieux. Of course it was a hoax ; but it is worthy of notice that the editor of the Brisbane Courier had really been mis- led, as he admitted a few weeks later, with a candour which did him credit. 1 1 Many fail to see a joke when it is gravely propounded in print, who would at once recognise it as such, were it uttered verbally, with however serious a countenance. Possibly this is due to the necessary absence in the printed account of the indications by which we recog- nise that a speaker is jesting as a certain expression of countenance, or a certain intonation of voice, by which the grave utterer of a spoken jest conveys his real meaning. In a paper which recently appeared in the Gentleman 's Magazitte, Mr. Foster (Thomas of that ilk) propounded very gravely the theory that our Nursery Rhymes have in reality had their origin in Nature Myths. He explained, for instance, that the v rhymes relating to Little Jack Horner were originally descriptive of sunrise in winter : Little Jack is the sun in winter, the Christmas pie is the cloud-covered sky ; the thumb represents the sun's first ray piercing 34$ FAMILIAR SCIENCE STUDIES. This wonderful discovery, however, besides being worth publishing as a joke (though rather a mischievous one, as will presently be shown), did good service also by eliciting from a distinguished physician certain statements respecting the possibility of suspending animation, which otherwise might have remained for some time unpublished. I propose here to consider these statements, and the strange possibili- ties which some of them seem to suggest. In the first place, however, it may be worth while to recall the chief state- ments in the clever Australian story, as some of Dr. Richard- son's statements refer specially to that narrative. I shall take the opportunity of indicating certain curious features of resemblance between the Australian story, which really had its origin in America (I am assured that it was pub- lished a year earlier in a New York paper), and an American hoax which acquired a wide celebrity some forty years ago, the so-called Lunar Hoax. As it is certain that the two stories came from different persons, the resemblance referred to seems to suggest that the special mental qualities (defects bien entendu} which cause some to take delight in such in- ventions, are commonly associated with a characteristic style of writing. If Buffon was right, indeed, in saying, Le style c'est de Phomme meme, we can readily understand that clever hoaxers should thus have a style peculiar to them- selves. It can hardly be considered essential to the right com- prehension of scientific experiments that a picturesque account should be given of the place where the experiments were made. The history of the wonderful Australian dis- covery opens nevertheless as follows : ' Many of the readers of the Brisbane Courier who know Sydney Harbour through the clouds ; and Jack's rejoicing means the brightness of full sunlight. So also the rhymes beginning Ilcy Diddle Diddle are shown to be of deep and solemn import, all in manifest burlesque of some recent extravagant interpretations of certain ancient stories by Goklziher, Steinthal, a ad others. Yet this fun was seriously criticised by more than half the critics, by some approvingly, by some otherwise. SUSPENDED ANIMATION. 347 will remember the long inlet opposite the heads known as Middle Harbour, which, in a succession of land-locked reaches, stretches away like a chain of lakes for over twenty miles. On one of these reaches, made more than ordinarily picturesque by the bold headlands that drop almost sheer into the water, stand, on about an acre of grassy flat, fringed by white beach on which the clear waters of the harbour lap, two low brick buildings. Here, in perfect seclusion, and with a careful avoidance of publicity, is being conducted an experiment, the success of which, now established beyond any doubt, must have a wider effect upon the future pro- sperity of Australia than any project ever contemplated.' It was precisely in this tone that the author of the ' Lunar Hoax ' l opened his account of those ' recent discoveries in astronomy which will build an imperishable monument to the age in which we live, and confer upon the present generation of the human race a proud distinction through all future time.' ' It has been poetically said,' he remarks though probably he would have found some difficulty in saying where or by whom this had been said, ' that the stars of heaven are the hereditary regalia of man, as the intellectual sovereign of the animal creation ; he may now fold the zodiac around him with a loftier consciousness of his mental supremacy ' (a sublime idea, irresistibly sugges- tive of the description which an American humourist gave of a certain actor's representation of the death of Richard III., 'he wrapped the star-spangled banner around him, and died like the son of a hoss "). It next becomes necessary to describe the persons en- gaged in pursuing the experiments by which the art of freezing animals alive is to be attained. 'The gentlemen engaged in this enterprise are Signer Rotura, whose re- searches into the botany and natural history of South America have rendered his name eminent ; and Mr. James Grant, a pupil of the late Mr. Nicolle, so long associated 1 For a full account of this clever hoax the reader is referred to my ' Myths and Marvels of Astronomy.' 348 FAMILIAR SCIENCE STUDIES. with Mr. Thomas Mort in his freezing process. Next to the late Mr. Nicolle, Mr. James Grant can claim pre-emi- nence of knowledge in the science of generating cold, and his freezing chamber at Woolhara has long been known as the seat of valuable experiments originated in his, Mr. Nicolle's, lifetime.' Is it merely an accident, by the way, or is it due to the circumstance that exceptional powers of invention in general matters are often found in company with singular poverty of invention as to details, that two of the names here mentioned closely resemble names con- nected with the Lunar Hoax? It was Nicollet who in reality devised the Lunar Hoax, though Richard Alton Locke, the reputed author, probably gave to the story its final form ; and, again, the story purported to come from Dr. Grant, of Glasgow. In the earlier narrative, again, as in the later, due care was taken to impress readers with the belief that those who had made the discovery, or taken part in the work, were worthy of all confidence. Sir W. Herschel was the inventor of the optical device by which the inhabi- tants of the moon were to be rendered visible, a plan which ' evinced the most profound research in optical science, and the most dexterous ingenuity in mechanical contrivance. But his son, Sir John Herschel, nursed and cradled in the observatory, and a practical astronomer from his boyhood, determined upon testing it at whatever cost.' Among his companions he had ' Dr. Andrew Grant, Lieutenant Drum- mond of the Royal Engineers, and a large party of the best English mechanics.' The accounts of preliminary researches, doubts, and difficulties are in both cases very similar in tone. ' It appears that five months ago,' says the narrator of the Australian hoax, ' Signer Rotura called upon Mr. Grant to invoke his assistance in a scheme for the transmission of live stock to Europe. Signor Rotura averred that he had discovered a South American vegetable poison, allied to the well-known woolara (sic) that had the power of perfectly suspending animation, and that the trance thus produced SUSPENDED ANIMATION. 349 continued until the application of another vegetable essence caused the blood to resume its circulation and the heart its functions. So perfect, moreover, was this suspension of life that Signer Rotura had found in a warm climate decompo- sition set in at the extremities after a week of this living death, and he imagined that if the body in this inert state were reduced to a temperature sufficiently low to arrest decomposition, the trance might be kept up for months, possibly for years. He frankly owned that he had never tried this preserving of the tissues by cold, and could not confidently speak as to its effect upon the after-restoration of the animal operated on. Before he left Mr. Grant he had turned that gentleman's doubts into wondering curiosity by experimenting on his dog.' The account of this experi- ment I defer for a moment till I have shown how closely in several respects this portion of the Australian hoax resembles the corresponding part of the American story. It will be observed that the great discovery is presented as simply a very surprising development of a process which is strictly within the limits, not only of what is possible, but of what is known. So also in the case of the Lunar Hoax, the amazing magnifying power by which living creatures in the moon were said to have been rendered visible, was presented as simply a very remarkable development of the familiar properties of the telescope. In both cases, the circum- stances which in reality limit the possible extension of the properties in question were kept conveniently concealed from view. In both cases, doubts and difficulties were urged with an apparent frankness intended to disarm sus- picion. In both cases, also, the inventor of the new method by which difficulties were to be overcome is represented as in conference with a man of nearly equal skill, who urges the doubts naturally suggested by the wonderful nature of the promised achievements In the Lunar Hoax, Sir John Herschcl and Sir David Brewster are thus represented in conference. Herschel asks whether the difficulty arising from deficient illumination may not be overcome by effecting 350 FAMILIAR SCIENCE STUDIES. a transfusion of artificial light through the focal image. Brewster, startled at the novel thought, as he well might be, hesitatingly refers 'to the refrangibility of rays and the angle of incidence,' which is effective though glorious in its ab- surdity. (Yet it has been gravely asserted that this non- sense deceived Arago.) 'Sir John, grown more confident, adduced the example of the Newtonian reflector, in which the refrangibility was arrested by the second speculum and the angle of incidence restored by the third' (a bewilderingly ridiculous statement). '"And," continued he, "why cannot the illuminated microscope, say the hydro-oxygen, be applied to render distinct, and if necessary even to magnify, the focal object?" Sir David sprang from his chair in an ecstasy of conviction, and leaping half-way to the ceiling' (from which we may infer that he was somewhat more than tile montc), ' exclaimed, "Thou art the man ! '" The method devised in each case being once accepted as sound, the rest of course readily follows. In the case of the Lunar Hoax a number of discoveries are made which need not here be described * (though I shall take occasion presently to quote some passages relating to them which closely resemble in style certain passages in the Australian narrative). In the later hoax, the illustrative experiments are forthwith introduced. Signor Rotura, having so far persuaded Mr. Grant of the validity of the plan as to induce him to allow a favourite dog to be experimented upon, ' in- jected two drops of his liquid, mixed with a little glycerine, into a small puncture made in the dog's ear. In three or four minutes, the animal was perfectly rigid, the four legs stretched backward, eyes wide open, pupils very much dilated, and exhibiting symptoms very similar to those caused by strychnine, except that there had been no previous struggle or pain. Begging his owner to have no apprehen- sion for the life of his favourite animal, Signor Rotura lifted the dog carefully and placed him on a shelf in a cupboard, 1 The most curious are given in the ninth essay of my work referred to in the preceding note. SUSPENDED ANIMATION. 351 where he begged he might be left till the following day, when he promised to call at ten o'clock and revive the apparently dead brute. Mr. Grant continually during that day and night visited the cupboard, and so perfectly was life suspended in his favourite no motion of the pulse or heart giving any indication of the possibility of revival that he confesses he felt all the sharpest reproaches of remorse at having sacrificed a faithful friend to a doubtful and dan- gerous experiment. The temperature of the body, too, in the first four hours gradually lowered to 25 degrees Fahren- heit below ordinary blood temperature, which increased his fears as to the result ; and by morning the body was as cold as in natural death. At ten o'clock next morning, according to promise, Signer Rotura presented himself, and laughing at Mr. Grant's fears, requested a tub 'of warm water to be brought. He tested this with the thermometer at 32 degrees Fahrenheit ' (which, being the temperature of freezing water, can hardly be called warm), ' and in this laid the dog, head under.' In reply to Mr. Grant's objections Signer Rotura assured him that, as animation must remain entirely sus- pended until the administration of the antidote, no water could be drawn into the lungs, and that the immersion of the body was simply to bring it again to a blood-heat. After about ten minutes of this bath the body was taken out, and another liquid injected in a puncture made in the neck. 'Mr. Grant tells me,' proceeds the veracious narrator, ' that the revival of Turk was the most startling thing he ever witnessed ; and having since seen the experiment made upon a sheep, I can fully confirm his statement. The dog first showed the return of life in the eye ' (winking, doubt- less, at the joke), 'and after five and a half minutes he drew a long breath, and the rigidity left his limbs. In a few minutes more he commenced gently wagging his tail, and then slowly got up, stretched himself, and trotted off as though nothing had happened.' From this moment Mr. Grant had full faith in Signor Rotura's discovery, and pro- mised him all the assistance in his power. They next 352 FAMILIAR SCIENCE STUDIES. determined to try freezing the body. But the first two ex- periments were not encouraging. Mr. Grant fortunately did not allow his favourite dog to be experimented upon further, so a strange dog was put into the freezing-room at Mr. Grant's works for four days, after having in the first place had his animation suspended by Signer Rotura. Although this animal survived so far as to draw a long breath, the vital energies appeared too exhausted for a complete rally, and the animal died. So also did the next two animals experimented on, a cat and a dog. ' In the meantime, however, Dr. Barker had been taken into their counsels, and at his suggestion respiration was encouraged, as in the case of persons drowned, by artificial compression and expansion of the lungs. Dr. Barker was of opinion that, as the heart in every case began to beat, it was a want of vital force to set the lungs in proper motion that caused death. The result showed his surmises to be entirely correct. A number of animals whose lives had been sealed up in this artificial death have been kept in the freezing chamber from one to five weeks, and it is found that though the shock to the system from this freezing is very great, it is not increased by duration of time.' I need not follow the hoaxer's account of the buildings erected for the further prosecution of these researches. One point, however, may be mentioned, which illustrates the resemblance I have already mentioned as existing between this Australian narrative and the Lunar Hoax. In describing the works erected at Middle Harbour, the Australian account carefully notes that the necessary funds were provided by Mr. Christopher Newton, of Pitt Street. In like manner, in the Lunar Hoax we are told that the plate-glass required for the optical arrangement devised by Sir J. Herschel was ' obtained, by consent be it observed, from the shop-window of M. Desanges, the Jeweller to his ex-majesty Charles X., in High Street.' Now comes the culminating experiment, the circum- stances of which are the more worthy of being carefully SUSPENDED ANIMATION. 353 noted, because it is distinctly stated by Dr. Richardson that none of the experiments described in this narrative, apocryphal though they may really be, can be regarded as beyond the range of scientific possibilities : ' Arrived at the works in Middle Harbour, I was taken into the build- ing that contains Mr. Grant's apparatus for generating cold. .... Attached to this is the freezing chamber, a small, dark room, about eight feet by ten. Here were eighteen sheep, four lambs, and three pigs, stacked on their sides in a heap, alive, which Mr. Grant told me had been in their present position for nineteen days, and were to remain there for another three months. Selecting one of the lambs, Signer Rotura put it on his shoulder, and carried it outside into the other building, where a number of shallow cemented tanks were in the floor, having hot and cold water taps to each tank, with a thermometer hanging alongside. One of these tanks are quickly filled, and its temperature tested by the Signor, I meantime examining with the greatest curiosity and wonder the nineteen- days-dead lamb. The days of miracles truly seem to have come back to us, and many of those stories discarded as absurdities seem to me less improbable than this fact, witnessed by myself. There was the lamb, to all appearance dead, and as hard almost as a stone, the only difference perceptible to me between his condition and actual death being the absence of dull glassi- ness about the eye which still retained its brilliant transpar- ency. Indeed, this brilliancy of the eye, which is height- ened by the enlargement of the pupil, is very striking, and lends a rather weird appearance to the bodies. The lamb was gently dropped into the warm bath, and was allowed to remain in it about twenty- three minutes, its head being raised above the water twice for the introduction of the thermometer into its mouth, and then it was taken out and placed on its sic'e on the floor, Signor Rotura quickly divid- ing the wool on its neck, and inserting the sharp point of a small silver syringe under the skin and injecting the anti- dote. This was a pale green liquid, and, as I believe, a A A 354 FAMILIAR SCIENCE STUDIES. decoction from the root of the Asiracharlis, found in South America. The lamb was then turned on its back, Signer Rotura standing across it gently compressing its ribs with his knees and hands in such a manner as to imitate their natural depression and expansion during breathing. In ten minutes the animal was struggUng to free itself, and when released skipped out through the door and went gambolling and bleating over the little garden in front. Nothing has ever impressed me so entirely with a sense of the marvellous. One is almost tempted to ask, in the presence of such a discovery, whether death itself may not ultimately be baffled by scientific investigation.' In the Lunar Hoax there is a passage resembling in tone the lively account of the lamb's behaviour when released. Herds of agile creatures like antelopes were seen in the moon, * abounding in the acclivi- tous glades of the woods.' ' This beautiful creature afforded us,' says the narrator, ' the most exquisite amusement. The mimicry of its movements upon our white-painted canvas was as faithful and luminous as that of animals within a few yards of the camera obscura. Frequently, when attempting to put our fingers upon its beard, it would suddenly bound away, as if conscious of our earthly impertinence ; but then others would appear, whom we could not prevent nibbling the herbage, say or do to them what we would.' And again, a little further on : ' We fairly laughed at the recognition of so familiar an acquaintance as a sheep in so distant a land a good large sheep, which would not have disgraced the farms of Leicestershire or the shambles of Leadenhall Market ; presently they appeared in great numbers, and on reducing the lenses we found them in flocks over a great part of the valley. I need not say how desirous we were of find- ing shepherds to these flocks, and even a man with blue apron and rolled-up sleeves would have been a welcome sight to us, if not to the sheep ; but they fed in peace, lords of their own pastures, without either piotector or destroyer in human shape.' Not less amusing, though more gravely written, is the SUSPENDED ANIMATION. 355 account of the benefits likely to follow from the use of the wonderful process for freezing animals alive. Cargoes of live sheep can be readily sent from Australia to Europe. Any that cannot be restored to life will still be good meat ; while the rest can be turned to pasture or driven alive to market. With bullocks the case would not be quite so simple, because of their greater size and weight, which would render them more difficult to handle with safety. The carcass being rendered brittle by freezing, they are so much the more liable to injury. ' It sounded odd to hear Mr. Grant and Signer Rotura laying stress upon the danger of breakage in a long voyage.' This one can readily imagine. Some of the remoter consequences of the discovery are touched on by the narrator, though but lightly, as if he saw the necessity of keeping his wonders within reasonable limits. Signer Rotura, ' though he had never attempted his experiment on a human being,' which was considerate on his part, ' had no doubt at all as to its perfect safety.' He had requested Sir Henry Parkes to allow him to operate on the next felon under capital sentence. This, by the way, was a compromising statement on our hoaxer's part. It requires very little aquaintance with our laws to know that no one could allow a felon condemned to death to be ex- perimented on in this or in any other manner. Such a man is condemned to die, and to die without any preliminary tortures, bodily or mental, other than those inseparable from the legally adopted method of bringing death about. He can neither be allowed to remain alive after an experiment, and necessarily free (because he has not been condemned to other punishment than the death penalty), nor can he be first experimented upon and then hanged. So that that single sentence in the narrative should have shown every one that it was a hoax, even if the inherent absurdity of many other parts of the story had not shown this very clearly. As to whether a temporary suspension of the vital faculties would affect the longevity of the patient, Signer Rotura expressed himself somewhat doubtful ; he believed, 356 FAMILIAR SCIENCE STUDIES. however, that the duration of life might in this way be pro- longed for years. 'I was anxious,' says the hoaxer, 'to know if a period of, say, five years of this inertness were submitted to, whether it would be so much cut out of one's life, or if it would be simply five years of unconscious exist- ence tacked on to one's sentient life. Signer Rotura could give no positive answer, but he believes, as no change takes place or can take place while this frozen trance continues, no consumption, destruction, or reparation of tissue being possible, it would be so many unvalued and profitless years added to a lifetime.' Of some of the strange ideas suggested by this conception I shall take occasion to speak further on ; I must for the present turn, however from the consideration of this ingenious hoax to discuss the scientific possibilities which underlie the narrative, or at least some parts of the narrative. In the first place, it must be noticed that in the pheno- mena of hibernation we have what at a first view seems closely to resemble the results of Signer Rotura's apocryphal experiments. As I remarked in the Times, the idea under- lying the Australian story is that the hibernation of animals can be artificially imitated and extended, so that as certain animals lie in a state of torpor and insensibility throughout the winter months, all animals also may perhaps be caused to lie in such a state for an indefinite length of time, if only a suitable degree of cold is maintained, and some special contrivance adopted to prevent insensibility from passing into death. The phenomena of hibernation are indeed so sur- prising, when rightly understood, that inexperienced persons might well believe in almost any wonders resulting from the artificial production (which, be it remembered, is altogether possible) of the hibernating condition, and the artificial ex- tension of this condition to other animals than those which at present hibernate, and to long periods of time. It has been justly said, that if hibernation had only been noticed among cold-blooded animals, its possibility in the case of mammals would have seemed inconceivable. The first SUSPENDED ANIMATION. 357 news that the bat and hedgehog pass into the state of com- plete hibernation, would probably have been received as either a daring hoax or a very gross blunder. Let us consider what hibernation really is. When, as winter approaches and their insect food disappears, the bat and the hedgehog resign themselves to torpor, the processes which we are in the habit of associating with vitality gradually diminish in activity. The breathing becomes slower and slower, the heart beats more and more slowly, more and more feebly. At last the breathing ceases altogether. The circulation does not wholly cease however. So far as is known, the life of warm-blooded animals cannot continue after the circulation has entirely ceased for more than a certain not very considerable length of time. 1 The chemical changes on which animal heat depends, and without which there can be no active vitality, cease with the cession of respiration. But dormant vitality is still maintained in hibernation, because the heart's fibre, excited to contract by the carbonised blood, continues to propel the blood through the torpid body. This slow circulation of venous blood continues during the whole period of hibernation. It is the only vital process which can be recognised ; and it is not easy to understand how the life of any warm-blooded animal can be maintained in this way. The explanation usually offered is that the material conveyed by the absorbents suffices to counterbalance the process of waste occasioned by the slow circulation. But this does not in reality touch the chief difficulty presented by the phenomena of hiberna- tion. So far as mere waste is concerned (as I have elsewhere pointed out) the imagined Australian process is as effectual as hibernation ; in that process, of course the circulation would be as completely checked as the respiration ; thus there would be no waste, and the absorbents (which would 1 Few probably are aware how long some animals may remain with- out breathing and yet survive. Kittens and puppies have been brought to life after being immersed in water for nearly three-quarters of an hour. 358 FAMILIAR SCIENCE STUDIES. also be absolutely dormant) would not have to do even that slight amount of work which they accomplish during hiber- nation. Science can only say that the known cases of hibernation among warm-blooded animals show that the vital forces may be reduced much lower without destroying life, than but for them we should have deemed conceivable. But next let us consider what science has to say as to the artificial suspension of vitality. In Dr. Richardson's paper on this subject there is much which seems almost as sur- prising as anything in the Australian story. Indeed, he seems scarcely to have felt assured that that story really was a hoax. ' The statements,' he says, ' which, under the head of "A Wonderful Discovery," are copied from the Brisbane Courier, seem greatly to have astonished the reading public. To what extent the statements are true or untrue it is im- possible to say. The whole may be a cleverly- written fiction, and certain of the words and names used seem, according to some readers, to suggest that view ; but be this so or not, I wish to indicate that some part at all events of what is stated might be true, and is certainly within the range of possibility.' ' The discovery,' he proceeds, ' which is de- scribed in the communication under notice, is not in principle new; on the subject of suspension of animation I have myself been making experimental inquiries for twenty-five years at least, and have communicated to the scientific world many essays, lectures, and demonstrations, relating to it. I have twice read papers bearing on this inquiry to the Royal Society, once to the British Association for the Advancement of Science, two or three times in my lectures on Experi- mental and Practical Medicine, and published one in Nature. In respect to the particular point of the preservation of animal bodies for food, I dwelt on this topic in the lectures delivered before the Society of Arts, in April and May of last year (1878), explaining very definitely that the course of research in the direction of preservation must ultimately lead to a process by which we should keep the structures of animals in a form of suspended molecular life.' In other SUSPENDED ANIMATION. 359 words, Dr. Richardson had indicated the possibility of doing precisely that which would have constituted the chief value of the Australian discovery, if this had been real. Let us next consider what is known respecting the possibility of suspending a conscious and active life. This is first stated in general terms by Dr. Richardson as follows : ' If an animal perfectly free from disease be subjected to the action of some chemical agents or physical agencies which have the property of reducing to the extremest limit the motor forces of the body, the muscular irritability, and the nervous stimulus to muscular action, and if the sus- pension of the muscular irritability and of the nervous ex- citation be made at once and equally, the body even of a warm-blooded animal may be brought down to a condition so closely resembling death, that the most careful examination may fail to detect any signs of life.' This general statement must be carefully studied if the reader desires thoroughly to understand at once the power and the limits of the power of science in this direction. The motor forces, the muscular irritability, and the nervous stimulus to muscular action, can be reduced to a certain extent without destroy- ing life, but not absolutely without destroying life. The reduction of the muscular irritability must be made at once and equally ; if the muscular irritability is reduced to its low- est limit while the nervous excitation remains unaltered, or is less reduced, death ensues ; and vice -versa, if the nervous excitation is reduced to its lowest limits while the muscular irritability remains unaltered, or is little reduced, death equally follows. Then it is to be noticed that though when the state of seeming death is brought about, the most care- ful examination may fail to detect any signs of life, it does not follow that science may not find perfectly sure means of detecting cases where life still exists but is at its very lowest. Of course all the ordinary tests, in which so many place complete reliance a mirror placed close to the mouth, a finger on the pulse, hand or ear to the breast ! over the heart, ' Objection has been taken to the italicised words in the following 360 FAMILIAR SCIENCE STUDIES. and so forth would be utterly inadequate, in such a case, to reveal any signs of life. That doctors have been deceived by cases of suspended vitality not artificially produced, but presenting similar phenomena, is well known. A case in point may not be out of place here, as illustrating well certain features of suspended animation, and showing the possibility that in some cases consciousness may remain, even when the most careful examination detects no traces of life. The case is described by Dr. Alexander Crichton, in his ' Inquiry into the Nature and Origin of Mental Derangement.' ' A young lady, who had seemed gradually to sink until she died, had been placed in her coffin, careful scrutiny reveal- ing no signs of vitality. On the day appointed for her funeral, several hymns were sung before her door. She was conscious of all that happened around her, and heard her friends lamenting her death. She felt them put on the dead-clothes, and lay her in the coffin, which produced an passage from ' No Thoroughfare ' (one of the parts certainly written by Dickens and not by Wilkie Collins) : ' The cry came up : " His heart still beats against mine. I warm him in my arms. I have cast off the rope, for the ice melts under us, and the rope would separate me from him; but I am not afraid." .'. . . The cry came up, "We are sinking lower, but his heart still beats against mine." .... The cry came up, " We are sinking still, and we are deadly cold. His heart no longer beats against mine. Let no one come down to add to our weight. Lower the rope only." .... The cry came up with a deathly silence, " Raise ! softly !".... She broke from them all and sank over him on his litter, with both her loving hands upon the heart that stood still. 1 It has been supposed that Dickens wilfully departed here from truth, in order to leave the impression on the reader that Vendale was assuredly dead. That he wished to convey this impression is obvious. He often showed similar care to remove, if possible, all hope fi om the anxious reader's mind (markedly so in his latest and unfinished work, where nevertheless any one well acquainted with Dickens's manner knows not only that Drood is alive, but that disguised as Datchery he was to have watched Jasper to the end). But in reality, it has happened more than once that persons have been restored to life who have been found in snow-drifts not merely reduced to complete insensibility, but without any recognisable heart-beat. Dickens had probably heard of such cases when in Switzerland. SUSPENDED ANIMATION. 361 indescribable mental anxiety. She tried to cry but her mind was without power, and could not act on the body. It was equally impossible to her to stretch out her arms or to open her eyes or to cry, although she continually endeavoured to do so. The internal anguish of her mind was, however, at its utmost height when the funeral hymns began to be sung and when the lid of the coffin was about to be nailed on. The thought that she was to be buried alive was the first one which gave activity to her mind, and caused it to operate on her corporeal frame. Just as the people were about to nail on the lid, a kind of perspiration was observed to appear on the surface of the body. It grew greater every moment, and at last a kind of convulsive motion was observed in the hands and feet of the corpse. A few minutes after, during which fresh signs of returning life appeared, she at once opened her eyes, and uttered a most pitiable shriek.' In this case it was considered that the state of trance had been brought about by the excessive contractile action of the nervous centres. St. Augustine, by the way, remarks in his ' De Civitate Dei ' on the case ot a certain priest called Restitutus (appropriately enough), who could when he wished withdraw himself from life in such sort that he did not feel when twitched or stung, but might even be burned without suffering pain except afterwards from the wound so produced. Not only did he not struggle or even move, but like a dead person he did not breathe, yet afterwards he said that he could hear the voices of those around him (if they spoke loudly) as if from a great distance (de longtnquo). To return, however, to Dr. Richardson's discussion of the artificial suspension of active life. He recognises three degrees of muscular irritability, to which he has given the names of active efficient, passive efficient, and negative, though doubtless he would recog- nise the probability that the line separating the first from the second may not always be easily traced, and that, though there is a most definite distinction between the second and 362 FAMILIAR SCIENCE STUDIES. the third, the actual position of the boundary line has not as yet been determined. In other words, so far as the fiist and second states are concerned, there are not two degrees only, but many. As regards the third or negative state, which is only another way of describing death, there is, of course, only one degree, though the evidence as to the existence of this state may be more or less complete and obvious. Dr. Richardson defines the active efficient state of muscular irritability as that ' represented in the ordinary living muscle in which the heart is working at full tension and all parts of the body are thoroughly supplied with blood, with perfection of consciousness in waking hours, and, in a word, full life.' The second, or passive efficient state, ' is represented in suspended animation, in which the heart is working regularly but at low tension, supplying the muscles and other parts with sufficient blood to maintain the molecular life, but no more.' The third of these states the negative ' is represented when there is no motion whatever of blood through the body, as in an animal entirely frozen.' With the first and third of these states I have in reality nothing to do, unless indeed it could be shown that the third or negative state can be produced without causing death. Perhaps in assuming, as I did above, that this state is identical with the state of the dead, I was, in fact, assuming what science has yet to demonstrate. I may at any rate, however, say without fear of valid contradiction, that science has as yet never succeeded in showing that this negative state may be attained even for a moment without death ensuing ; and the probability (almost amounting to certainty) is that death and this change of state have in every instance been simultaneous. Dr. Richardson speaks of the second stage as that in which animation is usually suspended ; but he does not show that the third stage can even possibly be attained without death. The second stage, or stage of passive efficiency, closely resembles the third, ' but differs from it in that, under favour- SUSPENDED ANIMATION. 363 ing circumstances, the whole of the phenomena of the ac- tive efficient stage may be perfectly resumed, the heart sud- denly enlarging in volume from its filling with blood, and reanimating the whole organism by the force of its renewed stroke in full tension. So far as we have yet proceeded,' continues Dr. Richardson, ' the whole phenomena of restora- tion from death are accomplished during this stage,' meaning, it would seem, that in all instances of restoration the restor- ation has been from the second, never from the third stage. ' To those who are not accustomed to see them they are no doubt very wonderful, looking like veritable restorations from death. They surprise even medical men the first time they are witnessed by them.' He gives an interesting illustration. At a meeting of the British Medical Association at Leeds, 'a member of the Association was showing to a large audience the action of nitrous oxide gas, using a rabbit as the subject of his demonstration. The animal was removed from the narcotising chamber a little too late, for it had ceased to breathe, and it was placed on the table to all appearance dead. 7 ' At this stage,' he proceeds, ' I went to the table, and by use of a small pair of double-acting bellows restored respiration. In about four minutes there was revival of active irritability in the abdominal muscles, and two minutes later the animal leaped again into life, as if it had merely been asleep. There was nothing remarkable in the fact ; but it excited, even in so cultivated an audience as was then present, the liveliest surprise.' But when we learn the condition necessary that a body which has once been reduced to the state of passive effici- ency should be restored to active life, we recognise that even when science has learned how to reduce vitality to a minimum without destroying it, few will care to risk the process, either in their own persons or in the case of those dear to them. Besides the condition already indicated, that the muscular irritability and the nervous excitation must be simultaneously and equally reduced, it is essential that the blood, the muscular fluid, and the nervous fluid should all 364 FAMILIAR SCIENCE STUDIES. three remain in what Dr. Richardson calls the aqueous con- dition, and not become what he calls pectous, a word which we must understand to bear the same relation to the word solid or crystalline that the word ' aqueous,' as used by Dr. Richardson, bears to the word watery. If all three fluids remain in the aqueous condition, ' the period during which life may be restored is left undefined. It may be a very long period, including weeks, and possibly months, granting that decomposition of the tissues is not established, and even after a limited process of decomposition, there may be renewal of life in cold-blooded animals. But if pectous change begins in any one of the structures I have named, it extends like a crystallisation quickly through all the structures and thereupon recovery is impossible, for the change in one of the parts is sufficient to prevent the restoration of all. Thus the heart may be beating, but the blood being pectous it beats in vain ; or the heart may beat and the blood may flow, but the voluntary muscles being pectous the circulating action is vain ; or the heart may beat, the blood may flow, and the muscles may remain in the aqueous condition, but the nerves being pectous the circulating action is in vain ; or sometimes the heart may come to rest, and the other parts may remain susceptible, but the motion of the heart and blood not being present to quicken them into activity, their life is in vain.' Add to this, that the restoration of the motor forces, of the muscular irritability, and of the nervous excitation, must be as simultaneous and as equal as their reduction had been, and we begin to recognise decided ob- jections to the too frequent suspension of animation, even when the most perfect artificial means have been devised for bringing about that interesting result. Although, however, we may not feel encouraged to be- lieve that many will care to have experiments tried on them- selves in this direction, we may still examine with interest the results of experimental research and experience. These agree in showing that there are means by which active life may be suspended, while at the same time the aqueous con- SUSPENDED ANIMATION. 365 dition of the fluids mentioned above (the blood, the muscu- lar fluid, and the nervous fluid, the two latter of which are for convenience called the colloidal animal fluids, and are derived from the blood) is retained. The first and in some respects the most efficient of these means is cold. The blood and the colloidal fluids remain in the aqueous condition when the body is exposed to cold at freezing-point. ' At this same point all vital acts, except- ing perhaps the motion of the heart ' (it is Dr. Richardson, be it remembered, who thus uses the significant word ' per- haps '), ' may be temporarily arrested in an animal, and then some animals may continue apparently dead for long inter- vals of time, and may yet return to life under conditions favourable to recovery.' Dr. Richardson gives a singular illustration of this, describing an experiment which must have appeared even more surprising to those who witnessed it than that in which the rabbit was restored to life. ' In one of my lectures on death from cold,' he says, ' which I delivered in the winter session of 1867, some fish which during a hard frost had been frozen in a tank at Newcastle- on-Tyne, were sent up to me by rail. They were produced in the completely frozen state at the lecture, and by careful thawing many of them were restored to perfect life. At my Croomian lecture on muscular irritability after systemic death, a similar fact was illustrated from frogs. It would appear, indeed, that so far as cold-blooded animals are con- cerned, there is no recognisable limit to the time during which they may remain thus frozen yet afterwards recover. But, even in their case, much skill is required to make the recovery sure. ' If in thawing them the utmost care is not taken to thaw gradually, and at a temperature always below the natural temperature of the living animal, the fluids will pass from the frozen state through the aqueous into the pec- tous so rapidly that death from pectous change will be pro- nounced without perceiving any intermediate or life stage at all.' Naturally it is much more difficult to restore life in the case of warm-blooded animals. Indeed, Dr. Richardson 366 FAMILIAR SCIENCE STUDIES. remarks, that in the case of the more complex and differ- ently shielded organs of warm-blooded animals, it is next to impossible to thaw equally and simultaneously all the colloidal fluids. ' In very young animals it can be done. Young kittens, a day or two old, that have been drowned in ice-cold water, will recover after two hours' immersion almost to a certainty, if brought into dry air at a temperature of 98 degrees Fahrenheit. The gentlest motion of the body will be sufficient to re-start the respiration, and therewith the life.' Remarking on such cases as these, Dr. Richardson notes that the nearest natural approach to the stage of passive efficiency is seen in hibernating animals. He states, how- ever, that in hibernation the complete state of passive efficiency is not produced. He does not accept the opinion of those who consider that in true hibernation breathing ceases as above described. A slow respiration continues, he believes, as well as that low stage of active efficiency of circulation which we have already indicated. ' The hiber- nating animal sleeps only ; and while sleeping it consumes or wastes ; and if the cold be prolonged it may die from waking.' More decisive, because surer, is the evidence derived from the possibility of waking the hibernating animals by the common method used for waking a sleeper. This certainly seems to show that animation is not positively suspended. He asks next the question whether an animal like a fish, frozen equally through all its structures, is to be regarded as actually dead in the strict sense of the word or not, seeing that if it be uniformly and equally thawed it may recover from this perfectly frozen state. ' In like manner,' he says, ' it may be doubted whether a healthy warm-blooded animal suddenly and equally frozen through all its parts is dead, although it is not recoverable.' If, as seems certainly to be the case, the animal dies because in the very act of trying to restore it some inequality in the process is almost sure to determine a fatal issue, some vital centre passing SUSPENDED ANIMATION. 367 into the petrous state, the animal could not have been dead before restoration was attempted ; for the dead cannot die again. Albeit, the outlook is not encouraging, at any rate so far as the use of cold alone for maintaining suspended animation in full-grown warm-blooded animals is concerned. Cold will, however, for a long time maintain ready for motion active organs locally subject to it. Even after death this effect of cold ' may be locally demonstrated,' Dr. Richardson tells us, ' and has sometimes been so demonstrated to the wonder of the world.' 'For instance, on January 17, in the year 1803, Aldini, the nephew of Galvani, created the greatest astonishment in London by a series of experiments which he conducted on a malefactor, twenty-six years old, named John Foster, who was executed at Newgate, and whose body, an hour after execution, was delivered over to Mr. Keate, Master of the College of Surgeons, for research. The body had been exposed for an hour to an atmosphere two degrees below freezing point, 1 and from that cause, though Aldini does not seem to have recognised the fact, the voluntary muscles retained their irritability to such a degree that when Aldini began to pass voltaic currents through the body, some of the bystanders seem to have concluded that the unfortunate malefactor had come again to life. It is significant also that Aldini in his report says that his object was not to produce reanimation, but to ob- tain a practical knowledge how far galvanism might be employed as an auxiliary to recover persons who were accidently suffocated, as though he himself were in some 1 Dr. Richardson will certainly excite the contempt of the northern professor who rebuked me recently for speaking of heat when I should have said temperature. ' An atmosphere two degrees below freezing- point ' is an expression as inadmissible, if we must be punctilious in such matters, as the expressions ' blood heat, ' ' a heat of ten degrees, ' and so forth. Possibly, however, it is not desirable to be punctilious when there is no possibility of being misunderstood, especially as it may be noticed (the Edinburgh professor has often afforded striking illustra- tions of the fact by errors of his own) that too great an effort to be punctilious often results in very remarkable incorrectness of expression. 368 FAMILIAR SCIENCE STUDIES. doubt, that is, not in doubt only about the power of gal- vanism, but in doubt whether Foster had been restored to life for a while, or not ! Dr. Richardson has himself re- peated, on lower animals, these experiments of Aldini's, except that the animals on which he had experimented have passed into death under chloroform, not through suffocation. His object, in fact:, was to determine the best treatment for human beings who sink under chloroform and other anaesthetics. He finds that in warm weather he fails to get the same results. Noticing this, he says, ' I experimented at and below the freezing-point, and then found that by the electrical discharge, and by injection of water heated to 130 degrees ' (again this terrible inexactness of expression) ' into the muscles through the arteries, active muscular movements could be produced in warm-blooded animals many hours after death. Thus, for lecture experiment, I have removed one muscle from the body of an animal that had slept to death from chloroform, and putting the muscle in a glass tube surrounded with ice and salt, I have kept it for several clays in a condition for its making a final muscular con- traction, do some mechanical work, such as moving a long needle on the face of a dial, or discharging a pistol. In muscles so removed from the body and preserved ready for motion there is, however, only one final act. For as the blood and nervous supply are both cut off from it, there is nothing left in it but the reserved something that was fixed by the cold. But I do not see any reason why this should not be maintained in reservation for weeks or months, as easily as days, in a fixed cold atmosphere.' Cold being, however, obviously insufficient of itself for the suspension of active life in warm-blooded animals, at least if such life is eventually to be restored, let us next consider some of the agencies which either alone or aided by cold may suspend without destroying life. The first known of all such agencies was mandragora. Dioscorides describes a wine, called morion, which was made from the leaves and the root of mandragora, and pos- SUSPENDED ANIMATION. 369 sessed properties resembling those of chloral hydrate. That it must have been an effective narcotic is shown by the cir- cumstance that painful operations were performed on patients subjected to its influence, without their suffering the least pain, or even feeling. The sleep thus produced lasted several hours. Dr. Richardson considers that the use of this agent was probably continued until the twelfth or thirteenth century. ' From the use of it doubtless came,' he says, ' the Shaksperean legend of Juliet.' He strangely omits to notice that Shakspeare elsewhere speaks of this narcotic by name, where lago says of Othello : ' Not poppy, nor mandragora, Nor all the drowsy syrups of the world, Shall ever med'cine thee to that sweet sleep Which thou own'dst yesterday.' Probably the use of mandragora as a narcotic may have continued much later than the thirteenth century. In earlier times it was certainly used as opium is now used, not for medicinal purposes, but to produce for a while an agreeable sensation of dreamy drowsiness. ' There were those,' says Dr. Richardson, in an interesting article on Narcotics in the Contemporary Review, 'who drank of it for taste or pleasure, and who were spoken of as ' man- dragorites,' as we might speak of " alcoholists " or " chloral- ists." They passed into the land of sleep and dream, and waking up in scare and alarm were the screaming man- drakes of an ancient civilisation.' He has himself made the ' morion ' of the ancients, dispensing the prescription of Dioscorides and Pliny. ' The same chemist, Mr. Han- bury,' he says, ' who first put chloral into my hands for experiment, also procured for me the root of the true man- dragora. From that root I made the morion, tested it on myself, tried its effects, and re-proved, after a lapse perhaps of four or five centuries, that it had all the properties originally ascribed to it.' The ' deadly nightshade ' has similar properties. (In fact, morion was originally made from the Atropa belladonna, B B 370 FAMILIAR SCIENCE STUDIES. not from its ally the Atropa mandragora.} In 1851, Dr. Richardson attended two children who were poisoned for a time from eating the berries and chewing the leaves of the nightshade, which they had gathered near Richmond. They were brought home insensible, he says, ' and they lay in a condition of suspended life for seven hours, the greatest care being required to detect either the respiration or the movements of the heart; they nevertheless recovered.' With the nitrite of amyl. Dr. Richardson has suspended the life of a frog for nine days, yet the creature was then restored to full and vigorous life. He has shown also that the same power of suspension, though in less degree, ' could be produced in warm-blooded animals, and that the heart of a warm-blooded animal would contract for a period of eighteen hours after apparent death.' The action of nitrite of amyl seems to resemble that of cold. In the pleasing language of the doctors, ' it prevents the pectous change of colloidal matter, and so prevents rigor mortis, coagulation of blood, and solidification of nervous centres and cords.' So long as this change is prevented, active life can be re- stored. But when in these experiments ' the pectous change occurred, all was over, and resolution into new forms of matter by putrefaction was the result.' From the analogy of some of the symptoms resulting from the use of nitrite of amyl with the symptoms of catalepsy, Dr. Richard- son has ' ventured to suggest that under some abnormal conditions the human body itself, in its own chemistry, may produce an agent which causes the suspended life observed during the cataleptic condition.' The suggestion has an interest apart from the question of the possibility of safely suspending animation for considerable periods of time : it might be possible to detect the nature of the agent thus produced by the chemistry of the human body (if the theory is correct), and thus to learn how its power might be coun- teracted. Chloral hydrate seems singularly efficient in producing the semblance of death, so completely, indeed, as to de- SUSPENDED ANIMATION. 371 ceive even the elect. Dr. Richardson states that at the meeting of the British Association at Exeter, some pigeons which had been put to sleep by the needle injection of a large dose of chloral, ' fell into such complete resemblance of death that they passed for dead among an audience con- taining many physiologists and other men of science. For my own part,' he proceeds, ' I could detect no sign of life in them, and they were laid in one of the out-offices of the museum of the infirmary as dead. In this condition they were left late at night, but in the following morning they were found alive, and as well as if nothing hurtful had hap- pended to them.' Similar effects seem to be produced by the deadly poisons cyanogen gas and hydrocyanic acid, though in the following case, narrated by Dr. Richardson, the animal experimented upon (not with the idea of even- tually restoring it to life) belonged to a race so specially tenacious of life that some may consider only one of its pro- verbial nine lives to have been affected. In the laboratory of a large drug establishment a cat, ' by request of its owner, was killed, as was assumed, instantaneously and painlessly by a large dose of Scheele's acid. The animal appeared to die without a pang, and, presenting every appearance of death, was laid in a sink to be removed on the next morn- ing. At night the animal was lying still in form of death in the tank beneath a tap. In the morning it was found alive and well, but with the fur wet from the dropping of water from the tap.' This fact was communicated to Dr. Richard- son by an eminent chemist under whose direct observation it occurred, in corroboration of an observation of his own similar in character. Our old friend alcohol (if friend it can be called) pos- sesses the power of suspending active vitality without destroying life, or at any rate without depriving the muscles of their excitability. Dr. Richardson records the case of a drunken man who, while on the ice at the ' Welsh Harp ' lake, fell into the water through an opening in the ice, and was for more than fifteen minutes completely immersed. B B 2 372 FAMILIAR SCIENCE STUDIES. He was extricated to all appearance dead, but under artifi- cial respiration was restored to consciousness, though he did not survive for many hours. On the whole, alcoholic sus- pension of life does not appear to be the best method avail- able. To test it, the patient must first get ' very, very drunk;' and even then, like the soldiers in the old song, must go on drinking, lest the experiment should terminate simply in the fiasco of a drunken sleep. The last agent for suspending life referred to by Dr. Richardson is pure oxygen. But he has not yet obtained such information on the power of oxygen in this respect as he hopes to do. Summing up the results of the various experiments made with narcotics and other agents for suspending life, Dr. Richardson remarks that much is already known in the world of science in respect to the suspension of animal life by artificial means : ' cold, as well as various chemical agents, has this power, and it is worthy of note that cold, together with the agents named, is antiseptic, as though whatever suspended living action, suspended also by some necessary and correlative influence the process of putrefactive change.' He points out that if the news from Brisbane were reliable, it would be clear that what had been done had been effected by the combination of one of the chemical agents above named, or of a similar agent, with cold. The only question which would remain as of moment is, not whether a new principle has been developed, but whether in matter of detail a new product has been discovered which, better than any of the agents we already possess, destroys and suspends animation. ' In organic chemistry,' he proceeds, ' there are, I doubt not, hundreds of substances which, like mandragora and nitrite of amyl, would suspend the vital process, and it may be a new experimenter has met with surh an agent. It is not incredible, indeed, that the Indian Fakirs possess a vegetable extract or essence which possesses the same power, and by means of which they perform their as yet unexplained feat of prolonged living burial.' But he SUSPENDED ANIMATION. 373 is careful to note the weak points of the Australian story viz., first, the statement that the method used is a secret, ' for men of true science know no such word ; ' secondly, that the experimenter has himself to go to America to pro- cure more supplies of his agents ; and, thirdly, that he requires two agents, one of which is an antidote to the other. As respects this third point, he asks very pertinently how an antidote can be absorbed and enter into the circula- tion in a body p radically dead. It is, of course, now well known that the whole story was a hoax, and a mischievous one. Several Australian farmers travelled long distances to Sydney to make inquiries about a method which promised such important results, only to find that there was not a particle of truth in the story. 374 FAMILIAR SCIENCE STUDIES. OUR ASTRONOMERS ROYAL. IN the sixteenth century men began to travel boldly across the ocean, whole fleets taking such journeys as until then had been undertaken now and then by some daring sea captain. It was early in August 1492 that Columbus had set sail, in a ship of not quite a hundred tons burden, across the wide Atlantic, and seventy days later, on Friday, October 12, 1492, he sighted an island of the Bahama group (most probably Cat Island, though some maintain the claims of Turks' Island), and supposing he had reached the Indies by a westerly route, gave to the insular region the name it still bears the West Indies. Inexact measure- ments of the earth's globe, and imperfect means of determin- ing his westerly range of travel, led to this utter miscon- ception of the true position on the earth of the region to which his daring expedition had led him. So far as such occasional journeys were concerned, men might have con- tinued to remain content with their imperfect astronomical knowledge. But when in the course of a few decades navigation extended, it became essential that seamen should have some means of determining their position on the ocean- Yet years passed, and though every sea captain could on any clear day or night determine with sufficient accuracy his latitude, or distance from the equator, no means had been devised for determining even roughly the longitude? or the distance east or west from any given point on the earth from which (as from Greenwich, Paris, or Washington in our own time) longitude may be measured. OUR ASTRONOMERS ROYAL. 375 The nature of the difficulty which in the sixteenth century, and still more in the seventeenth, exercised astro- nomers and seamen may be readily indicated. Imagine a captain in the open ocean without any knowledge of his position, but with instruments for determining the apparent positions of the heavenly bodies in the sky. Then on the first clear night he can observe the elevation of the pole star, and though the pole star is not actually at the pole of the heavens, the observation will give him a rough indication of his latitude. For the pole of the heavens is the point towards which the axis of the earth points, and it is easily seen that the nearer a place is on the equator (the great circle lying exactly midway between the ends of that axis) the nearer the visible pole of the heavens will be to the horizon. An observer who should pass uniformly from the equator to either pole of the earth, would find the pole of the heavens passing as uniformly from the horizon l to the point overhead. Its arc distance from the horizon would all the time exactly correspond to his arc distances from the equator. So that if the pole star were exactly at the pole of the heavens, an observer, by determining its apparent height, would at once determine his latitude, or distance from the equator. And though the pole star does not occupy that precise position, yet it moves only in a small circle around the true pole, and by noting it either when just above or just below the pole, or when exactly to the right or exactly to the left of the pole, the true position of the pole itself becomes known, simply because the distance of the pole star from the pole is known. In the southern seas, where there is no star very near the pole, the case is not so simple, but even there any star circling at a known distance around the pole would give the southerly latitude. But as a matter of fact the sun is usually observed for the latitude. For his distance north or south of the equator on any given day of 1 I take no account here of the effects of the refractive or bending action of our own air on the rays of light from a star, but suppose the observation corrected for refraction as it is technically expressed. 376 FAMILIAR SCIENCE STUDIES. the year is known, so that by observing him at noon when he is at his highest and due south, either just above or just below the highest point of the equator on the sky, we learn the apparent height of this highest point of the equator. A line to this point makes of course exactly a right angle with a line to the pole of the .heavens ; and thus we learn the latitude as certainly in this way as \ve could by observing a star actually at the pole, if such a star there were ; and as it is always more convenient to observe in the daytime than at night, it is in this way usually that latitude is determined. Moreover, although instruments were less exact and ingeni- ous in the sixteenth century than now, and the position of the sun day after day with respect to the equator was less exactly determined, this method was as available (so far as general principles were concerned) at that time as at present. But how should an observer, placed as we have supposed in the open sea, determine how far east or west he was of any given place on the earth ? The aspect of the starlit heavens, and the daily motions of the sun and planets, are almost exactly the same at stations in the same latitude, how- ever far apart they may be. The motions of the moon, on ac- count of her relative proximity to the earth, are very slightly different at different stations in the same latitude, but the difference is so slight that without excellent instruments and the most perfect knowledge of the moon's motions, no ob- server could pretend to determine his longitude from obser- vations of the moon even on land, far less from the unstable deck of a ship at sea. The real difference between two stations far apart in longitude, that is, in an east and west direction, is as great as the difference between two stations as far apart in latitude ; but whereas the latter difference is one which may be studied and determined at any time, the other is a difference depending entirely on the time. Thus if A and B are two observers far apart in a north and south direction, either can at any time determine the apparent elevation of the pole of the heavens as seen from his station, and so learn his latitude. The difference OUR ASTRONOMERS ROYAL. 377 between these two elevations is the same all the time. If A could telegraph to B, and vice versa, either would give the other at any time the same news about the position of their respective poles. But if two observers, C and D, were in the same latitude and at stations far apart in longitude, say C far to the east of D, though C and D at any given moment would have the stellar groups very differ- ently arranged with respect to the horizon, yet the aspect seen by C at any given moment would be shown to D after a certain definite time interval had elapsed. It would be impossible for either C or D to tell how far east or west their respective positions were from Greenwich or other fixed point on the earth, or how far east C was from D, by mere observations of the heavenly bodies however carefully such observations might be made (apart always from those exact observations of the lunar movements to which I have referred above). But if C could telegraph to D describing the exact aspect of his skyscape at any moment, then D, by waiting till his skyscape presented the same aspect, could tell exactly how far west l he was from C. If, for instance, a quarter of a day elapsed, D would know he was a quarter of the way round the earth west (measuring along their common circle of lati- tude, or along the equator from the point due south of C to the point due south of D), or perhaps I shall be better under- stood by saying that in this case a quarter rotation of the earth round her axis has carried D's place to the position before occupied by C. Or, if D had a clock showing true time at C's station, and so knew the precise epoch when the heavens seen by C would have such and such an aspect, he would, by noting how much later his own skies assumed that as- pect, become aware how far west his position was from C's. But if his timepiece had gone wrong, he would be pro tanto mistaken. Such a mistake to a captain at sea might mean that a coast which he supposed to be far to the west or east 1 The earth rotates of course from west to east, and so causes all the heavenly bodies to apparently rotate from east to west. 378 FAMILIAR SCIENCE STUDIES. of him would be close at hand, and in a short time he might run his ship upon it and be destroyed. For safe navigation in open ocean, then, special know- ledge of the movements of the heavenly bodies is required. Even to determine latitude well a seaman requires excellent instruments, and carefully constructed tables of the motions of the sun, moon, planets, and stars. For longitude he requires still more thorough investigation of the moon's movements (at least for long lasting ocean journeys), and in addition he should have most accurate time measurers. How accurately time should be measured for this purpose will be inferred from the following considerations. At the equator an hour corresponds to fifteen degrees of longitude, or four minutes to one degree, or about 69^ nautical miles ; thus four seconds correspond to one nautical mile, and one second to rather more than 500 yards. In latitude 60 degrees north these distances are diminished one half ; but still so small an error as a second in time corresponds to about 260 yards, and an error of seven seconds, such an error as the best stationary clock might easily acquire in a week, would correspond to an error as to position of more than a geographical mile ! It will be readily understood that even in the sixteenth century, when hundreds of ships crossed the Atlantic, Pacific, and Indian Oceans, there was occasion for very careful study of the celestial movements, very excellent instruments, and very accurate time-measuring apparatus. How much greater was the need in the seventeenth century, when for every ship that had crossed the ocean in the days of Henry VIII., there were hundreds on its broad bosom ? It was thus that the necessity arose for national obser- vatories, not intended, as many imagine, for the study of astronomy as a science (though the science of astronomy is undoubtedly advanced in a most important manner by such observatories), but for the survey of the heavens and the exact measurement of time. Precisely as navigation would be unsafe unless the terrestrial globe were carefully surveyed, OUR ASTRONOMERS ROYAL. 379 and the true position of every coast line, nay, even of every rock and reef, accurately determined, as well as all changes which such coast lines, islands, rocks, reefs, &c., may under- go, so would navigation be unsafe unless the celestial globe, within which as it were the earth is suspended, had been carefully surveyed, and the true position of every star, the exact paths along which sun, moon, and planets travel, all accurately determined. And in passing it may be noticed that the work of a national observatory (where alone such survey of the heavens can be conducted) bears somewhat the same relation to the higher astronomical research, that the trigonometrical and topographical survey of the earth's surface bears to the profounder studies of the geologist, the biologist, and the paleontologist. Yet it was not till the year 1674 that any definite scheme for systematic survey of the heavens, in the interests of navigation and commerce, was planned in this country. It had been pointed out by a Frenchman, Le Sieur de St. Pierre, that if the motion of the moon as supposed to be seen from the earth's centre could be accurately predicted, then a seaman who should at any moment observe the exact position of the moon in the heavens, would know the precise instant of terrestrial time (say the true London time) at that moment. Thence, as the difference of longitude between two stations is measurable by the difference of time l between those stations, the latitude of the ship could be exactly determined. Charles II., to whom the plan was proposed by Le Sieur de St. Pierre, referred it to a commission of officers and scientific men. One of these, Sir Jonas Moore, 1 That is, the difference between the time of noon, or of the coming to the south of any known fixed star, at those two stations. It should not be necessary to explain this, because the words ' difference of time ' can bear no other interpretation, seeing that it is the same moment of absolute time at any instant all over the world and throughout the uni- verse. Yet repeatedly I have been asked what astronomers can mean by the time being different at different stations. A rough way of ex- pressing their meaning is by saying that the time of day is different at different stations, 380 FAMILIAR SCIENCE STUDIES. sought the opinion of Flamsteed on the subject, Flamsteed being well known at that time as a skilful astronomer. Flamsteed stated that in his opinion the knowledge of the inoon's motions at that epoch was far too inexact for the purpose intended. He said that ' even the places of the stars in existing catalogues were grievously faulty.' It was as though a geographer should have said that none of the charts used by navigators showed the positions of coast lines with any approach to accuracy. Charles II., who really showed a most commendable zeal for science in this matter, was much struck by Flam- steed's remark, and very sensibly pointed out that if astro- nomical knowledge were thus defective, the best thing to be done was to set to work at once, and zealously to correct the defect. Under the auspices then of the king, of whom Rochester wrongly said that ' he never said a foolish thing and never did a wise one,' Greenwich Observatory was built, and in 1676 Flamsteed, who had been appointed Astronomical Observator, 1 at a salary of ioo/. a year, entered into residence at the Observatory. The instruments which he principally used in his work as Astronomical Observator were not in use until 1689. And here it may be asked how it was that a much greater man than Flamsteed, a man who reached the zenith of his fame during Flamsteed's tenure of the office of Astronomer Royal, but had already attained a widespread reputation when Greenwich Observatory was founded, was not appointed to be Astronomical Observator. Whether the office was ever offered to Sir Isaac Newton or not, I do not know, but most assuredly if it were so offered, it is most fortunate for science that the offer was not accepted. Prob- ably Newton would not half so efficiently as Flamsteed 1 This title is still retained in official documents, and is undoubtedly a more suitable title than that of Astronomer Royal, seeing that astro- nomical surveying, not astronomical research, is the chief duty of the office. OUR ASTRONOMERS ROYAL. 381 have executed the observations which this observer made, though men inferior to either might have executed those observations as well as Flamsteed or better. But certainly no one could have done Newton's work had he neglected it for the routine work at Greenwich. Yet we must not forget that without the systematic observations of Flamsteed, Newton would never have been able to place the theory of the universe on that firm basis whereon he established it in his ' Principia.' The architect, however great his genius, cannot complete his conceptions without the aid of the builder, any more than the builder can erect an edifice with- out the materials necessary for his work. Flamsteed laboured at Greenwich under difficulties such as none of his successors have had to encounter. His salary, as already mentioned, was but one hundred pounds per annum, and even this pittance was often ill-paid. He had to buy or make his own instruments. To defray the expenses he thus incurred, he was obliged to take pupils. At first he observed with a sextant belonging to Sir Jonas Moore, who also lent him two clocks ; some other instru- ments were lent him by the Royal Society. The sextant was of iron and seven feet in radius. The clocks were con- structed by Tompion, the most celebrated clockmaker of his day. The pendulums were thirteen feet long, and swung a complete or double vibration in four seconds, that is, beat two second, so that their length was four times the length of a pendulum beating seconds, or about thirteen feet. They were so constructed that they required winding only once a year. Flamsteed also brought with him from Derby to Greenwich a quadrant three feet in diameter. With these instruments, strangely in contrast with those now in use, Flamsteed began his labours at Greenwich on October 29, 1676. I need hardly say that I do not here propose to give any detailed account either of the methods followed by Flamsteed and his successors, or of the instruments they employed in their work. But it may be interesting to notice 382 FAMILIAR SCIENCE STUDIES. how utterly unlike was the plan first followed from that no\y universally employed. Flamsteed's first observation of the stars, or his survey of the heavens, was conducted much as a trigonometrical survey of a terrestrial tract is carried out. He measured with the sextant the apparent arc-distance separating a star from each of two stars (or from more than two) whose positions were already known, and thence calcu- lated the position of the star. The method is very rough, and could lead but to imperfect results. At the present day astronomers follow an entirely different and far more satis- factory plan. A telescope is caused to swing so as to sweep the meridian, that is, the circle on the heavens passing from the south point of the horizon to the point over head and thence to the north point of the horizon. Every heavenly body visible in our northern heavens must in its daily rota- tion around the polar axis of the skies cross the meridian once at least. (If it is one of the stars within ' the circle of perpetual apparition,' or stars near enough to the pole not to set when due north, the heavenly body crosses the meri- dian twice, once above the pole and once below it, in each diurnal circuit.) The telescope then which sweeps the meridian serves to show at what elevation and at what time any heavenly body crosses that circle of the heavens, and thus shows the body's distance from the pole, and its rota- tional distance from any fixed circle through the poles from which the astronomer may find it convenient to measure such rotations. Whereas in the first method, the astronomer had to measure arcs in all imaginable directions ; he has by the modern method to measure only vertical arcs, and these always along one and the same semicircle from south to north. The superiority of the modern method, 1 as 1 I speak of this method as modern, but there are reasons for re- garding it, as in principle, exceedingly ancient. For in the great pyra- mid, which was manifestly intended for astronomical observation (though afterwards cased over so that none who came after its owner's death should use it for that purpose), we find the great ascending gallery, 150 feet in length and 28 feet in, height, constructed so as to bear pre- OUR ASTRONOMERS ROYAL. 383 respects uniformity of procedure and of result, will be mani- fest to all. There are other not less important advantages which only the mathematician can fully appreciate. Flamsteed retained the office of Astronomical Observator to the end of his life, which occurred on the last day of the year 1719. His first observation was made on October 29, 1676, but it was not until September u, 1689, that he began regular observations of stars on the meridian with a mural arc, an instrument so constructed as to swing on the face of a vertical north and south wall (whence its name), and with a sweep of one hundred and forty degrees on the meridian. The forty-three years of Flamsteed's tenure of the office did not pass without some unseemly quarrels, chiefly caused by the impatience with which contemporary astronomers awaited the publication of his results. We find him, in October 1700, writing thus to Dr. Smith, of Oxford : 'Briefly, sir, I am ready to put the observations into the press as soon as they that are concerned shall afford me assistants to copy them and finish the calculations. But if none be afforded, both they and I must sit down contented, till I can finish them with such hands as I have ; when I doubt not but to publish them, as they ought to be, hand- somely and in good order, and to satisfy the world, whilst I have been barbarously traduced by base and silly people, that I have spent my time much better than I should have done if, to satisfy them, I had published anything sooner and imperfect.' The impatience of his contemporaries, however, caused him to depart from. the course on which he had thus deter- mined. He drew an estimate of the extent of the work which had to be prepared for the press. This estimate was cisely on the meridian, a long arc of which it commanded ; while many of the details of this gallery are such as an astronomer intending it for the purpose indicated would have been certain to give to it, and such as on any other hypothesis appear to be without reasonable interpre- tation. 384 FAMILIAR SCIENCE STUDIES. read at a meeting of the Royal Society on November 15, 1704, and was unanimously approved. Prince George of Denmark, Queen Anne's husband, undertook to pay all the expenses of publication, and a committee, consisting of Newton, Wren, and three others, was appointed to examine Flamsteed's manuscripts. The committee recommended that the observations should all be published. Flamsteed placed in their hands a copy of the observations so far made, but stipulated that no steps should be taken toward their publication. So at least he asserted afterwards ; but it is clear the stipulation was not such as to prevent the work being sent to the printers as it was. When, however, he should have supplied the rest, Flamsteed broke his agree- ment with the committee, delaying the printing for no other purpose, so far as appears, but to obtain better terms. In 1708 Prince George died, and a further delay ensued. But as Flamsteed himself showed no disposition to supply the required copy, complaints were made which led to the appointment of a board of visitors, consisting of the Presi- dent of the Royal Society, and such other members of the Council of that Society as he should deem fit to take part with him in the work of supervision. They were authorised to demand of the Astronomical Observator, six months after the close of each successive year, a true and fair copy of his annual observations, and also to direct him to make such observations as they should consider desirable. They were also to inspect the instruments, and to see that these were maintained in proper and serviceable condition. Professor Grant, in his excellent ' History of Physical Astronomy,' remarks on this important event in the annals of the Royal Observatory : ' The origin of the Board of Visitors is clearly traceable to the unfortunate misunder- standing that prevailed between Flamsteed on the one hand, and his scientific countrymen generally on the other. It has continued to exercise its functions to the present day. The salutary influence of such a board of inspection is indis- OUR ASTRONOMERS ROYAL. 385 putable, for while on the one hand it serves to prevent the application of the resources of the Observatory to any un- warrantable purposes, on the other it has the effect of period- ically relieving the conscientious astronomer, from the responsibility attaching to the discharge of his onerous duties, and thereby operates as an encouragement of future exertion. It is gratifying to reflect that during the last hundred years, at least, it is only in the latter respect that the advantages resulting from the establishment of the Board of Visitors have been apparent.' 1 In the spring of 1711 Flamsteed's observations were published in a folio volume. The incomplete catalogue of stars which Flamsteed had placed in the hands of the com- mittee in 1704 appeared in this volume, notwithstanding his alleged stipulation that it should be regarded only as a pledge for his subsequent delivery of a complete catalogue into their hands. But there is no room for doubt that even if the stipulation were made as alleged, it was not binding under the circumstances. Had the complete catalogue been placed in the printer's hands in reasonable time, there would undoubtedly have been no excuse for the issue of the incomplete one ; but year after year had passed without any fulfilment of Flamsteed's agreement to complete the catalogue, and the course pursued by the Committee was the only one left open to them. If Flamsteed's stipulation could be regarded as under any and all conditions closing 1 At the accession of William IV. a new warrant was issued, by which the constitution of the Board of Visitors was to some degree modified. The Royal Astronomical Society had then recently been formed, and received its charter at that time. As the new society was formed specially for the advancement of astronomy, whereas the Royal Society took all science (and more) as its province, and so might have for its president a man very slightly acquainted with astronomy, it was fitting that a share, at least in the supervision of the national Astro- nomical Observatory, should be assigned to the Society specially de- voted to astronomy. Accordingly the two Societies the Royal and the Astronomical are, according to the new warrant, represented equally in the Board of Visitors. C C 386 FAMILIAR SCIENCE STUDIES. this course against them, the incomplete catalogue had no value as a pledge. The quarrels which arose between Flamsteed on the one part and Newton and Halley on the other, were first made matter of public discussion in 1835, by Mr. Francis Baily. Finding in Flamsteed's own manuscripts and autobiography a number of statements injurious to the characters of Newton and Halley, Mr. Baily unwisely published what he called an 'Account of the Life of Flamsteed/ which in- volved in effect an ex parte and unjust attack upon those eminent men. In 1837 Mr. Baily published a supplement, in which he stated that he had ' sought in vain for docu- ments which might tend either to extenuate or explain the conduct of Newton and Halley.' He cannot have searched very carefully, for such documents existed precisely where one would have expected to find them, namely, among Sir Isaac Newton's papers. Among these papers Sir David Brewster discovered a series of letters and other documents, completely exculpating Newton and Halley from the charges rashly brought against them by Mr. Baily, and placing the character of Flamsteed, their calumniator, in a very unfavour- able light. Apparently the sole cause of Flamsteed's delay in the first instance, and anger with Newton and Halley in the second, was a greed of money. Albeit, Flamsteed did good work as Astronomical Observator. Professor Grant thus sums up his work : ' Flamsteed is universally admitted to have been one of the most eminent practical astronomers of the age in which he lived. His merits do not, indeed, appear at first sight so conspicuous as those of some of his illustrious contem- poraries with whom he may be compared, although at the same time they are no less substantial. In carrying out views of practical utility, with a scrupulous attention to accuracy in the most minute details, in fortitude of resolu- tion under adverse circumstances, and persevering adherence to continuity and regularity of observation throughout a long career, he has few rivals in any age or country. He OUR ASTRONOMERS ROYAL. 387 was thus enabled to establish the fundamental points of practical astronomy upon a new basis, and to rear a super- structure which, for many years afterwards, served as a land- mark of vast importance to astronomers. . . : As first astronomer of the Royal Observatory of Greenwich, he set an example to his successors the beneficial influence of which cannot for a moment be doubted ; nor while that noble establishment continues to maintain its proud pre- eminence [high position ?] among the institutions devoted to practical astronomy, will the labours of its original director, prosecuted with such unwearied perseverance throughout a long career, despite the depressing influence of constitu- tional ill-health [and the unrelenting hostility of a powerful faction l ], cease to be held in respectful remembrance by his countrymen.' Flamsteed was succeeded by Halley. But as all Flam- steed's instruments were removed from Greenwich, no observations could be made till 1721. On October i in that year Halley made his first observation with a transit instru- ment said to have been made by Dr. Hooke. A greater astronomer than Flamsteed, perhaps inferior only to Sir Isaac Newton (certainly inferior only to him among the English astronomers of his day), Halley was by no means so skilful in the practical work of a sky-surveying observatory. In the first place, Halley was in his sixty-fourth year when he accepted the appointment. As Professor Grant remarks, it is surprising, when we consider his age, ' that he should have undertaken the discharge of duties of 1 This was written at a time when it was supposed that the attack made by Mr. Baily on Newton and Halley represented the true state of the case instead of being a mere ex parte statement. I believe the view I have expressed in my sketch of Flamsteed's life, in the Encyclo- pedia JBritannica, is sound viz., that the necessity for publishing Sir David Brewster's refutation was scarcely a less misfortune for science than was the original and most foolish blunder of Baily's in publishing his ill-considered attack. Scientific squabbles are degrading enough when they occur without being raked up a century afterwards. 388 FAMILIAR SCIENCE STUDIES. so onerous a nature as those attached to the situation of Astronomer Royal.' The habits of minute attention to de- tails, required for successful work in practical astronomy, are not readily acquired in advanced life. But Halley seems to have had little original aptitude for such work, and indeed to have undervalued (a common fault) the qualities he did not possess. We may pay but little attention to Baily's severe criticism of Halley's observations as not worth print- ing, because Baily may have been to some degree prejudiced against Halley after reading Flamsteed's animadversions. But Maskelyne had earlier told Delambre that Halley's ob- servations (extending from October 1721 to December 31, 1739) were hardly better than Flamsteed's, a severe criticism when the rapid progress of improvement in the instruments of observation in those days is taken into account Halley died on January 14, 1742, in the eighty-sixth year of his age. During more than twenty-four months before his death he had made no observations, 1 a circum- stance not to be wondered at when we consider how old he was. What one does wonder at is that being too old to discharge the duties of his situation he did not resign. Bradley, who succeeded Halley as Astronomer Royal in 1742 (his nomination is dated February 2, 1742), was one of the ablest, perhaps the very ablest, of all who have held the office. While astronomy owes to him, as it does not to any other Astronomer Royal, some of the greatest disco- veries which have adorned the science, these were such as 1 At a meeting of the Royal Society on March 2, 1727, Sir Isaac Newton, then President, called attention to the circumstance that Halley had not supplied the Board of Visitors, in accordance with the authority given them, a true and fair copy, within six months after the lapse of each successive year, of the observations made during such year. He pointed out that the continued neglect of this regulation might be detrimental to the public interest. Halley, who was present, made the rather lame excuse that he thought it better to keep the obser- vations in his own custody, so that he might finish the theory he designed to build on them before others could reap the benefit of his labours. OUR ASTRONOMERS ROYAL. . 389 belonged to the field of his labours as a practical observer. His discovery of the aberration of light was indeed made before he accepted the situation of Astronomical Observator at Greenwich ; but in the prosecution of the observations which led to that discovery he was fitting himself for the position he afterwards held. His more difficult and less striking, but in reality more important, 1 discovery of the nuta- tion of the earth's_axis was made while he was at Greenwich. It will serve to indicate the general character of the work at Greenwich, as well as to show what progress practical astronomy was making, to consider but we must do so very briefly the nature of these discoveries. For guidance in navigation and travelling generally, as well as in the measurement of time for civil and other pur- poses, the stars and other heavenly bodies are regarded by the astronomer as sky marks, whose observed direction gives certain information as to position or as to time. But that the information should be trustworthy, the causes which may lead to erroneous ideas as to a heavenly body's direction must be understood and their effects corrected. Speaking generally, it may be stated that, in the first place, not a single star visible in the sky at any moment is really where it seems to be ; and in the second, every star's position on the star vault is constantly, though slowly, changing. As it is the specific office of an Astronomical Observator to learn precisely where the heavenly bodies are, he must manifestly find out all the circumstances which might cause him to be deceived. Some of the sources of error are sufficiently ob- vious. A rough instrument, such as an ingenious schoolboy could construct in an hour or two, would suffice to indicate the deceptive effect of our own air, whose refractive action on rays of light causes every star to appear somewhat higher in the heavens than it really is. Other sources of error are less easily ascertained. Again, though the reeling of the earth like a gigantic top, under the attractions of the sun and 1 More important in its bearing on physical astronomy, though less important as regards practical observation. 390 FAMILIAR SCIENCE STUDIES. moon, does not cause any star to appear in a direction in which it does not actually lie, yet by constantly changing the position of every star with respect to the poles of the heavens (more correctly by constantly changing the position of these poles on the star sphere), this motion causes a steady though slow change in the calculated position of every star. So also does the slow motion of each star or sun along its own special path in space. The aberration of light is a displacement of the former kind, nutation a displacement of the latter kind. Light streams forth in all directions with enormous velocity from each star, while the earth rushes with enormous velocity round the sun. The latter velocity, though enormous, is but small compared with the former. Yet it has to be taken into account in determining the direction whence the light of a star comes, just as the velocity of a ship propelled other- wise than by a stern wind, has to be taken into account in determining the direction in which the wind is blowing. 1 1 It is worthy of mention that Bradley was led to the interpretation of the aberration of the fixed stars by the recognition of precisely this analogous phenomenon. Dr. Robison, of Edinburgh, relates the story in his article on Seamanship. The following account is from Dr. Thomson's History of the Royal Society : ' When Bradley despaired of being able to account for the phenomena which he had observed, a satisfactory explanation of it occurred all at once to him when he was not in search of it. He accompanied a pleasure party in a sail upon the River Thames. The boat in which they were was provided with a mast, which had a vane upon the top of it. It blew a moderate wind, and the party sailed up and down the river for a considerable time. Dr. Bradley remarked that every time the boat put about, the vane at the top of the boat's mast shifted a little as if there had been a slight change in the direction of the wind. He observed this three or four times without speaking ; at last he mentioned it to the sailors, and ex- pressed his surprise that the wind should shift so regularly every time they put about. The sailors told him the wind had not shifted, but that the apparent change was owing to the change in the direction of the boat, and assured him that the same thing invariably happened in all cases. Bradley was quickly able to interpret the phenomena, and found in its interpretation that of the aberration of the fixed stars. OUR ASTRONOMERS ROYAL. 391 With a wind blowing from the side (the nautical reader will excuse my avoidance of technical terms) the forward motion of the ship causes the apparent wind to come from a point nearer that towards the ship is travelling than is, the point from which the real wind is blowing. In other words, the wind is made to appear less favourable than it really is. We may, in fact, regard the motion of the ship as producing a wind of equal velocity blowing dead against rhe ship's course, and this wind has to be combined with the real wind to give the direction of the apparent wind. The light coming from a star with a velocity of more than 180,000 miles per second has similarly to be combined with the effects of the earth's forward motion at the rate of about 18 miles per second ; and the apparent direction from which the star's rays seem to come (in other words, the apparent position of the star) is nearer to that point on the star-sphere towards which the earth is travelling than in the actual position of the star. So that just as an exactly head wind and an exactly stern wind are the only winds not affected in apparent direction by a ship's motion, so a star lying exactly in the direction towards which, and a star lying exactly in the direction from which, the earth is moving, would be the only stars in the heavens seen precisely in their true position (so far at least as aberration is concerned). The greatest possible displacement due to this cause occurs in the case of stars situated anywhere on the great circle lying between the two points just named, where there is no displacement. It is not great, simply because the earth's velocity in her orbit is but about the ten thousandth part of the velocity of light. l Still it is not one of those exceedingly minute quantities which tax the astronomer's means of instrumental observation. It amounts, in fact, to about the ninetieth part of the appa- rent diameter of the moon. 1 If we take along the circumference of a circle an arc equal in length to about the ten thousandth part of the radius, and draw radii to the two ends of this minute arc, the angle between these radii will correspond to the maximum apparent displacement of a star due to aberration, 392 FAMILIAR SCIENCE STUDIES. Even if we only consider the effect of such a displace- ment as this, if undetected, to the seaman, it appears by no means of small importance. Supposing a star on the equator, and displaced on account of aberration either eastwards or westwards by the greatest amount which this cause of dis- placement can produce, or about 20^ seconds of arc. Then since 15 degrees of arc on the heavens correspond to one hour of diurnal rotation, it follows that 15 minutes of arc correspond to one minute of time, and 15 seconds of arcs to one second of time. Thus 20 seconds of arc correspond to i seconds of time, and an error of this amount would be equi- valent in the determination of a ship's longitude to an error of more than 620 yards. But in reality the effect of neglecting such a correction as that due to aberration is not to be mea- sured in this way by its direct action. Indirectly, regarding the stars as skymarks by which the movements of sun, moon, and planets are measured, the correction due to aberration becomes of yet greater importance. It should be noticed that Bradley's great discovery might have been based on Flamsteed's observations alone. For though Flamsteed himself failed to detect the aberration of the fixed stars, he made his observations so carefully and well, that from the simple study of his various observa- tions of the several stars at different seasons, the amount of displacement caused by aberration can be determined almost as exactly as from the best observations of recent times. The nutation of the fixed stars is a displacement smaller in amount, and not affecting the direction in which the stars appear to lie, but the position of the earth from which we see them. The reeling motion of the earth detected by Hipparchus (though Ptolemy usually gets the credit of the discovery) is caused by the perturbing action of the sun and moon on the earth's spheroidal globe. Were the earth a perfect sphere, there would be no such motion. Nutation may be described as a quivering of the earth as she thus reels. Were the disturbing action of the sun and moon OUR ASTRONOMERS ROYAL. 393 constant, this reeling would be uniform ; but as the moon's path round the earth varies in position (in inclination, shape, &c.), the disturbing action varies, and thus the reeling varies in rate, and the slope of the reeling earth's axis varies also, or the axis of the reeling earth may be said to quiver. In reality there is a small and relatively rapid reeling super- added to the great slow reeling. The axial slope of the small reel so to describe what corresponds to the inclina- tion of a reeling top's axis to the vertical, amounts only to about 9^- seconds, and each reel is accomplished in about 1 8^ years, whereas the slope of the great precessional reel amounts to about 23^ degrees, and each reel requires about 25,900 years. Thus the pole of the heavens revolves in 25,900 years in a great circle 47 degrees in diameter, while it also revolves around the mean position due to this pre- cessional reeling in a circle really an oval 18| seconds in diameter, in a period of about 18^ years. All the stars are affected, so far as their position with respect to the poles is concerned, by these motions. The nutation thus intro- duces a correction of all stellar positions, which must be taken into account in all observations of the stars. I have considered these discoveries by Bradley because, as I have said, they are the most important of all the dis- coveries (almost the only important discoveries) made by astronomers carrying out the systematic work of practical observation, in other words attending to the business which they are paid to do. Bradley's last observation at Greenwich was made on July 16, 1762. He was succeeded by Dr. Bliss, Savilian Professor of Geometry at Oxford, who had few of the qualifications necessary for the office of Astronomical Obser- vator. He died early in 1765, his last observation having been made on March 1 5 in that year. Bliss was succeeded by Maskelyne, whose first observa- tion was made on May 7, 1765. He used the same instru- ments as Bradley, but he adopted a system better calculated to lead to trustworthy and valuable results. He limited his 34 FAMtLlAR SCIENCE STUDIES. observations to a select number of stars (besides, of course, the sun, moon, and planets). He observed these stars on every available occasion, and based on these observations a catalogue, which, though containing but thirty-six stars, was far more accurate than any previously formed. This plan of observation he continued throughout the whole period of his tenure of office, his first observation being made, as already mentioned, on May 7, 1765, his last on December 31, 1810. His actual period of office was slightly greater than 45! years, and has been surpassed only by the period during which Sir G. Airy held the office. We owe to Maskelyne the establishment of the ' Nautical Almanac,' which first appeared in 1767. It cannot be said that the Royal Observatory had fairly begun even to fulfil the purpose for which it was established until the ' Nautical Almanac' appeared. During his entire period of office Maskelyne superintended the publication of the almanac. When Maskelyne was made Astronomer Royal, there was no very eminent English astronomer to whom persons ignorant of the special duties of the office might have thought that the position should have been offered. Sir W. Herschel was teaching music until 1766, when he was appointed organist at Halifax, and his earliest regular obser- vations were made in 1776. It need hardly be said that later, during at least the last twenty years of Maskelyne's life, there could be no comparison between him and Sir W. Herschel as astronomers. Maskelyne was the more precise surveyor, but his name is associated with none of the great discoveries which constitute the glory of astronomy. Of William Herschel it has been justly said, cxlorum pe.rrupit daustra; he burst the bonds of the heavens, he penetrated beyond the limits that had before restrained men's views, and searched boldly into the depths of the universe. Of Maskelyne we can only say that he helped to assign the true position of certain celestial skymarks. But then this was the duty which Maskelyne was engaged to do j he did it honestly and well. OVR ASTRONOMERS ROYAL. 395 Eleven days after Maskelyne's last observation had been made, his successor, John Pond, made his first observation January n, 1811. Although his name is little known, indeed, scarcely known at all outside the ranks of profes- sional astronomers, he was one of the ablest of his class. He extended Maskelyne's method of sidereal astronomy to more than 1,000 stars, his catalogue being 'generally admitted/ says Prof. Grant, ' to be one of the most accurate productions of the kind that has ever been given to the world/ Fine instruments by Troughton were employed by him, and in the course of a controversy with Brinkley as to the distances of the fixed stars he invented a method of observing stars by reflection at the surface of mercury which notably increased the accuracy of certain orders of observations. During Pond's tenure of the office the career of Sir W. Herschel came to its end, and that of his almost equally distinguished son began. When Pond retired from office, in the autumn of 1835, Sir John Herschel was already recognised as England's greatest astronomer. Fortunately for science, no one was so ill-advised as to propose that this eminent man, already deeply engaged in the researches which have rendered his name illustrious, should be ap- pointed to the office rendered vacant by Pond's retirement. (Fortunately for science, at least, on the assumption doubt- less incorrect that if he had been offered the appointment, he would have left his congenial field of labours to accept others of far less scientific importance, for which he was far less fitted.) A successor to Pond was sought for among men already working in the same field, that is, already en- gaged in the work of exact surveying of the heavens. A most fortunate choice was made in the selection of George Biddell Airy, who, during his tenure of office (the longest hitherto by a few weeks, as compared with the next, Mas- kelyne's), has done more than any of his predecessors, save perhaps Bradley, to give to Greenwich its present high posi- tion among national observatories. He was already eminent in his special department of astronomical work, having ably 396 FAMILIAR SCIENCE STUDIES. directed the Cambridge Observatory during seven years. He had there introduced two features, unknown till then in the work of public observatories, viz., the reduction of all ob- servations by the observer himself instead of subordinates, and the systematic observation of the planets, a department of astronomy long neglected at Greenwich. Space does not remain for the description of the special work of Sir G. Airy. What remains must be devoted to some remarks on the mistaken ideas which many seem to have formed respecting the duties of the office, and on the unsuitable and in many cases preposterous selections made by newspaper writers for a successor to Airy. The late Professor De Morgan, in his ' Budget of Para- doxes,' relates an amusing story about Flamsteed, the first of our Astronomers Royal. An old woman who had lost a bundle of linen came to Flamsteed to learn its whereabouts, being under the impression that it was one of the duties, if not the chief duty, of an Astronomer Royal to answer such questions as are customarily addressed, by ignorant persons, to astrological charlatans. Flamsteed, proposing to amuse himself at the old woman's expense, ' drew a circle, put a square into it, and gravely pointed out a ditch near her cottage, in which he said it would be found .' He meant, says De Morgan, to have given the woman a little good advice when she came back ; but unfortunately for his pur- pose, the bundle was found in the very place which he had indicated. It is added, though De Morgan does not men- tion the fact, that Flamsteed determined thenceforth to have nothing to do with astrology even in fun. It would seem, from much that has been written about the office of Astronomer Royal, that the general public are scarcely better informed on the subject than the old lady who mistook the Astronomer Royal of her time for a con- juror. Persons were named as likely to succeed Airy who would have teen as ill-fitted for the office as a sea captain for a generalship, a general for the command of a fleet, or an historian for the office of prime minister. Even those who OUR ASTRONOMERS ROYAL. 397 have rightly apprehended that the office is one requiring special training, as well as original aptitude and capacity, have in many cases failed to note that such special training as observers in any great observatory may obtain, though fitting them for the charge of ordinary observatories, may not by any means fit them to take charge of a great national observatory. It must not be supposed that I make these remarks in depreciation of any of those who were named as likely to succeed the Astronomer Royal in the office to which Mr. W. M. Christie, formerly first assistant at Greenwich, has been appointed. Most of those who were thus named were persons who, by their method of life and study, removed themselves from even the possibility of being thought of in connection with the office, and, as it were, declined to have it offered to them. There is one road, and only one, in which a man, fit as respects capacity, can put himself in the way of the office, and even that road eventually branches out into several, one only of which leads to the goal in question. A skilful mathematician, with first-rate working powers, who shall begin, from the time of taking a high degree at the university, to work in one of the subordinate offices at Greenwich, taking shortly (in virtue of his position as a mathematician) one of the chief of these subordinate offices, may later become one of those from whom a new Astro- nomer Royal can be selected. But such a one may become, after a few years at Greenwich, the head of some important Government observatory, a position of greater emolument and perhaps of greater dignity, but one which, should he occupy it many years, unfits him for the office which is justly regarded as the highest which a professional astro- nomer can occupy. The reason of this is not far to seek. The routine at Greenwich is necessarily unlike that at other observatories. Much of the work which must be done at Greenwich is by no means essential elsewhere, and in turn much of the work which can be done with great advantage at other observatories (we are speaking all the time, be it 398 FAMILIAR SCIENCE STUDIES. understood, of Government observatories) would be entirely out of place at Greenwich. Now, even though the system at Greenwich were thoroughly stereotyped, which is far from being the case, a few years' absence from Greenwich work would render even the ablest astronomer less fit to take charge of our great national observatory than one who had been engaged in superintending such work during those years. Seeing, however, that the system at Greenwich, though to all intents and purposes fixed, does yet in details undergo modifications that, in fact, being a living organisa- tion, it grou>s, we can readily see that even the most skilful astronomer can only retain the fullest fitness for the office of Astronomer Royal, by remaining at Greenwich, and by working continuously under the direct supervision of the actual holder of that office. When such a man, other- wise possessing the requisite capacity, succeeds to the posi- tion of Astronomer Royal, there is the greatest chance that the change will cause no hitch, even for the shortest period, in the work of the great national observatory, and this, after all, is the point in which the public is most inte- rested. The fitness (in these respects) of the appointment re- cently made will therefore be readily understood, and it will be seen also why several of those named by persons unac- quainted with the requirements of the office were, for various reasons, more or less unsuited for the post. The greatest master living of the mathematics of astronomy, although at the head of an important observatory, would not only have been in all probability a less efficient Astronomer Royal than one who had been working for years at Greenwich, but his transference to the office (had he been willing to accept it) would have been a serious loss to science, because in the office of Astronomer Royal he would have been unable to continue those researches in which he has few or no equals. One of the greatest professors (if not actually the greatest) of pure mathematics could as ill be spared from his special labours, even if he possessed the knowledge of routine work OUR ASTRONOMERS ROYAL. 399 essential in the chief of our national observatory. It should hardly be necessary to say that the indefatigable director of the 'Nautical Almanac,' although for a long time the head (and a most skilful and successful head) of a fine private observatory, would be ill placed as chief at Greenwich if for no other reason for this, that he is the fittest man living for the post he actually holds. Again there are men who, by their telescopic researches in what may be called the physics of astronomy, by spec- troscopic observations and discoveries, by their analysis of the great mass of observations gathered by others, and in other ways, are deservedly regarded as having notably ad- vanced our astronomical knowledge, who would yet be al- together unfit to take charge even of the commonest routine work at Greenwich ; and even though they could, would only do so at the expense of more important work for which they are pre-eminently fitted. Most of these, indeed, are independent workers in astronomy, who are not willing (and have through the whole course of their lives shown that they are unwilling) to accept what would be to them the comparative slavery of a salaried office. One astronomer indeed, and only one of those who were mentioned as likely to succeed the Astronomer Royal, could have taken his place without loss to the public, either, on the one hand, because of unfitness for the post, or, on the other, because no one else could so well do work given up that the office might be taken. I refer to an astronomer who has quite recently left the charge of one of our most important colonial observatories to take a leading astronomical office at Oxford. That astronomer had for several years held the position of chief assistant at Greenwich, and had the Astronomer Royal resigned four or five years ago, would almost certainly have succeeded him. But, as I have already pointed out, an absence of several years from Green- wich diminishes an astronomer's fitness for the special duties (in particular the superintendence of routine work) belonging to the office of Astronomer Royal. Without 400 FAMILIAR SCIENCE STUDIES. touching in any way upon the question of relative capacity, zeal, or energy, I may say that in all probability the public interests were better served by the appointment to this office of the younger man who has during the last few years held the position of chief assistant at Greenwich. I have touched on the erroneous ideas which many persons entertain respecting the duties of an Astronomer Royal. 1 may conveniently conclude by noting the admir- able way in which the actual duties of the office have been discharged by the venerable astronomer who has so long held that important position. If we do not find his name asso- ciated with striking discoveries respecting the sun and moon, planets, stars, and comets, it has been because the duties of his office have been inconsistent with the researches by which alone such discoveries can be effected. An Airy has no right to undertake such work as has ennobled the names of a Newton or a Herschel. His duty to the nation, in whose service he has taken office, requires that he should devote his energies first and chiefly to the control and super- ntendence of that systematic observatory work which is so important to the nation as forming the very basis of our commercial system. Not only the property, but the lives of millions depend more or less directly on the accuracy and completeness with which that system is carried out. I may add what may seem to some a common-place consideration which presents, however, the common-sense practical view of the matter, that the nation pays a certain sum yearly to the Astronomer Royal for the performance of certain work, and therefore has a right (each one of us has a right) to claim that that work and no other shall be done no other work at least which would prevent that work from being well and thoroughly done. An Astronomer Royal who should devote any large portion of his time to independent researches, such as the Herschels, Huggins, Lassell, Draper, and other private astronomers have undertaken, might become very eminent for his discoveries in physical astronomy, but it would be at the expense of the country in whose OUR ASTRONOMERS ROYAL, 401 service he had accepted office, in the opinion of all right- minded men his distinction would be to his discredit. The Astronomer Royal who has just completed his long term of office has achieved though his official career has not been absolutely without mistakes a worthier reputation, in this, that he has worked with such zeal and energy in the duties properly belonging to his office, that even the hardest- working professional astronomer might well hesitate to suc- ceed him in a position always important, but which he has made most arduous. FAMILIAR SCIENCE STUDIES. PHOTOGRAPHS OF A GALLOPING HORSE. ABOUT two years ago I heard for the first time of a photo- graphic achievement which seemed to me at the time scarce credible, and which I was presently assured by one of our ablest English photographers was absolutely outside the bounds of possibility, to wit, the photographic presentation of a galloping horse. Of instantaneous photography, so called, I had of course heard, and I had seen the process in operation. But I knew that the actual exposure in what is called instantaneous photography is not less than a second, even in that arrangement which was called some ten or twelve years ago pistolgraphy. Again, I knew that the sun had been photographed in a period certainly not exceeding the i,oooth part of a second. But the shortness of the ex- posure in that case was a necessity instead of involving a difficulty ; for the brightness of the solar image is such that an exposure of the tenth or even the hundredth part of a second would suffice to entirely ' burn out ' the details of the photographic picture. To photograph a galloping horse, however, with distinctness, requires on the one hand an exposure of much less than a second, or even than the tenth or hundredth part of a second ; while, on the other hand, the luminosity of the image cannot, under any cir- cumstances, be greater than that which, when ordinary photographs are taken, involves an exposure of several seconds at least. As to the first point, it is easy to see that an exposure PHOTOGRAPHS OF A GALLOPING HORSE. 403 of a second would result in entirely blurring the outlines of the horse's limbs. A galloping horse advances ordinarily at the rate of a mile in less that two minutes. In the photo- graphs of which I had heard, the rate mentioned was^a mile in im. 403., or thirty-six miles per hour. Taking the last- named rate, or a mile in a 100 seconds, the galloping horse advances one hundredth part of a mile, or nearly eighteen yards, in a second, and therefore, as a horse at rest occupies a width of less than three yards, it is hardly necessary to say the picture obtained from an exposure of one second would be a mere confused blur. The image obtained in the tenth of a second would be no better, as the blurring would correspond to a width of nearly two yards. In the hundredth part of a second the image would be blurred to a width corresponding to more than half a foot so that, al- though the picture of the horse as a whole might be perhaps just recognisable as a horse, the limbs would be confused beyond recognition. To get a picture which should show the limbs of a galloping horse with anything like distinct- ness, the blurring should not exceed a width corresponding to one inch in the life-size image of a horse. Now in what precedes I have only taken into account the forward motion of the horse as a whole ; but in considering the definition of the limbs we have to remember that these are not only advancing with the body, but are moved also in relation to the body, and that when the limbs are being thrown forward, this forward motion is added to the advancing motion of the body. Now the forward motion of the limbs varies in rate, from nothing when the limbs are farthest forward and farthest back, to a maximum somewhere near the middle of their forward sweep. This maximum cannot be less than the advancing motion of the horse, and is probably much greater. 1 As we must add this forward motion to the ad- 1 In the case of a carriage, we get in the motion of the wheels what corresponds to the relative motion of the horse's limbs. In this case, we know that the relative forward motion of the top of the wheel, and the relative backward motion of the bottom of the wheel are eaclj D D 2 4 o !. FAMILIAR SCIENCE STUDIES. vancing motion of the horse as a whole, we get for the maxi- mum forward motion of a limb (meaning now the full for- ward motion, not only the motion relatively to the body) twice the advancing motion of the horse. We have seen that with an exposure of one second the blurring of the body of the horse would have a width corresponding to half a foot in the life-size image of a horse. The blurring of the limbs would vary from nothing to a width corresponding to a foot. That the blurring then, should nowhere exceed a width corresponding to an inch, the exposure should not ex- ceed the i,2ooth part of a second in duration. As a matter of fact, satisfactory pictures were not obtained until the ex- posure had been reduced to the 2,oooth part of a second, and in later pictures the exposure has been reduced to the 5,oooth part of a second. And here, in passing, I may answer an objection which will occur perhaps to many readers. I remember that after mentioning in a lecture at Sydney, New South Wales, the brief exposure of Janssen's solar negatives, I was asked by one of the chief photographers of New South Wales, who had been present, how I could venture to speak of an ex- posure of the i,6ooth part of a second, when no means could possibly be devised for measuring so short a period of time. I was able to reply that not only had Janssen been able in the most satisfactory manner to measure the exposure of his plates to the solar image, but that science had been able to measure periods of time so short as the ioo,oooth, and even the 2oo,oooth part of a second. Nay, Wheat- stone claims, and not without good reason, that, when attempting to determine the duration of a lightning flash, he measured periods very much shorter even than this. It sounds at first hearing altogether incredible, and indeed ab- surd, that men should pretend to measure by optical and mechanical means (for so has the task been achieved) a period which is a very small fraction of the duration of a equal to the advancing motion of the carriage, so that the top of the wheel is advancing twice as fast as the carriage, while the bottom of the wheel is momentarily at rest. PHOTOGRAPHS OF A GALLOPING HORSE. 405 luminous impression on the eye. Yet in reality this has been done by taking advantage of the very circumstance which seems at first sight to render it impossible. The method is so ingenious, and at the same time so simple, that it will be well to consider it here as an introduction to the less, minute subdivisions of time involved in the processes which form the subject of this essay. Conceive a rather large disc of ebony, round the edge of which are inlaid radiating lines of silver wire, exceedingly fine. Say, for instance, that there are 1,600 equidistant ra- diating lines, or in each quadrant 400, so that each centigrade degree (100 to the quadrant) is divided into four parts. If each wire is the hundredth of an inch in thickness, and the disc is one foot in diameter, the black space between the ends of the wires will be one-hundredth and a quarter (of a hundredth) in width. Now, suppose this disc set in rapid rotation, making, for instance, a hundred rotations per second. Then, in the i6o,oooth part of a second, one of the radiat- ing wires will be carried to the position which, at the begin- ning of that short period, had been occupied by its next neighbour. But the forward edge of a wire will be carried to the position which had been occupied by the backward (or following) edge in a shorter time still manifestly in five- ninths of the short period ; for the breadth of the black space between the wires is five-ninths of the distance from centre to centre of successive wires. Thus, if the disc is whirling in darkness, and is suddenly lit up by a flash of lightning, and .the flash lasts five-ninths of the i6o,oooth part of a second, or lasts one 288,ooothof a second, the disc will appear as if bordered by a continuous ring of silver ; for during that time every part of the edge will have been occu- pied by lightning-lit silver, and as the eye retains a luminous impression for fully one-tenth of a second, the light from every part of the edge of the disc will appear to form a single image, in which the spokes of wire will not be separately discernible. If the lightning flash lasted half that time, the black spaces would be discernible, but would seem to be but half their real width, half their width being cut off during the continuance of 406 FAMILIAR SCIENCE STUDIES. the flash. If the flash lasted a fourth of the above-mentioned time, only one-fourth of the width of the black space would be cut off, so that its width would appear but three-fourths of what it really was, and so forth for yet shorter periods. But this will suffice to show that Wheatstone could measure by this method, as he claimed, the millionth part of a second. For manifestly the eye could readily detect the diminution of the black spaces by a full fourth of its amount, and this reduction (on our assumptions as to the size of the disc and the rate of its rotation) would be produced if a lightning flash lasted but one i,i52,oooth, or less than the millionth part of a second. Thus, when Wheatstone stated, as the result of his experiments, that a lightning flash does not last the millionth part of a second, he was not (as some rashly asserted) announcing over-confidently what could not by any possibility have been established by evidence, but was, in fact, simply asserting what he had satisfactorily proved. Yet how wonderful it seems at first that science should be able to say, as it did in this case, that a luminous appearance, visible for fully the tenth of a second, lasts in reality less than the 20,oooth, or even than the ioo,oooth, part of that time. 1 We see, then, that it is not only possible, but an easy matter, to measure periods of time much shorter than the i,oooth or io,oooth part of a second. But it might still seem marvellous, and in fact it is, that science should be 1 Within a few hours of writing the above lines, I witnessed at the observatory of Dr. Henry Draper, of New York, a very simple experi- ment illustrating the instantaneous character of the electric spark, and also the intermittance of a luminosity which, as judged by the eye, appears persistent. While the electric discharge was taking place in a series of rapidly following sparks, the hand held steadily in front of the light appeared to be quite steadily illuminated ; but if the hand was rapidly fluttered about, a multitude of distinct images of the hand were seen, producing an appearance as of a multiform hand with multitudinous (and ever varying) fingers attached to it, the explanation being that the hand was successively visible and invisible, and many successive images were seen in different positions during each tenth of a second of the duration of luminous impressions. PHOTOGRAPHS OF A GALLOPING HORSE. 407 able so to arrange matter that in such a minute period of time an image should be taken which shall be clear and well denned in all its details. Yet this has been achieved, and some of the results of the application of this process have now to be considered. In the best paintings of horse-races, charges, the hunt- ing-field, and so forth, we have what may be regarded as a conventional view of the horse at full gallop. He is shown with the two fore legs thrown well forward and the two hind legs thrown well back in the attitude, in fact, which is indicated by the French expression venire a terre, applied to an animal at full gallop. Anyone who has watched a race or a charge of galloping horses, will certainly be prepared to affirm that this attitude is one of those which a horse assumes in galloping. It is, of course, to some degree absurd that this one attitude, which is only (even on this assumption) assumed at certain definite instants by the horse at full gallop, should be presented as the only or almost the only attitude recognisable in a group of galloping horses. Still, the idea generally entertained by those who study pictures of the kind is that this attitude is the most characteristic, and the one best suited for delineation. Accordingly, paintings and drawings of galloping horses which present this attitude and no other, are amongst those most admired by the artistic world. So soon, however, as we test by instantaneous photo- graphy the movements of a horse, we find that this ad- mired and presumedly characteristic attitude is not one which really characterises the gallop. Not only is this the case, but the attitude is actually never assumed at all by a horse either in this or in any other gait. And, on the other hand, we find that positions are assumed by the galloping horse which no one would for a moment have supposed possible. The positions shown in Mr. Muybridge's photographs are eleven, and these include all the movements made in one complete stride. It requires some care to distinguish 4 o8 FAMILIAR SCIENCE STUDIES. the movements of the different legs. Let us follow the movements seriatim. The first position to the series is that shown in Fig. i. Here the horse seems to be balanced on one fore leg, the two hind legs being thrown into the position often shown in drawings of a leaping horse. The other fore leg is thrown back in a position suggestive of rest rather than of the violent action of a galloping horse's limbs. The four legs are num- bered so that their subsequent motions may be followed. It must be remembered that this picture does not belong to the initial series of movements by which a trot or a canter is changed into a gallop. The animal thus photographed was in full gallop all the time. In this position the fore leg FIG. i. marked i appears to bear the entire weight of the body, but, in reality, it does not (although the contrary has been main- tained). The body has been propelled forwards and slightly upwards somewhat earlier, as will presently appear, and fore foot i is in reality scarcely supporting the body at all, but simply adding to the propulsive motion, the body need- ing for the moment little support. Fig. 2 shows the horse twenty-seven inches further for- ward. (It may be noticed in passing that Fig. 1 1 shows a position of the body between the positions shown in Fig. i and Fig. 2.) The fore leg marked i has continued to pro- pel the body forward until this leg had become so aslant (see Fig. n) that the hoof has to leave the ground, and is thrown back as shown in Fig. 2. Fore leg 2 has been PHOTOGRAPHS OF A GALLOPING HORSE. 409 carried forward, the hoof rising and the leg becoming more sharply bent. Both hind legs have been thrown forward, but leg 4 more than leg 3, so that the hoofs are rather nearer together than in Fig. 2. In the interval between the positions shown in Figs, i FIG. 2. and 2 there had been propulsion, though not very forcibly, only one leg touching the ground, and that only during a. portion of the time. As the pictures are made at equal distances of 27 inches apart, the time between Fig. i and Fig. 2 is to some degree diminished by the additional velo- FIG. 3. city due to this propulsive motion. On the other hand, as all four limbs are in the air during the interval of time between Figs. 2 and 3, there has not been, in this case, any propulsive action, and the body of the horse has therefore been all the time, though but slightly, losing forward velo- city. We note a considerable alteration in the position of 4io FAMILIAR SCIENCE STUDIES. all four limbs. Fore leg i has been thrown forward, so far as the upper part of the limb is concerned, but the lower part of the limb has been thrown upward. Fore leg 2 has been thrown forward, and is now slightly less bent. Hind leg 3 seems, at first sight, scarcely changed in position ; but, in reality, it has been thrown forward and then backward to nearly the position it had when Fig. 2 was taken. Hind leg 4 has been thrown further forward. Between Fig. 3 and Fig. 4 the body has been entirely in the air until just before Fig. 4 was taken, when hind leg 3 had just touched the ground. Thus the interval in time, as there had been no propulsive motion, has been rather greater between Figs. 3 and 4 than between Figs. 2 and 3, FIG. 4. and greater still than between Figs, i and 2. A correspond- ingly greater change has taken place in the position of the limbs. Fore leg i has been curled up under the body, the upper part of the limb being thrown forward. Fore leg 2 has been thrown more markedly forward and partly unbent. Hind leg 3 has been set down by being thrown backward, and hind leg 4 has been thrown forward nearly to the farthest. In this position the body is advancing almost at its slowest though, of course, it will be understood that in saying this I do not mean to describe the rate of advance as greatly reduced. The body has been only carried for- ward seven feet four inches from the position it had in Fig. i, and its rate of advance has scarcely been reduced at all. Nevertheless, such reduction as the rate of advance does PHOTOGRAPHS OF A GALLOPING HORSE, 411 undergo during the swift gallop of the horse attains its maximum at about this position. In Fig. 4 the fore legs have changed notably in position. Fore leg i has been thrown upward (so far as the upper half is concerned) and forward. Fore leg 2 has been thrown for- ward in preparation for the work which this leg will have to do after the hind legs have done theirs. Of the hind legs, No. 3, which in the position of Fig. 4 had just begun the work of propulsion, has driven the body well forward, so that this limb has become nearly upright. The other hind leg seems to be nearly in the same position as in Fig. 4, but in reality it is now being carried backwards, whereas, in the former position, it was travelling forwards. This leg is the FIG. 5. one which is next to take the work of propulsion. Notice that i is the left fore leg and 2 the right. Between the work of these two legs, both hind legs do their work of propulsion : the left fore leg's work is followed by that of the right hind leg, then the left hind leg does its work and next the right fore leg. In the position shown in Fig. 6 both hind legs are at work, giving to the body its strongest propulsion both for- wards and upwards, but chiefly forwards. Hind leg 3 has nearly done its work ; hind leg 4 has little more than begun. Fore leg i has been thrown upwards and forwards, slightly unbending. Fore leg 2 has been straightened into a position which no one would imagine to be ever assumed by a horse's leg. However, one can at once see that the attitude is 412 FAMILIAR SCIENCE STUDIES. indicative of the energy which is about to be put into the backward stroke given by this fore limb. In considering this picture, and indeed all those in which a hoof touches the ground, it must be borne in mind that the attitude is not one assumed by the horse for any definite period of time, however short. It is difficult to dispossess oneself of the notion that this is the case, and the absurdity of some of the attitudes in our series of pictures arises chiefly from this mistaken conception. Regarding these attitudes as simply passed through during the horse's rapid rush forward in swift gallop, they no longer appear so absurd ; though, even as thus viewed, there is some difficulty in imagining that attitudes so unlike those which the eye can recognise FIG. 6. as a horse gallops past, should be assumed once in each stride. In Fig. 6 we see the horse in that part of his action which is most energetic in the galloping gait. At this stage of his stride, and at this stage only, those two legs are at work in propelling the horse forward which have the greatest propulsive power. Strictly speaking, the stride should be regarded as commenced from this attitude ; and I should so have dealt with the series of pictures had it chanced that they represented precisely one stride. Since, however, Fig. 1 1 shows a position about a foot in advance of that shown in Fig. i, but about as much behind that shown in Fig. 2, the series only runs by equal intervals from Fig. i to Fig. n, and it was necessary therefore to commence with Fig. i, though that really belongs to the middle of a stride. PHOTOGRAPHS OF A GALLOPING HORSE. 413 In Fig. 7 two feet are shown touching the ground, one a fore foot, the other a hind foot. Leg 2, which in the last figure was preparing for propulsive action, is here fully en- gaged in it. But the two hind legs have already given a strong propulsive impetus to the body, and hind leg 4 is still urging the body forward. It is only necessary to compare these two legs to see how much more powerful the propulsive action of the hind legs must be than is that of the fore legs. I would venture to predict that if ever an experimental test is applied by which the propulsive action of the fore and hind legs is compared, the former will be found at least three times as effective as the latter. It will be remem- bered that 2 is the right foreleg and that 4 is the left hind FIG. 7. foot. We notice, further, that the gallop is not a symmet- rical gait, as the trot is. For in the trot right and left fore legs work in similar ways with left and right hind legs re- spectively. But we see, from the series of figures illustrating the gallop, that whereas the right fore leg works with the left hind leg, the left fore leg does not work with the right hind leg. Each of these legs the left fore leg and the right hind leg does its work alone, except that the right hind leg during a part of its work receives help from the other hind leg, but at no time from either fore leg. Such at least is the case illustrated in our series of figures ; of course, the gallop can equally be executed when the right and left fore legs do the work which the left and right fore legs are here represented as doing, the hind legs also interchanging their 414 FAMILIAR SCIENCE STUDIES. work. In fact, the illustrations would have appeared pre- cisely as they do if the work of the two fore legs, as of the two hind legs, had thus been interchanged. In Fig. 8 the two hind legs are both thrown back, and are, for the moment, in a position not very unlike that in which these limbs are commonly represented in pictures of a galloping horse. But the fore limbs are posed as the fore limbs of a horse never were shown in a picture. Fore leg 2 is at work urging the horse forward, or rather it is maintaining and increasing the forward motion given by the energetic action of the hind legs. Fore leg i has been straightened from the position shown in Fig. 7, but it is to be noticed^that in the interval between the positions shown in FIG. Figs 7 and 8 this leg has reached its highest motion upward, and is now on its way downward. Notice also that the fore legs are always more or less bent when rising, but as they are brought downwards to give their stroke, they are straight- ened, even from the beginning of this downward motion. Compare, for instance, the pose of fore leg 2 in Figs. 5 and 6, and again the fore leg i in Figs. 7 and 8. Notice also that each leg remains straight in sweeping round through about a right angle, fore leg 2 from the position of Fig. 6 to that of Fig. 9, and fore leg i from the position of Fig. 8 to that of Fig. 1 1. In Fig. 9, fore leg 2 is shown doing the last part of its work of propulsion, while fore leg i is just about to begin its work. The hind legs are so nearly in the same position PHOTOGRAPHS OF A GALLOPING HORSE. 415 in the picture that it is not easy to tell which is which. However, a little consideration will show that the leg whose hock shows highest is, as marked, fore leg 3, or the right. For notice that in Fig. 3 the right fore leg (3) has nearly the same position as the left fore leg (4) in Fig. 5. In Fig: 4 and Fig. 6 these legs have respectively nearly the same positions. So have they in Figs 5 and 7 ; in Figs. 6 and 8, though here the slight difference in time between the action of the right fore leg in one picture and the left fore leg in the next picture but one, is shown by the right fore leg being on the ground in Fig. 6, while the left fore leg has just been lifted from the ground in Fig. 8. We infer, then, that the left fore leg in Fig. 9 has nearly the same position as the] right FIG. 9. fore leg (3) in Fig. 7, in other words is nearly straight. Therefore the other, or more bent leg in Fig. 9, is the right fore leg (3). We see, in fact, that just as the fore legs begin to straighten just after they begin to descend for their propulsive stroke, so the fore legs continue nearly straight after their propulsive stroke, until just before they reach their greatest height. In Fig. 9 hind leg 4 is travelling back- wards and passing hind leg 3, which has just begun to travel forwards, precisely as in Fig. 3 hind leg 4, travelling fonvards, is passing hind leg 3 travelling backwards. The vigorous action of fore leg 2, and the vigorous attitude preparative for action of fore leg i, form very striking characteristics of Fig. 9. Nothing could serve better to show how the fore legs do their work than this picture, and yet nothing could 4 i6 FAMILIAR SCIENCE STUDIES. be more unlike the conventional position of the fore legs of a galloping horse in pictures. The hind legs look more as shown in the pictures, yet neither are these as any artist who valued his reputation would care to show them in a painting. FIG. 10. In the next position we see the hind legs thrown into an attitude familiar enough in drawings of galloping and leaping horses. Hind leg 3 has been advanced somewhat from the position it had in Fig. 9. Fore leg i has commenced the work of propulsion, while fore leg 2 has completed its work FIG. n. and has already become considerably bent, and the foot is well raised from the ground. Finally, in Fig. n, we see the end of the stride begun so far as the left fore foot is concerned from the position shown in Fig. i. As already mentioned, the stride may more properly be regarded as beginning with the action of PHOTOGRAPHS OF A GALLOPING HORSE. 417 the hind legs. But we must consider the stride actually photographed. In Fig. 1 1 we see the fore leg nearly at the end of its work in adding to the forward motion of the body. Fore leg 2 has been carried forward to a position somewhat in advance of that shown in Fig. i. So also both the hind legs are in advance of the position there shown. Fig. 1 2 simply shows the horse standing at rest. In considering this series of pictures separately, we are struck by the absolute want of resemblance between nearly all of them and the attitudes we are in the habit of regarding as belonging to the galloping horse. The second and third figures alone seem at all natural, though even these would scarcely be regarded as admissible into a painting represent- FIG. 12. ing a charge or race. Notice further that these two are the only pictures in which no leg of the horse touches the ground. In all the other nine at least two of the legs seem absurdly posed, in several three seem so, while in two all four legs have a preposterous appearance. Yet it is found that so soon as the pictures, instead of being studied separately and with steady gaze, are submitted in rapid succession to the eye, each remaining but a fraction of a second in view in other words, when they are studied in a manner more nearly corresponding to that in which the actual movements of a galloping horse are seen the views which had appeared separately absurd become merged into a view showing the horse as he actually appears in the gallop. By arranging them uniformly round the outside of E E 4 i 8 FAMILIAR SCIENCE STUDIES. a rather large disc, only a small portion of the upper part of which can be seen at a single view, and setting this disc in rapid rotation, so that picture after picture comes into view and remains in view but a moment, we are able to see the horse galloping as in nature, stride succeeding stride, and every circumstance of the motion, even to the waving of the tail and mane, being truthfully and therefore naturally presented. Mr. Muybridge himself considers that since these views are severally truthful, however absurd they may appear to those accustomed to study the usual artistic pictures of galloping horses, we should infer that pictures such as these ought to replace the conventional attitudes which have been so long in vogue. Here I must confess that, admirer though I am of his work, I am altogether at issue with him. A picture should represent what we see, and he would be the first to admit that the eye cannot properly be said to see any one of the attitudes he has shown to be really assumed by the galloping horse. He might reply to this that neither can the eye be said to see, nor can it see, any of the attitudes shown by artists, for the simple reason that these attitudes have no real existence in nature. But a picture to be true must show what the eye seems to see. Even in such matters as colouring and shading, the artist has to depart from what nature really presents. In order to produce an appearance of reality, he must modify the colours and the shades until in some cases they are utterly unlike those actually existing. Now if this is the case where at any rate the objects depicted are at rest, so that one would say the representation if really correct should, when duly studied, appear to be truthful, how much more may we expect it to be the case where the object represented is moving so rapidly that the eye cannot detect the real nature of the attitudes successively assumed ! We might, indeed, antici- pate that in such a case no drawing could possibly represent the appearance of the moving object. In many cases this is actually so. But in others, as in that of a carriage rapidly advancing, we know that the appearances recognised by the eye can be readily enough represented. Now take such PHOTOGRAPHS OF A GALLOPING HORSE. 419 a case as this. At any instant of time the wheel of a rapidly advancing carriage has its spokes in some definite position, and we might draw them in such a position, and regard the wheel when so drawn as correctly represented. But we know that if it were so drawn the carriage .would appear to be at rest ; and that to convey the idea of rapid motion, the wheels of a carriage must be represented as it really appears to the eye, with the spokes blended together into confused discs. When the wheels are so drawn, and accessories drawn in so as to suggest the idea of rapid motion, as post-boys leaning forward and flourishing their whips, the dust rising around the wheels, and so forth, we obtain a picture which conveys the idea of a rapidly ad- vancing carriage. The mere fact, then, that a galloping horse assumes such attitudes as are shown in our series of figures is no argument in favour of the introduction of such attitudes into a drawing of a race or charge. One might as reasonably represent cannon balls in mid-air, in a battle scene, as we see in some of the illustrations of Froissart's 'Chronicles.' Cannon balls and musket balls are certainly in the air during a brisk exchange of missiles, but as no one can see them they have no proper place in a picture. On the other hand, it is difficult to understand how the conventional attitudes of a galloping horse came to be em- ployed ; for they certainly are not seen during a charge or race, though the idea conveyed may be that such attitudes are not only assumed by the galloping horse, but are actually characteristic of his actions. It may perhaps be, that the attitudes approaching those seen in the pictures are retained longer than the others which seem unnatural. Thus the general effect is, we may assume, that conveyed by the pictures. And yet it is strange, if this be so, that the hind legs do not pass through those positions which seem natural at the same time that the fore legs are passing through their natural attitudes. Thus the positions of the hind legs in Figs. 8, 9, 10, and n, are not unlike those shown in the pictures, but in all these figures the fore legs are in positions which seem altogether unnatural. On the 420 FAMILIAR SCIENCE STUDIES. other hand, in Figs. 2, 3, 4, and 5, the fore legs are in natural positions; while the hind legs are in positions more or less unnatural. (Of course, in using the words natural and unnatural, I refer only to the conventional ideas as to the action of the galloping horse ; all the positions of the eleven figures are really natural, though they are un- familiar to the eye.) So that, in fact, it seems as though the conventional attitudes of a galloping horse were obtained by combining the position of the fore legs in one part of the stride with that of the hind legs in another. Yet though this seems strange, it is after all akin to the circumstance that in picturing a rapidly rotating wheel we show the spokes in a number of positions which they do not simultaneously occupy. As in the case of the rotating wheel so in that of the galloping horse, the movements are too quick to be followed by the eye, and so several positions really occupied at different times are combined together into a single im- pression. Where the movements are slower, so that the eye can recognise the several positions pretty clearly, the features of different positions would not be thus combined. For instance, an artist's pictures of a trotting horse, even when the pace to be represented is very rapid, do not differ much from those obtained by instantaneous photography. Of twelve such photographs obtained by Mr. Muybridge only two seem to differ and those not greatly from such views as might be given in a picture of a trotting match. So again the pictures of a walking horse, of a man walking at full speed, and of a man running at moderate speed, all closely resemble such drawings as an artist would make. But in the case of a man running at full speed, and still more in that of a man taking a high leap, the attitudes are such as have never been shown in any picture, such in fact as have never been seen, simply because, though all the attitudes are of necessity really assumed, they are assumed for so brief an interval of time, and so rapidly exchanged for others quite unlike them, that the eye is not cognisant even of their momentary existence. We may note also, as another reason PHOTOGRAPHS OF A GALLOPING HORSE. 421 why some of the attitudes of a leaping or swiftly running man seem unnatural (and of course the same reasoning applies to a galloping horse), that they are attitudes which cannot be maintained even for a single second, but are only passed through in the course of a certain series of energetic actions ; so that the pictures look like ill-drawn representations of impossible attitudes. The great value of such pictures lies in the evidence which they afford as to the real nature of the movements in- volved in particular gaits or exercises, as for the horse in the gallop, canter, run, or trot, and for the man in the high leap (running or standing), the long leap, the run, the swift walk, and so forth. They serve to correct some erroneous ideas as to the nature of such movements, ideas even enter- tained (in the case of exercises for men) by those who are most skilled in leaping or running. For instance, Mr. Muybridge informed me that the most skilful runners are positive that, in running swiftly, they bring the toes to the ground before the heel ; and certainly most runners, if not all, would think so : but the instantaneous pictures show that in rapid running the heel comes first to the ground. This was shown in every case, even where the runner had been told beforehand that the photographs would put to the test his own confidently expressed opinion that he brought the toes to the ground first. In pictures of a very swift runner at full speed, the toes appear thrown ridiculously upwards, just as absurdly as the hoofs of the fore feet of the horse appear in Figs. 6 and 8 of our series. (On considera- tion, I am inclined to think the evidence on which Mr. Muybridge depends is open to some degree of question. His views show, as I have myself had the opportunity of noting, that the toes are pointed upwards as the foot descends, till at any rate it is quite near to the ground ; but so far as I recollect, they do not show that at the last there is not a rapid motion of the forward part of the foot, bringing the toes down before the heel. Note, for instance, how in Fig. 7 the hoof, which had been pointed upwards in the previous 422 FAMILIAR SCIENCE STUDIES. position, Fig. 6, has come down to the ground before the fetlock, which in Fig. 8 has reached the ground ; and, still more to the purpose, note how in Fig. 9 we see the hoof before reaching the ground already thrown far downward of the position, relatively to the fetlock, which it had had in Fig. 8. Mr. Muybridge, by the way, asserts that all animals bring the heels to the ground, in rapid running, before the toes : this, of course, would relate only to the hind feet, and is not supported by the views of our series, even if the fetlock be regarded as the heel. But in reality the fetlock corresponds to the ball of the foot, not to the heel, the heel corresponding to the horse's hock, which never touches the ground at all, except when the animal rears till he is abso- lutely upright.) I should like to see Mr. Muybridge's method applied to a number of other movements, which so far as I know he has not yet tested ; in particular to the movements of a man's body and limbs in rowing, first in heavier boats, then in lapsteaked gigs, then in racing boats : and in steady pulling, as well as in the fiercest spurts. Mr. Muybridge claims that in his later photographs the exposure, as tested by the distinctness of the outlines, cannot be more than the 5,oooth part of a second. 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