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application to solar and stellar chemistry; but because we might now be in possession of the inconceivable riches of astronomical results which we expect from the next ten years' investigation by spectrum analysis, had Stokes given his theory to the world when it first occurred to him.

To Kirchhoff belongs, I believe, solely the great credit of having first actually sought for and found other metals than sodium in the sun by the method of spectrum analysis. His publication of October 1859 inaugurated the practice of solar and stellar chemistry, and gave spectrum analysis an impulse to which in a great measure is due its splendidly successful cultivation by the labours of many able investigators within the last ten years.

To prodigious and wearing toil of Kirchhoff himself, and of Angström, we owe large-scale maps of the solar spectrum, incomparably superior in minuteness and accuracy of delineation to anything ever attempted previously. These maps now constitute the standards of reference for all workers in the field. Plücker and Hittorf opened ground in advancing the physics of spectrum analysis, and made the important discovery of changes in the spectra of ignited gases produced by changes in the phy. sical condition of the gas. The scientific value of the meetings of the British Association is well illustrated by the fact that it was through conversation with Plücker at the Newcastle meeting that Lockyer was first led into the investigation of the effects of varied pressure on the quality of the light emitted by glowing gas which he and Frankland have prosecuted with such admirable success. Scientific wealth tends to accumulation according to the law of compound interest. Every addition to knowledge of properties of matter supplies the naturalist with new instrumental means for discovering and interpreting phenomena of nature, which in their turn afford foundations for fresh generalisations, bringing gains of permanent value into the great storehouse of philosophy. Thus Frankland, led, from observing the want of brightness of a candle burning in a tent on the summit of Mont Blanc, to scrutinise Davy's theory of flame, discovered that brightness without incandescent solid particles is given to a purely gaseous flame by augmented pressure, and that a dense ignited gas gives a spectrum comparable with that of the light from an incandescent solid or liquid. Lockyer joined him; and the two found that every incandescent substance gives a continuous spectrum-that an incandescent gas under varied pressure gives bright bars across the continuous spectrum, some of which, from the sharp, hard and fast lines observed where the gas is in a state of extreme attenuation, broaden out on each side into nebulous bands as the density is increased, and are ultimately lost in the continuous spectrum when the condensation is pushed on till the gas becomes a fluid no longer to be called gaseous. More recently they have examined the influence of temperature, and have obtained results which seemed to show that a highly attenuated gas, which at a high temperature gives several bright lines, gives a smaller and smaller number of lines, of sufficient brightness to be visible, when the temperature is lowered, the density being kept unchanged. I cannot refrain here from remarking how admirably this beautiful investigation harmonises with Andrews's great discovery of continuity between the gaseous and liquid states. Such things make the life-blood of science. In contemplating them we feel as if led out from narrow waters of scholastic dogma to a refreshing excursion on the broad and deep ocean of truth, where we learn from the wonders we see that there are endlessly more and more glorious wonders still unseen.

Stokes's dynamical theory supplies the key to the philosophy of Frankland and Lockyer's discovery. Any atom of gas when struck and left to itself vibrates with perfect purity its fundamental note or notes. In a highly attenuated gas each atom is very rarely in collision with other atoms, and therefore is nearly at all times in a state of true vibration. Hence the spectrum of a highly attenuated gas consists of one or more perfectly sharp bright lines, with a scarcely perceptible continuous gradation of prismatic colour. In denser gas each atom is frequently in collision, but still is for much more time free, in intervals between collisions, than engaged in collision; so that not only is the atom itself thrown sensibly out of tune during a sensible proportion of its whole time, but the confused jangle of vibrations in every variety of period during the actual collision becomes more considerable in its influence. Hence bright lines in the spectrum broaden out somewhat, and the continuous spectrum becomes less faint. In still denser gas each atom may be almost as much time in collision as free, and the spectrum then consists of broad nebulous bands crossing a continuous spectrum of considerable brightness. When the medium is so dense that each atom is

always in collision, that is to say never free from influence of its neighbours, the spectrum will generally be continuous, and may present little or no appearance of bands, or even of maxima of brightness. In this condition the fluid can be no longer regarded as a gas, and we must judge of its relation to the vaporous or liquid states according to the critical conditions discovered by Andrews.

While these great investigations of properties of matter were going on, naturalists were not idle with the newly recognised power of the spectroscope at their service. Chemists soon followed the example of Bunsen in discovering new metals in terrestrial matter by the old blow-pipe and prism test of Fox Talbot and Herschel. Biologists applied spectrum analysis to animal and vegetable chemistry, and to sanitary investigations. But it is in astronomy that spectroscopic research has been carried on with the greatest activity, and been most richly rewarded with results. The chemist and the astronomer have joined their forces. An astronomical observatory has now, appended to it, a stock of reagents such as hitherto was only to be found in the chemical laboratory. A devoted corps of volunteers of all nations, whose motto might well be Ubique, have directed their artillery to every region of the universe. The sun, the spots on his surface, the corona and the red and yellow prominences seen round him during total eclipses, the moon, the planets, comets, auroras, nebule, white stars, yellow stars, red stars, variable and temporary stars, each tested by the prisni, was compelled to show its distinguishing prismatic colours. Rarely before in the history of science has enthusiastic perseverance directed by penetrative genius produced within ten years so brilliant a succession of discoveries. It is not merely the chemistry of sun and stars, as first suggested, that is subjected to analysis by the spectroscope. Their whole laws of being ar now subjects of direct investigation; and already we have glimpses of their evolutional history through the stupendous power of this most subtle and delicate test. We had only solar and stellar chemistry; we now have solar and stellar physiology.

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It is an old idea that the colour of a star may be influenced by its motion relatively to the eye of the spectator, so as to be tinged with red if it moves from the earth, or blue if it moves towards the earth. William Allen Miller, Huggins, and Maxwell showed how, by aid of the spectroscope, this idea may be made the foundation of a method of measuring the relative velocity with which a star approaches to or recedes from the earth. The principle is, first to identify, if possible, one or more of the lines in the spectrum of the star, with a line or lines in the spectrum of sodium, or some other terrestrial substance, and then (by observing the star and the artificial light simultaneously by the same spectroscope) to find the difference, if any, between their refrangibilities. From this difference of refrangibility the ratio of the periods of the two lights is calculated, according to data determined by Fraunhofer from comparisons between the positions of the dark lines in the prismatic spectrum and in his own "interference spectrum" (produced by substituting for the prism a fine grating). A first comparatively rough application of the test by Miller and Huggins to a large number of the principal stars of our skies, including Aldebaran, a Orionis, B Pegasi, Sirius, a Lyræ, Capella, Arcturus, Pollux, Castor (which they had observed rather for the chemical purpose than for this), proved that not one of them had so great a velocity as 315 kilometres per second to or from the earth, which is a most momentous result in respect of cosmical dynamics. Afterwards Huggins made special observations of the velocity test, and succeeded in making the measurement in one case, that of Sirius, which he then found to be receding from the earth at the rate of 66 kilometres per second. This, corrected for the velocity of the earth at the time of the observation, gave a velocity of Sirius, relative to the Sun, amounting to 47 kilometres per second. The minuteness of the difference to be measured, and the smllness ofa the amount of light, even when the brightest star is observed, renders the observation extremely difficult. Still, with such great skill as Mr. Huggins has brought to bear on the investigation, it can scarcely be doubted that velocities of many other stars may be measured. What is now wanted is, certainly not greater skill, perhaps not even more powerful instruments, but more instruments and more observers. Lockyer's applications of the velocity test to the relative motions of different gases in the Sun's photosphere, spots, chromosphere, and chromospheric prominences, and his observations of the varying spectra presented by the same substance as it moves from one position to

another in the Sun's atmosphere, and his interpretation of these observations according to the laboratory results of Frankland and himself, go far towards confirming the conviction that in a few years all the marvels of the Sun will be dynamically explained according to known properties of matter.

During six or eight precious minutes of time, spectroscopes have been applied to the solar atmosphere and to the corona seen round the dark disc of the moon eclipsing the sun. Some of the wonderful results of such observations, made in India on the occasion of the eclipse of August 1868, were described by Prof. Stokes in a previous address. Valuable results have, through the liberal assistance given by the British and American Governments, been obtained also from the total eclipse of last December, notwithstanding a generally unfavourable condition of weather. It seems to have been proved that at least some sensible part of the light of the "corona is a terrestrial atmospheric halo or dispersive reflection of the light of the glowing hydrogen and "helium "* round the sun. I believe I may say on the present occasion when preparation mast again be made to utilise a Total Eclipse of the sun, that the British Association confidently trusts to our Government exercising the same wise liberality as heretofore in the interests of science.

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ing his surface within a distance equal to one-eighth of his radius. All things considered, there seems little probability in the hypothesis that solar radiation is compensated to any appreciable degree, by heat generated by meteors falling in, at present; and, as it can be shown that no chemical theory is tenable,* it must be concluded as most probable that the Sun is at present more an incandescent liquid mass cooling."+

Thus on purely astronomical grounds was I long ago led to abandon as very improbable the hypothesis that the Sun's heat is supplied dynamically from year to year by the influx of meteors. But now spectrum analysis gives proof finally conclusive against it.

Each meteor circulating round the Sun must fall in along a very gradual spiral path, and before reaching the Sun must have been for a long time exposed to an enormous heating effect from his radiation when very near, and must thus have been driven into vapour before actually falling into the Sun. Thus, if Mayer's hypothesis is correct, friction between vortices of meteoric vapours and the Sun's atmosphere must be the immediate cause of solar heat; and the velocity with which these vapours circulate round equaterial parts of the Sun must amount to 435 kilometres per second. The spectrum test of velocity applied by Lockyer showed but a twentieth part of this amount as the greatest ob served relative velocity between different vapours in the Sun's atmosphere.

At the first Liverpool meeting of the British Association (1854), in advancing a gravitational theory to account for all the heat, light, and motions of the universe, I urged that the immediately antecedent condition of the matter of which the Sun and Planets were formed, not being fiery, could not have been gaseous; but that it probably was solid, and may have been like the meteoric stones which we still so frequently meet with through space. The discovery of Huggins, that the light of the Nebula, so far as hitherto sensible to us, proceeds from incandescent hydrogen and nitrogen gases, and that the heads of comets also give us light of incandescent gas, seems at first sight literally to fulfil that part of the Nebular hypothesis to which I had obBut a solution, which seems to me in the highest degree probable, has been suggested by Tait. He supposes that it may be by ignited gaseous exhalations proceeding from the collisions of meteoric stones that Nebula and the heads of Comets show themselves to us, and he suggested, at a former meeting of the Association, that experiments should be made for the purpose of applying spectrum analysis to the light which has been observed in gunnery trials. such as those at Shoeburyness, when iron strikes against iron at a great velocity, but varied by substituting for the iron various solid materials, metallic or stony. Hitherto this suggestion has not been acted upon; but surely it is one the carrying out of which ought to be promoted by the British Association.

The old nebular hypothesis supposes the solar system and other similar systems through the universe which we see at a distance as stars, to have originated in the condensation of fiery nebulous matter. This hypothesis was invented before the discovery of thermo-dynamics, or the nebul would not have been supposed to be fiery; and the idea seems never to have occurred to any of its inventors or carly supporters that the matter, the condensation of which they supposed to constitute the Sun and stars, could have been other than fiery in the beginning. Mayer first suggested that the heat of the Sun may be due to gravitation; but he supposed meteors falling in to keep always generating the heat which is radiated year by year from the Sun. Helmholtz, on the other hand, adopting the nebular hypothesis, showed in 1854 that it was not necessary to suppose the nebulous matter to have been originally fiery, but that mutual gravitation between its parts may have generated the heat to which the pre-jected. sent high temperature of the Sun is due. Further he made the important observations that the potential energy of gravitation in the Sun is even now far from exhausted; but that with further and further shrinking more and more heat is to be generated, and that thus we can conceive the Sun even now to possess a sufficient store of energy to produce heat and light, almost as at present, for several million years of time future. It ought, however, to be added that this condensation can only follow from cooling, and therefore that Helmholtz's gravitational explanation of future Sunheat amounts really to showing that the Sun's thermal capacity is enormously greater, in virtue of the mutual gravitation between the parts of so enormous a mass, than the sum of the thermal capacities of separate and smaller bodies of the same material and the same total mass. Reasons for adopting this theory, and the consequences which follow from it, are discussed in an article "On the Age of the Sun's Heat," published in Macmillan's Magazine for March, 1862.

For a few years Mayer's theory of solar heat had seemed to me probable; but I had been led to regard it as no longer tenable, because I had been in the first place driven, by consideration of the very approximate constancy of the Earth's period of revolution round the Sun for the last 2000 years, to conclude that "The principal source, perhaps the sole appreciably effective "source of Sun-heat, is in bodies circulating round the Sun at present inside "the Earth's orbit " +; and because Le Verrier's researches on the motion of the planet Mercury, though giving evidence of a sensible influence attributable to matter circulating as a great number of small planets within his orbit round the Sun, showed that the amount of matter that could possibly be assumed to circulate at any considerable distance from the Sun must be very small; and therefore "if the meteoric influx taking place at present is enough to produce any appreciable portion of the heat radiated away, it must be supposed to be from matter circulating round the Sun, within very short distances of his surface. The density of this meteoric cloud would have to be supposed so great that comets could scarcely have escaped as comets actually have escaped, showing no discoverable effects of resistance, after pass

* Frankland and Lockyer find the yellow prominences to give a very decided bright line not far from D, but hitherto not identified with any terrestrial flame. It seems to indicate a new substance, which they propose to call Helium.

On the Mechanical Energies of the Solar System. Transactions of the Royal Society of Edinburgh, 1854; and Phil. Mag. 1854, second half year.

Most important steps have been recently made towards the discovery of the nature of comets; establishing with nothing short of certainty the truth of a hypothesis which had long appeared to me probable,-that they consist of groups of meteoric stones; -accounting satisfactorily for the light of the nucleus; and giving a simple and rational explanation of phenomena presented by the tails of comets which had been regarded by the greatest astronomers as almost preternaturally marvellous. The meteoric hypothesis to which I have referred remained a mere hypothesis (I do not know that it was ever even published) until, in 1866, Schiaparelli calculated, from observations on the August meteors, an orbit for these bodies which he found to agree almost perfectly with the orbit of the great comet of 1862 as calculated by Oppolzer; and so discovered and demonstrated that a comet consists of a group of meteoric stones. Professor Newton, of Yale College, United States, by examining ancient records, ascertained that in periods of about thirty-three years, since the year 902, there have been exceptionally brilliant displays of the November meteors. It had long been believed that these interesting visitants came from a train of small detached planets circulating round the Sun all in nearly the same orbit, and constituting a belt analogous to Saturn's ring, and that the reason for the comparatively large number of meteors which we observe annually about the 14th of November is, that at that time the earth's orbit cuts through the supposed meteoric belt. Professor Newton concluded from his investigation that there is a denser part of the group of meteors which extends over a portion of the orbit so great as to occupy about one-tenth or one-fifteenth of the * "Mechanical Energies," &c.

↑ "Age of the Sun's Heat" (Macmillan's Magazine, March 1862).

periodic time in passing any particular point, and gave a choice of five different periods for the revolution of this meteoric stream round the sun, any one of which would satisfy his statistical result. He further concluded that the line of nodes, that is to say, the line in which the plane of the meteoric belt cuts the plane of the Earth's orbit, has a progressive sidereal motion of about 52" 4 per annum. Here, then, was a splendid problem for the physical astronomer; and, happily, one well qualified for the task, took it up. Adams, by the application of a beautiful method invented by Gauss, found that of the five periods allowed by Newton just one permitted the motion of the line of nodes to be explained by the disturbing influence of Jupiter, Saturn, and other planets. The period chosen on these grounds is 33 years. The investigation showed further that the form of the orbit is a long ellipse, giving for shortest distance from the Sun 145 million kilometres, and for longest distance 2,895 million kilometres. Adams also worked out the longitude of the perihelion and the inclination of the orbit's plane of the ecliptic. The orbit which he thus found agreed so closely with that of Tempel's Comet I. 1866 that he was able to identify the comet and the meteoric belt.* The same conclusion had been pointed out a few weeks earlier by Schiaparelli, from calculations by himself on data supplied by direct observations on the meteors, and independently by Peters from calculations by Leverrier on the same foundation. It is therefore thoroughly established that Temple's Comet I. 1866 consists of an elliptic train of minute planets, of which a few thousands or millions fall to the earth annually about the 14th of November, when we cross their track. We have probably not yet passed through the very nucleus or densest part; but thirteen times, in Octobers and Novembers, from October 13, A.D. 902 to November 14, 1866 inclusive (this last time having been correctly predicted by Prof. Newton), we have passed through a part of the belt greatly denser than the average. The densest part of the train, when near enough to us, is visible as the head of the comet. This astounding result, taken along with Huggins's spectroscopic observations on the light of the heads and tails of comets, confirms most strikingly Tait's theory of comets, to which I have already referred; according to which the comet, a group of meteoric stones, is self-luminous in its nucleus, on account of collisions among its constituents, while its "tail" is merely a portion of the less dense part of the train illuminated by sunlight, and visible or invisible to us according to circumstances, not only of density, degree of illumination, and nearness, but also of tactic arrangement, as of a flock of birds or the edge of a cloud of tobabco smoke! What prodigious difficulties are to be explained, you may judge from two or three sentences which I shall read from Herschel's Astronomy, and from the fact that even Schiapa relli seems still to believe in the repulsion. "There is, beyond question, some profound secret and mystery of nature concerned in the phenomenon of their tails. Perhaps it is not too much to hope that future observation borrowing every aid from rational speculation, grounded on the progress of physical science generally (especially those branches of it which relate to the etherial or imponderable elements), may enable us ere long to penetrate this mystery, and to declare whether it is really matter in the ordinary anticipation of the term which is projected from their heads with such extraordinary velocity, and if not impelled, at least directed, in its course, by reference to the Sun, as its point of avoidance." +

"In no respect is the question as to the materiality of the tail more forcibly pressed on us for consideration than in that of the enormous sweep which it makes round the sun in perihelio, in * Signor Schiaparelli, Director of the Observatory of Milan, who, in a letter dated 51st December, 1866, pointed out that the elem nts of the orbit of the August Meteors, calculated from the observed position of their radiant poist on the supposition of the orbit being a very elongated ellipse agreed very closely with those of the orbit of Comet II 1862, calculated by Dr. Oppolzer. In the same letter Schiaparelli gives clements of the orbit of the November meteors, but these were not sufficiently accurate to enable him to identify the orbit with that of any known comet. On the 21st January, 1867, M. Leverrier gave more accurate elements of the orbit of the November Meteors, and in the "Astronomische Nachrichten" of January 9, Mr. C. F. W. Peters, of Altona, pointed out that these elements closely agreed with those of Temper's Comet (I. 1865, calculated by Dr. Oppol zer, ant on Feb. 2, Schiaparelli having recalculated the elements of the orbit of the meteors himself noticed the same agreement. Adams arrived quite independently at the conclu ion that the orbit of 3 years period is the one which must be chosen out of the five indicated by Prof. Newton. His calculations were sufficiently advanced before the letters referred to appeared, to show that the other four orbits offered by Newton were inadmissible. But the calculations to be gone through to find the secular mo ion of the node in such an elongated orbit as that of the meteors, were necessarily very long, so that they were not completed till about March 1867. They were communicated in that month to the Cambridge Philosophical Society, and in the month following to the Astronomical Society. ↑ Herschel's Astronomy, § 599.

the manner of a straight and rigid rod, in defiance of the law of gravitation, nay, even of the received laws of motion." *

"The projection of this ray. to so enormous a length, in a single day conveys an impression of the intensity of the forces acting to produce such a velocity of material transfer through space such as no other natural phenomenon is capable of exciting. It is clear that if we have to deal here with matter, such as we conceive it, viz., possessing inertia―at all, it must be under the dominion of forces incomparably more energetic than gravitation, and quite of a different nature."+

Think now of the admirable simplicity with which Tait's beautiful "sea-bird analogy," as it has been called, can explain all these phenomena.

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The essence of science, as is well illustrated by astronomy and cosmical physics, consists in inferring antecedent conditions, and anticipating future evolutions, from phenomena which have actually come under observation. In biology, the difficulties of successfully acting up to this ideal are prodigious. The earnest naturalists of the present day are, however, not appalled or paralysed by them, and are struggling boldly and laboriously to pass out of the mere "Natural History stage" of their study, and bring Zoology within the range of Natural Philosophy. A very ancient speculation, still clung to by many naturalists (so much so that I have a choice of modern terms to quote in expressing it) supposes that, under meteorological conditions very different from the present, dead matter may have run together or crystallised or fermented into "germs of life," or "organic cells," or "protoplasm.' But science brings a vast mass of inductive evidence against this hypothesis of spontaneous generation, as you have heard from my predecessor in the Pre-idential chair. Careful enough scrutiny has, in every case up to the present day, discovered life as antecedent to life. matter cannot become living without coming under the influence of matter previously alive. This seems to me as sure a teaching of science as the law of gravitation. I utterly repudiate, as opposed to all philosophical uniformitarianism, the assumption of "different meteorological condition"-that is to say, somewhat different vicissitudes of temperature, pressure, moisture, gaseous atmosphere-to produce or to permit that to take place by force or motion of dead matter alone, which is a direct contravention of what seems to us biological law. I am prepared for the answer, "our code of biological law is an expression of our ignorance as well of our knowledge." And I say yes: search for spontaneous generation out of inorganic materials; let any one not satisfied with the purely negative testimony of which we have now so much against it, throw him elf into the inquiry. Such investigations as those of Pasteur, Pouchet, and Bastian are among the most interesting and momentous in the whole range of Natural History, and their results, whether positive or negative, must richly reward the most careful and laborious experimenting. I confess to being deeply impressed by the evidence put before us by Professor Huxley, and I am ready to adopt, as an article of scientific faith, true through all space and through all time, that life proceeds from life, and from nothing but life.

How, then, did life originate on the Earth? Tracing the physical history of the Earth backwards, on strict dynamical principles, we are brought to a red-hot melted globe on which no life could exist. Hence when the Earth was first fit for life, there was no living thing on it. There were rocks solid and disintegrated, water, a'r all round, warmed and illuminated by a brilliant Sun, ready to become a garden. Did grass and trees and flowers spring into existence, in all the fulness of ripe beauty, by a fiat of Creative power? or did vegetation, growing up from seed sown, spread and multiply over the whole Earth? Science is bound, by the everlasting law of honour, to face fearlessly every problem which can fairly be presented to it. If a probable solution, consistent with the ordinary course of nature, can be found, we must not invoke an abnormal act of Creative Power. When a lava stream flows down the sides of Vesuvius or Etna it quickly cools and becomes solid; and after a few weeks or years it teems with vegetable and animal life, which for it originated by the transport of seed and ova and by the migration of individual living creatures When a volcanic island springs up from the sea, and after a few years is foun 1 clothed with vegetation, we do not hesitate to assume that seed has been wafted to it through the air, or floated to it on rafts. Is it not possible, and if possible, is it not probable, that the beginning of vegetable life on the earth is to be similarly explained?

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Every year thousands, probably millions, of fragments of solid matter fall upon the Earth-whence came these fragments? What is the previous history of any one of them? Was it created in the beginning of time an amorphous mass? This idea is so It is unacceptable that, tacitly or explicitly, all men discard it. often assumed that all, and it is certain that some, meteoric stones are fragments which had been broken off from greater masses and launched free into space. It is as sure that colli-ions must occur between great masses moving through space as it is that ships, steered without intelligence directed to prevent colli sion, could not cross and recross the Atlantic for thousands of years with immunity from collisions. When two great masses

come into collision in space it is certain that a large part of each is melted; but it seems also quite certain that in many cases a large quantity of débris must be shot forth in all directions, much of which may have experienced no greater violence than individual pieces of rock experience in a land-slip or in blasting by gunpowder. Should the time when this earth comes into collision with another body, comparable in dimensions to itself, be when it is still clothed as at present with vegetation, many great and small fragments carrying seed and living plants and animals would undoubtedly be scattered through space. Hence and because we all confidently believe that there are at present, and have been from time immemorial, many worlds of life besides our own, we must regard it as probable in the highest degree that there are countless seed bearing meteoric stones moving about through space. If, at the present instant, no life existed upon this earth, one such stone falling upon it might, by what we blindly call natural causes, lead to its becoming covered with vegetation. I am fully conscious of the many scientific objections which may be urged against this hypothesis, but I believe them to be all answerable. I have already taxed your patience too severely to allow me to think of discussing any of them on the present occasion. The hypothesis that life originated on this earth through moss-grown fragments from the ruins of another world may seem wild and visionary; all I maintain is that it is not unscientific. From the earth stocked with such vegetation as it could receive meteorically, to the earth teeming with all the endless variety of plants and animals which now inhabit it, the step is prodigious; yet, according to the doctrine of continuity, most ably laid before the Association by a predecessor in this chair (Mr. Grove), all creatures now living on earth have proceeded by orderly evolution from some such origin. Darwin concludes his great work on "The Origin of Species" with the following words :-"It is interesting to contemplate an entangled bank clothed with many plants of many kinds, with birds singing on the bushes, with various insects flitting about, and with worms crawling through the damp earth, and to reflect that these elaborately constructed forms, so different from each other, and dependent on each other in so complex a manner, have all been produced by laws acting around us." "There is grandeur in this view of life, with its several powers, having been originally breathed by

the Creator into a few forms or into one; and that, whilst this planet has gone cycling on according to the fixed law of gravity, from so simple a beginning endless forms, most beautiful and most wonderful, have been and are being evolved." With the feeling exp essed in these two sentences I most co dially sympathise.

I have omitted two sentences which come between them,

describing briefly the hypothesis of "the origin of species by natural election," because I have always felt that this hypothesis does not contain the true theory of evolution, if evolution there has been in biology. Sir John Herschel, in expres-ing a favourable judgment on the hypothesis of zoological evolution, with however, some reservation in respect to the origin of man, objected to the doctrine of natural selection, that it was too like the Laputan method of making books, and that it did not sufficiently take into account a continually guiding and controlling intelligence. This seems to me a most valuable and instructive criticism. I feel profoundly convinced that the argument of design has been greatly too much lost sight of in recent zoological speculations. Reaction against the frivolities of teleology, such as are to be found, not rarely, in the notes of the learned Commentators on Paley's "Natural Theology," has I believe had a temporary effect in turning attention from the solid and irrefia,able argument so well put forward in that excellent old book. But overwhelmingly strong proofs of intelligent and benevolent design lie all around us, and if ev r perplexities, whether metaphysical or scientific, turn us away from them for a time, they come back upon us with irresistible force, showing to us through nat are the influence of a free will, and teaching us that all living beings depend on one ever-acting Creator and Ruler.

SECTION A.

MATHEMATICAL AND PHYSICAL SCIENCE.

OPENING ADDRESS BY THE PRESIDENT, PROF. P. G. TAIT, M. A. IN opening the proceedings of this Section my immediate predecessors have exercised their ingenuity in presenting its widely different component subjects from their several points of view, and in endeavouring to coordinate them. What they were obliged to leave unfinished, it would be absurd in me to attempt to complete. It would be impossible, also, in the limits of a brief address, to give a detailed account of the recent progress of physical and mathematical knowledge. Such a work can only be produced by separate instalments, each written by a specialist, such as the admirable "Reports" which form from time to time the most valuable portions of our annual volume.

I shall therefore confine my remarks in the main to those two subjects, one in the mathematical, the other in the purely physical, division of our work, which are comparatively familiar to myself. I wish, if possible, to induce, ere it be too late, native mathematicians to pay much more attention than they have yet paid to Hami ton's magnificent Calculus of Quaternions, and to call the particular notice of physicists to our President's grand Principle of Dissipation of Energy. I think that these are, at this moment, the most important because the most promising parts of our field.

If nothing more could be said for Quaternions than that they enable us to exhibit in a singularly compact and elegant form, whose meaning is obvious at a glance on account of the utter inartificiality of the method, results which in the ordinary Cartesian coordinates are of the utmost complexity, a very powerful argument for their use would be furnished. But it would be unjust to Quaternions to be content with such a statement; for we are fully entitled to say that in all cases, even in those to which the Cartesian methods seem specially adapted, they give as simple an expression as any other method; while in the great majority of cases they give a vastly simpler one. In the common methods a judicious choice of coordinates is often of immense importance in simplifying an investigation; in Quaternions there is usually no choice, for (except when they degrade to mere scalars) they are in general utterly independent of any particular directions in space, and select of themselves the most natural reference lines for each particular problem. This is easily illustrated by the most elementary instances, such as the following:The general equation of Cones involves merely the direction of the vector of a point, while that of Surfaces of Revolution is a relation between the lengths of that vector and of its resolved part parallel to the axis, and Quaternions enable us by a mere mark to separate the ideas of length and direction without introducing the cumbrous and clumsy square roots of sums of squares which are otherwise necessary.

But, as it seems to me that mathematical methods should be sical applications, what can possibly from that point of view be specially valued in this Section as regards their fitness for phymore important than Hamilton's ? Physical analogies have often been invoked to make intelligible various mathematical processes. Witness the case of Statical Electricity, wherein Thomson has by the analogy of Heat-conduction, explained the meaning of various important theorems due to Green, Gauss, and others; and wherein Cerk-Maxwell has employed the properties of an imaginary incompressible liquid (devoid of inertia) to illustrate not merely these theorems, but even Thomson's Electrical Images. [In fact he has gone much further, having applied his analogy to the puzzling combinations presented by Electrodynamics.] There can be little doubt that these comparisons owe their birth to the small intelligibility, per se, of what has d2 been called Laplace's Operator, d2, which dz2

d2

dyz+

dxz + appears alike in all theories of attraction at a distance, in the steady flow of heat in a conductor, and in the steady motion of incompressible fluids. But when we are taught to understand the operator itself, we are able to dispense with these analogies, which, however, valuable and beautiful, have certainly to be used with extreme caution, as tending very often to confuse and mislead. Now Laplace's operator is merely the negative of the square of Hamilton's v, which is perfectly intelligible in itself and in all its combinations; and can be defined as giving the vector-rate of most rapid increase of any scalar func ion to which it is applied-giving, for instance, the vector-force from a potential, the heat-flux from a dis tribution of temperature, &c. Very simple functions of the same operator give the rate of increase of a quantity in any

assigned direction, the condensation and elementary rotation produced by given displacements of the parts of a system, &c. For instance, a very elementary application of v to the theory of attraction enables us to put one of its fundamental principles in the following extremely suggestive form :-If the displacement or velocity of each particle of a medium represent in magnitude and direction the electric force at that particle, the corresponding statical distribution of electricity is proportional everywhere to the condensation produced. Again, Green's celebrated theorem is at once seen to be merely the well-known equation of continuity expressed for a heterogeneous fluid, whose density at every point is proportional to one electric potential, and its displacement or velocity proportional to and in the direction of the electric force due to another potential. But this is not the time to pursue such an inquiry, for it would lead me at once to discussions as to the possible nature of electric phenomena and of gravitation. I believe myself to be fully justified in saying that, were the theory of this operator thoroughly developed and generally known, the whole mathematical treatment of such physical questions as those just mentioned would undergo an immediate and enormous simplification; and this, in its turn, would be at once followed by a proportionately large extension of our knowledge. *

And this is but one of the claims of Quaternions to the attention of physicists. When we come to the important questions of stress and strain in an elastic solid, we find again that all the elaborate and puzzling machinery of coordinates commonly employed can be at once comprehended and kept out of sight in a mere single symbol-a linear and vector function, which is selfconjugate if the strain be pure. This is simply, it appears to me, a proof either that the elaborate machinery ought never to have been introduced, or that its use was an indication of a comparatively savage state of mathematical civilisation. In the motion of a rigid solid about a fixed point, a Quaternion, represented by a single symbol which is a function of the time, gives us the operator which could bring the body by a single rotation from its initial position to its position at any assigned instant. In short, whenever with our usual means a result can be obtained in, or after much labour reduced to, a single form, Quaternions will give it at once in that form; so that nothing is ever lost in point of simplicity. On the other hand, in numberless cases the Quaternion result is immeasurably simpler and more intelligible than any which can be obtained or even expressed by the usual methods. And it is not to be supposed that the modern Higher Algebra, which has done so much to simplify and extend the ordinary Cartesian methods, would be ignored by the general employment of Quaternions; on the contrary, Determinants, Invariants, &c., present themselves in almost every Quaternion solution, and in forms which have received the full benefit of that simplification which Quaternions generally produce. Comparing a Quaternion investigation, no matter in what department, with the equivalent Cartesian one, even when the latter has availed itself to the utmost of the improvements suggested by Higher Algebra, one can hardly help making the remark that they contrast even more strongly than the decimal notation with the binary scale, or with the old Greek Arithmetic or than the well-ordered subdivisions of the metrical system with the preposterous no-systems of Great Britain, a mere fragment of which (in the form of Table of Weights and Measures) form, perhaps the most effective, if not

* The following extracts from letters of Sir W. R. Hamilton have a perfectly general application, so that I do not hesitate to publish them :-"De Morgan was the very first person to notice the Quaternions in print ; namely in a paper on Triple Algebra, in the Camb. Phil. Trans. of 18.4.

It was,

I think, about that time, or not very long afterwards, that he wrote to me, rearly as follows:-I suspect, Hamilton, that you have caught the right sow by the ear!' Between us, dear Mr. Tait, I think we shal begin the SHEARING of it!" "You might without offence to me, co sider that I abused the licence of hope, which may be indulged to an inventor, if I were to confess that I expect the Quaternions to supply, hereafter, not merely mathematical methods, but also physical suggestions. And, in particular, you are quite v elcome to smile, it I say that it does not seem extravagant to me to suppose that a full possession of those a priori principies of mine, about the multiplication of vectors :-including the law of the Four Scales, and the conception of the Extra-spatial Unit-which have as yet been not much more than hinted to the public-MIGHT have led (I do not at all mean that in my hands they ever would have done so) to an ANTICIPATION of the great discovery of OERSTED."

"It appears to me that one, and not the least, of the services which Quaternions may be expected to do to mathematical analysis generally, is that their introduction will compel those who adopt them, or even who admit that they may be reasonably a opted by other persons-to consider, or to admit, that others may uesfully iuquire, what common grounds can be established, for conclusions common to Quaternions and to older branches of mathematics."

"Could anything be simpler, or more satisfactory? Don't you feel, as well as think, that we are on a right track, and shall be thanked hereafter? Never mind when."

the most ingenious, of the many instruments of torture employed in our elementary teaching.

It is true that, in the eyes of the pure mathematician, Quaternions have one grand and fatal defect. They cannot be applied to space of n dimensions, they are contented to deal with those poor three dimensions in which mere mortals are doomed to dwell, but which cannot bound the limitless aspirations of a Cayley or a Sylvester. From the physical point of view this, instead of a defect, is to be regarded as the greatest possible recommendation. It shows, in fact, Quaternions to be a special instrument so constructed for application to the Actual as to have thrown overboard everything which is not absolutely necessary, without the slightest consideration whether or no it was thereby being rendered useless for applications to the Inconceivable.

But this

The late Sir John Herschel was one of the first to perceive the value of Quaternions: and there may be present some who remember him, at a British Association meeting not long after their invention, characterising them as a "Cornucopia from which, turn it how you will, something valuable is sure to fall." Is it not strange, to use no harsher word, that such a harvest has hitherto been left almost entirely to Hamilton himself? If but half a dozen tolerably good mathematicians, such as exist in scores in this country, were seriously to work at it, instead of spending (or rather wasting) their time, as so many who have the requisite leisure now do, in going over again what has been already done, or in working out mere details where a grand theory has been sketched, a very great immediate advance would be certain. From the majority of the papers in our few mathematical journals, one would almost be led to fancy that British mathematicians have too much pride to use a simple method while an unnecessarily complex one can be had. No more telling example of this could be wished for than the insane delusion under which they permit Euclid to be employed in our elementary teaching. They seem voluntarily to weight alike themselves and their pupils for the race; and a cynic might, perhaps without much injustice, say they do so that they may have mere self-imposed and avoidable difficulties to face instead of the new, real, and dreaded ones (belonging to regions hitherto unpenetrated) with which Quaternions would too soon enable them to come into contact. game will certainly end in disaster. As surely as mathematics came to a relative stand-still in this country for nearly a century after Newton, so surely will it do so again if we leave our eager and watchful rivals abroad to take the initiative in developing the grand method of Hamilton. And it is not alone French and Germans whom we have now to dread, Russia, America, regenerated Italy, and other nations, are all fairly entered for the contest. The flights of the imagination which occur to the pure mathematician are in general so much better described in his formul than in words, that it is not remarkable to find the subject treated by outsiders as something essentially cold and uninterestingwhile even the most abstruse branches of physics, as yet totally incapable of being popularised, attract the attention of the uninitiated. The reason may perhaps be sought in the fact that, while perhaps the only successful attempt to invest mathematical reasoning with a halo of glory-that made in this section by Prof. Sylvester- is known to a comparative few, several of the highest problems of physics are connected with those observations which are possible to the many. The smell of lightning has been observed for thousands of years, it required the sagacity of Schönbein to trace it to the formation of Ozone. Not to speak of the (probably fabulous) apple of Newton-what enormous consequences did he obtain by passing light through a mere wedge of glass, and by simply laying a lens on a flat plate! The patching of a trumpery model led Watt to his magnificent inventions. As children at the sea-shore playing with a "roaring buckie," or in later life lazily puffing out rings of tobacco-smoke, we are illustrating two of the splendid researches of Helmholtz. And our President, by the bold, because simple, use of reaction, has eclipsed even his former services to the Submarine Telegraph, and given it powers which but a few years ago would have been deemed unattainable.

In Experimental Physics our case is not hopeless, perhaps not as yet even alarming. Still something of the same kind may be said in this as in pure Mathematics. If Thomson's Theory of Dissipation, for instance, be not speedily developed in this country, we shall soon learn its consequences from abroad. The grand test of our science, the proof of its being a reality and not a mere inventing of new terms and squabbling as to what they shall mean, is that it is ever advancing. There is no standing still; there is no running round and round as in a beaten donkeytrack, coming back at the end of a century or so into the old posi

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