

270 

NATURE. 

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 
unacceptable that, tacitly or explicitly, all men discard it. It is 
ofien assumed that al, 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 déris must be shot forth in all directions, much 
of which may have experienced no greater violence than indivi- 
dual pieces of rock experience in a land-slip or in blasting by 
gunpowder. Should the time when this earth comes into colli- 
sion 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 be- 
cause 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 tte 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 occa- 
sion. 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 evolu- 
tion 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 wondertul, have been and are being evolved.” With the 
feeling exp essed in these two sentences I most cordially sympa- 
thise. I have omitted two sentences which come between them, 
describing briefly the hypothesis of ‘‘the origin of species by 
natural selection,” because I have always felt that this hypothesis 
does not contain the trne theory of evolution, if evolution there 
has been in biology. Sir John Herschel, in expressing a favour- 
able judgment on the hypothesis of zoological evolution, with 
however, some reservation in respect to the origin of man, ob- 
jected 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 mtelli- 
gence. This seems to me a most valuable and instructive cri- 
ticism. 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 Com- 
mentators on Paley’s ‘* Natural Theology,” has I believe had a 
temporary effect in turning attention from the solid and irre- 
fia 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 ever perplexities, whether meta- 
physical or scientific, turn us away from them for atime, they 
come back upon us with irresistible force, showing to us through 
nat ire 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, PRor, P. G, Tart, 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 knowle’ge. 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 physi- 
cal, 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 in- 
artificiality of the method, results which in the ordinary Car- 
tesian coordinates are of the utmost complexity, a very powerful 
argument for their use would be furnished, But it would be un- 
just to Quaternions to be content with such a statement; for 
we are fully entitled to say that in a// 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 20 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 illus- 
trated 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 /eng¢hs 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 intro- 
ducing 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 
specially valued in this Section as regards their fitness for phy- 
sical applications, what can possibly from that point of view be 
more important than Hamilton’s v ? 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 Cierk-Maxwell has employed the pro- 
perties 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, haying 
applied his analogy to the puzzling combinations presented by 
Electrodynamics. ] There can be little doubt that these compari- 
sons owe their birth to the small intelligibility, er se, of what has 
@2 @24  @ 
been called Laplace’s Operator, dat dy? * a which 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 incom- 
pressible 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 it- 
self and in all its combinations; and can be defined as 
giving the vector-rate of most rapid increase of any 
scalar funcion 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 

3, 1871 ; 


