422 
result of a previous state of things, and we find that this 
critical condition actually existed at an epoch not in the 
utmost depths of a past eternity, but separated from the pre- 
sent time by a finite interval. This idea of a beginning 
is one which the physical researches of recent times have 
brought home to us, more than any observer of the course of 
scientific thought in former times would have had reason to expect. 
But the mind of man is not like Fourier’s heated body, con- 
tinually settiing down into an ultimate state of quiet uniformity, 
the character of which we can already predict ; it is rather like a 
tree shooting out branches which adapt themselves to the new 
aspects of the sky towards which they climb, and roots which 
contort themselves among the strange strata of the earth into 
which they delve. To us who breathe only the spirit of our own 
age, and know only the characteristics of contemporary thought, 
it is as impossible to predict the general tone of the science of 
the future as it is to anticipate the particular discoveries which it 
will make. Physical research is continually revealing to us new 
features of natural processes, and we are thus compelled to search 
for new forms of thought appropriate to these features. Hence 
the importance of a careful study of those relations between 
mathematics and physics which determine the conditions under 
which the ideas derived from one department of physics may be 
salely used in forming ideas to be employed in a new depart- 
ment. The figure of speech or of thought by which we transfer 
the language and ideas of a familiar science to one with which 
we are less acquainted may be called scientific metaphor. Thus 
the words velocity, momentum, force, &c., have acquired certain 
precise meanings in elementary dynamics. They are also em- 
ployed in the dynamics of a connected system in a sense which, 
though perfectly analogous to the elementary sense, is wider and 
more general. These generalised forms of elementary ideas may 
be called metaphorical terms in the sense in which every abstract 
term is metaphorical. The characteristic of a truly scientific 
system of metaphors is that each term in its metaphorical use 
retains all the formal relations to the other terms of the system 
which it had in its original use. “The method is then truly scien- 
tific, that is, not only a legitimate product of science, but capable 
of generating science in its turn. There are certain electrical 
phenomena, again, which are connected together by relations of 
the same form as those which connect dynamical phenomena. 
To apply to these the phrases of dynamics with proper distinc- 
tions and provisional reservations is an example of a metaphor of 
a bolder kind ; but it is a legitimate metaphor if it conveys a true 
idea of the electrical relations to those who have been already 
trained in dynamics. Suppose, then, that we have successfully 
introduced certain ideas belonging to an elementary science by 
applying them metaphorically to some new class of phenomena. 
It becomes an important philosophical question to determine in 
what degree the applicability of the old ideas to the new subject 
may be taken as evidence that the new phenomena are physically 
similar to the old. The best instances for the determination of 
this question are those in which two different explanations have 
been given of the same thing. The most celebrated case of this 
kind is that of the corpuscular and the undulatory theories of 
light. Up to a certain point the phenomena of light are equally 
well explained by both ; beyond this point one of them fails. To 
understand the true relation of these theories in that part of the 
field where they seem equally applicable we must look at them 
in the light which Hamilton has thrown upon them by his dis- 
covery that to every brachystochrone problem there corresponds 
a problem of free motion, involving different velocities and times, 
but resulting in the same geometrical path. Professor Tait has 
written a very interesting paper on this subject. According to a 
theory of electricity which is making great progress in Germany 
two electrical particles act on one another directly at a distance, 
but with a force which, according to Weber, depends on their 
relative velocity, and according toa theory hinted at by Gauss, 
and developed by Riemann, Lorenz, and Neumann, acts not 
instantaneously, but after a time depending on the distance. The 
power with which this theory, in the hands of these eminent 
men, explains every kind of electrical phenomena must be studied 
in o-der to be appreciated. Another theory of electricity which 
I prefer denies action at a distance and attributes electric 
act'on to tensions and pressures in an all-pervading medium, 
these stresses being the same in kind with those familiar to 
engineers, and the medium being identical with that in which 
light is supposed to be propagated. Both these theories are 
found to explain not only the phenomena by the aid of 
which they were originally constructed, but other phenomena 
NATURE 
[Set 22, 1870 
which were not thought of, or perhaps not known at 
the time, and both have independently arrived at the same 
numerical result which gives the absolute velocity of light 
in terms of electrical quantities. That theories, apparently so. 
fundamentally opposed, should have so large a field of truth com- 
mon to both is a fact the philosophical importance of which we 
cannot fully appreciate till we have reached a scientific altitude 
from which the true relation between hypotheses so different can 
be seen. 
T shall only make one more remark on the relation between 
mathematics and physics. In themselves, one is an operation 
of the mind, the other is a dance of molecules. The molecules 
have laws of their own, some of which we select as most in- 
telligible to us and most amenable to our calculation. We form 
a theory from these partial data, and we ascribe any deviation of 
the actual phenomena from this theory to disturbing causes. At 
the same time, we confess that what we call disturbing causes are 
simply those parts of the true circumstances which we do not 
know or have neglected, and we endeavour in future to take 
account of them. We thus acknowledge that the so-called dis- 
turbance is a mere figment of the mind, not a fact of nature, and 
that in natural action there is no disturbance. But this is not 
the only way in which the harmony of the material with the 
mental operation may be disturbed. The mind of the mathe- 
matician is subject to many disturbing causes, such as fatigue, 
loss of memory, and hasty conclusions; and it is found that 
from these and other causes mathematicians make mistakes. I 
am not prepared to deny that, to some mind of a higher order 
than ours, each of these errors might be traced to the regular 
operation of the laws of actual thinking ; in fact we ourselves 
often do detect, not only errors of calculation, but the causes of 
these errors. This, however, by no means alters our conviction 
that they are errors, and that one process of thought is right and 
another process wrong. One of the most profound mathe- 
maticians and thinkers of our time, the late George Boole, when 
reflecting on the precise and aimost mathematical character of 
the laws of right thinking as compared with the exceedingly 
perplexing, though perhaps equally determinate, laws of actual 
and fallible thinking, was led to another of those points of view 
from which science seems to look out into a region beyond her 
own domain. ‘‘ We must admit,” he says, “that there exist 
laws ”’ (of thought) ‘* which even the rigour of their mathematical 
forms does not preserve from violation. We must ascribe to 
them an authority, the essence of which does not consist in power, 
a supremacy which the analogy of the inviolable order of the 
natural world in no way assists us to comprehend,” 
Section B,—Chemical Science.—President, Professor Roscoe, 
F.R.S. 
Report of the Committee on the Chemical Nature of Cast 
JIyon. —Mr. David Forbes, F.R.S., reported on _ behalf 
of Professor Abel, Dr. Matthiessen and himself, that it had 
not been in their power, as a Committee, to make any im- 
portant progress in the investigation of the chemical nature of 
cast iron during the past year. This was partly owing to the 
dismantled condition of the required apparatus, The Committee 
asked to be reappointed, so that the experiments might be re- 
sumed without much further delay. 
Ona New Chlorine Process without Manganese.—Mr. Henry 
Deacon, of Widnes. As the closing paragraph of Professor 
Roscoe’s address briefly and clearly described the essential nature 
of Mr. Deacon’s process, it is not necessary further to refer to 
it, except to state that hitherto Mr. Deacon has not succeeded 
in making the process a commercial success, and he prefers in 
the meantime to employ Mr. Weldon’s process, though he is 
satisfied that his own will yet become practically applicable in 
the production of chlorine for the manufacture of bleaching 
powder. 
Secrion C.—Geo/ogy.—President, Sir Philip de Malpas Grey 
Egerton, Bart., M.P., F.R.S. 
The President departed from the practice of giving an intro- 
ductory address, inasmuch as the time of the Section would be 
fully occupied with the reading and discussion of the papers to 
be submitted to it. 
On the Glaciated Surface of Triassic Rocks near Liverpool.— 
Mr. G. H. Morton. The grooves on{the rocks were of a uniform 
direction, 35° W. of N., and were due to the action of land ice. 
