Prof. Challis on Theoretical Physics. - 505 
them. He has not even alluded to my mathematics. I say, 
therefore, that there is no argument which I have to meet. 
In prosecuting physical inquiry, it appears to be necessary to 
proceed by way of hypotheses. But hypotheses of themselves 
teach nothing: we /earn by mathematics, as the very name im- 
plies, because by mathematics the truth of a hypothesis may be 
tested or established. The existence of gravity as a force, and 
the law of gravity, are truths which could not be ascertained 
by observation alone; but being taken to be true hypothe- 
tically, they are proved to be actually true, by the aid of mathe- 
matics. 
Hence hypotheses respecting the physical forces are deserving 
of consideration only so far as they afford a basis for mathemati- 
cal reasoning. In fact this quality of a hypothesis is a criterion 
of its truth, because all quantitative laws are deducible mathe- 
matically from ¢rwe hypotheses. In selecting hypotheses for the 
foundation of a general theory of the physical forces, [ had 
regard, in the first place, to their conformity with the antecedents 
of physical science, and then to the possibility of arguing from 
. them mathematically. I have not met-with any which in the 
latter respect are preferable to those I have selected, which, con- 
sequently, I have good reason to adhere to. 
To assume that an atom is of constant form and magnitude, 
is, | admit, virtually to call it an indivisible particle, and not, as 
Newton does, an undivided particle, “ particula indivisa.” But 
as the hypothesis is expressed in perfectly intelligible terms, it 
is open to no objection, provided we admit with Newton, that if 
by a single experiment it can be shown that the supposed indi- 
visibie. particle is divided when a solid mass is broken, the theory 
of atoms is untenable. When a physical hypothesis satisfies the 
condition of being expressed in terms which common experience 
renders intelligible, special observation and experiment, or com- 
parisons of its mathematical consequences with facts, alone deter- 
mine whether or not it be true. I do not admit that any meta- 
physical argument can be adduced either in support of, or against, 
a physical hypothesis. Meta-physics come after physics. Ifa 
general physical theory should be established on verified hypo- 
theses, we should have a secure basis for metaphysical reasoning; 
and possibly it might then appear that some of the speculative 
metaphysics which have prevailed during the last century are 
without foundation. 
By the same mode of reasoning, the hypothesis of a universal 
fluid ether, the pressure of which varies proportionally to its 
density,.1s unobjectionable as a hypothesis, simply because it is 
expressed im terms which experience has made intelligible. 
Whether it be a true hypothesis, that is, whether such an ether 
