14 
to results such as it is impossible to accept, I feel all the 
more assured of the correctness of the process of a 'priori 
reasoning I have entered upon, and accordingly I shall carry 
on the argument to the end, without having further regard 
to the adverse views of empirical theorists. 
20. Having now shown that the three hypotheses in sec. 10 
are proper for being employed as a basis of theoretical in- 
vestigations conducted by mathematical reasoning, and having 
also argued that empirical theory derived immediately from 
experiment, being contributory to the establishment of ultimate 
theory resting on true d priori hypotheses, cannot be contra- 
dictory to the latter, I proceed, in the third place, to inquire 
whether it can be proved that the three hypotheses constitute 
a true and adequate foundation of a general physical theory. 
V ery important consequences, relative to the material universe, 
follow from an affirmative answer to this inquiry. Now it 
may be taken for granted that the only possible way in which 
the answer can be reached, is to accept the hypotheses as 
foundations for applying mathematical reasoning in the several 
departments of physics in conformity with their respective 
definitions, and then to test numerical values obtained re- 
latively to given phenomena by means of the theoretical 
calculation, by comparisons with numerical values relative 
to the same phenomena obtained directly by experiment. More- 
over, the answer cannot be completely given till the test has 
been fully applied in every department of experimental physics. 
To contribute towards making progress in this large field of 
inquiry has been the professed object of my inathematico- 
physical researches during many years. Before adverting to 
the results arrived at, it will be proper to direct attention to 
a special dynamical quality pertaining to the atom, and es- 
sentially involved in those researches, which hitherto I have 
not expressly taken into consideration. 
21. According to definitions in secs. 10-12, the hypothetical 
spherical atom is not susceptible of change, either as to form 
or magnitude ; in other words, it is capable of unlimited 
resistance to pressure applied to its surface. This quality of 
the atom is particularly objected to by those physicists whose 
views of the relations of matter and force are professedly 
derived entirely from experiment, since, as it seems, they are 
unable, on that account, to admit that solid matter can be 
devoid of elasticity, yielding in greater or less degree to com- 
pression. But, according to our philosophy, this property 
cannot be included in the definition of the ultimate atom, 
because it involves variability as to form or condition, and 
is consequently the result of force acting according to laws, 
