78 C.8. Peirce on Chemical Theory of Interpenetration. 
Art. XII.—The Chemical Theory of Interpenetration; by CHARLES 
S. Prerrce, A.M. 
PHYSICISTS are now rapidly doing away with all theories which 
demand peculiar shapes and kinds of matter in favor of tho 
which demand peculiar vibrations. At this day, the arrow- 
shaped particles of the old theory of light seem grotesque. 
There is a good reason for this tendency. We require an ex- 
planation of forces. Now a force is only a mathematical func- 
tion of a change, and a change in space can only be conceived 
of a priori as a motion. To explain a thing is to bring it into 
the realm of our a priori conceptions. Hence, whenever we en- 
deavor to explain any force of nature by means of hypothetical 
shapes and properties of matter these only help us so far as they 
are conditions of certain motions. These mctions are the real 
explanation; and if we can succeed in getting the motions with- 
out the peculiarities of matter, our hypothesis will be so much 
the smaller. 
The object of the present article is to apply this principle to 
the Atomic Theory. 
I. In the first place, it is necessary to show that the hypothesis 
of atoms, in itself, explains nothing. 
That which the atomic theory undertakes to explain is the 
connection of integral numbers with chemical equivalents. 
An explanatory hypothesis is one which, being admitted, 
necessitates all the phenomena. The laws to be explained are 
as follows: 
1. The Law of Equivalents, or that if a units of one body 
combine with x of a second and y of a third; and if x of that 
second combines with d of a fourth, that y of the third will also 
combine with d of the fourth. 
The explanation is that these are the weights of the atoms and 
that bodies combine atom by atom. But how should we know 
that they combine atom by atom? This is an addition to the 
hypothesis. 
2. The Law of Multiple proportions, . 
How should we know that atoms will mix in any simpler 
ratios than black and white beans would if stirred up together? 
8. The Law of Combining Volumes of Gases. 
The explanation is that the atoms of all gases are equally 
distant. A new hypothesis. 
4. The Law of Volumes of Isomorphous Crystals. Another 
hypothesis needed. 
5. The Law of Thermal Equivalents of the Elements. 
Explanation: All atoms have the same capacity for heat. Still 
another hypothesis, which moreover does not apply to compounds. 
