7 
is no other course by which it can advance towards perfection 
than by improved methods of solving and interpreting the 
solutions of partial differential equations. As in the case of 
physical astronomy, hypotheses have first to be made (see sec. 
6*), differential equations have to be formed on the basis of the 
hypotheses, these equations have to be solved, and the solutions 
brought into comparison with the data of phenomena proposed 
for explanation. In proportion as special facts, or facts grouped 
under formulated laws, are by this process accounted for, 
the hypotheses are proved to be true, and our knowledge of 
the natural operations whereby phenomena are produced, is 
augmented. 
9. I have already, in secs. 13-29 of my Paper on “ The Meta- 
physics of Scripture,” indicated the principles which, according 
to the Newtonian philosophy, regulate the hypotheses of theo- 
retical physics. The most important governing principles are, 
first, that the essential or ultimate qualities of matter and force 
are such as can be fully understood from personal sensation and 
experience, and, in the second place, that qualities which are 
proper to be made the basis of theoretical calculation cannot 
themselves be quantitatively variable, or expressible in nu- 
merical terms, because it is the very purpose of theoretical 
inquiry to account for all facts and laws so expressible. 
Accordingly, the law of the inverse square, as involving a 
numerical term in its expression, ought to admit of being 
accounted for theoretically. This point will be adverted to 
farther on. 
10. After these preliminary considerations, I am prepared to 
state in distinct terms the hypotheses of theoretical physics 
which will be adopted in the subsequent general argument. 
They are simply these : — 
I. All matter that we are cognizant of by our senses is 
composed of discrete atoms. 
II. An atom is a very small sphere, inert, movable, and of 
finite and invariable magnitude. 
III. All active physical force is pressure upon the atoms 
of visible and tangible substances by a uniform and indefi- 
nitely extended ethereal medium, itself atomically constituted, 
and pressing always and everywhere in exact proportion to 
the number of its atoms, conceived to be all of the same size, 
in a given space, or, what for brevity will be called, “ its 
atomic density.” 
These hypotheses have been adopted in conformity with a priori 
principles enunciated by Newton at the beginning of the third 
book of the Principia and in its concluding paragraph. It is not 
