of Attractive and Repulsive Forces. 173 



by two regulative principles : — (1) they must be perfectly intel- 

 ligible from sensation and experience ; (2) they are required 

 to be appropriate foundations of mathematical reasoning. The 

 aether, being assumed to be susceptible of variation of density, 

 must be conceived to be atomicaily constituted, because we 

 have no experience of variation of density and pressure which 

 is not the result of atomic constitution. But for the purposes 

 of physical research, it suffices to regard the aether as a con- 

 tinuous substance, and to apply calculation to it as such, just 

 as the air is treated mathematically in Hydrodynamics, although 

 it is known to be composed of discrete atoms. After adopting 

 these views, the atoms of the aether do not individually come 

 under consideration. 



3. In this philosophy the only admissible form of force is 

 •pressure, because we have distinct perception of such force, 

 and such only, by personal act and sensation, as when the 

 hand is pressed against any substance. 



4. According to the foregoing principles of theoretical 

 physics it is not allowable to make any assumption respecting 

 the laws of action of the physical forces, inasmuch as these 

 laws have to be deduced by strict mathematical reasoning 

 from the above stated hypotheses. This I consider to be the 

 legitimate application of the rules and principles of philosophy 

 suggested by Newton at the beginning and the end of the 

 third book of the l Principia.' To deduce exclusively from these 

 hypotheses the modes of operation of the various physical 

 forces, and to compare the theoretical results with facts of 

 observation and experiment, might well seem to be an arduous 

 task. Since, however, the Newtonian principles of philosophy 

 can only by such means be tested or established, an upholder 

 of those views could not do otherwise than enter upon this 

 undertaking. Accordingly I have devoted much time and 

 research to problems the solutions of which are demanded by 

 this course of philosophy ; and, in particular, I have endea- 

 voured to infer the laws of attractive and repulsive forces from 

 modes of pressure of the aetherial medium. The furthest ad- 

 vance I have made towards the solution of this essentially 

 important but difficult problem is given in arts. 30-39 

 of a communication contained in the Number of the Philoso- 

 phical Magazine for September 1872. The object of the 

 present communication is to correct in certain respects that 

 investigation and to carry it a step further; and with this 

 object in view I shall begin with reproducing here so much 

 of the antecedent argument as may be required for making 

 intelligible the proposed extension of it. 



5. In the Philosophical Magazine for August 1862, but 



