Theory of Molecular Action according to Newton's Law. 207 



of saying a few words relative to the argument actually insisted 

 on by Mr. Earnshaw, we propose to examine briefly the con- 

 trary case. 



Let us suppose the medium unsymmetrical ; and let us 

 further conceive (which by no means necessarily follows) that 



cPV d?V d?V 



-T75J -r-n and -=T5 are not zero. Then, as Mr. Earnshaw 



df z dg* dh l 



has proved (Art. 12), there is at least one direction in which, 

 if a particle be moved, the immediate tendency is to cause it 

 to recede further from its position of rest. The consequence 

 will be, either that the other particles by their motion tend to 

 stop it, or that its motion continues. We have no hesitation 

 in affirming that the former is the case. If all the particles 

 commence to move in the same direction, the principle of the 

 conservation of the motion of the centre of gravity will be vio- 

 lated. If, on the contrary, some move in one direction, some 

 in the opposite, there must be vibration unless it can be shown 

 that the particles pass each other. In the latter case there 

 would be perpetual interchange of place amongst the particles. 

 This is certainly very unlikely : but even now admitting the 

 worst we can conceive, the possibility of such a system is not 

 disproved. As it stands at present, I am disposed to think 

 that the objections, based on a want of stability, have rather 

 strengthened than undermined the hypothesis of the inverse 

 square of the distance. The fact, that in a medium of sym- 

 metry the equilibrium is neuter, is a very strong one in favour 

 of the theory. But for this it might have required some violent 

 effort to move a particle at all : as it is, a very slight force will 

 cause motion, so that the medium possesses the character of 

 molecular non-resistance. We do not doubt, however, that 

 there are some difficulties attending this as well as every other 

 theory. To any which may be brought forward I will do 

 my best to reply. I trust that a desire for truth, rather than 

 a love of controversy, will appear in all that shall be said on 

 either side. 



Since the above remarks were written Mr. Earnshaw has 

 resumed his objections, in a paper which appears in the Phi- 

 losophical Magazine for July. Although all the arguments 

 which appear in that paper have not reference, either to the 

 want of fulfilment of the requisites for vibration, or to the 

 instability of the medium, yet to avoid confusion I propose to 

 reply to them in this place. The consideration of the other 

 two objections placed at the head of this paper will probably 

 demand a more detailed mathematical investigation than could 



