108 Mr EARNSHAW, ON THE NATURE 



We shall arrive at the same result if we consider an un crystallized 

 medium to be such that the force of restitution acts always in the 

 line of displacement; for in this case the parametric surface, the ge- 

 neral equation of which is 



2(» - 1) (C- C) = d}V.m? + d^V.f + d\V .*" (Art. 3). 



must be spherical ; which requires that 



d}V = d>V=dtV. 



18. It can be easily shewn that n must be greater than unity. 



For the number of particles at the distance r from the attracted 

 particle is proportional to r 2 , and therefore 



n - 2 m r 2 



2 oc 2 , 



- 1 



oc 2 



r n-\ ' 



hence, unless n be greater than unity, the effect of the more distant 

 parts of the medium upon the value of — - — 2— ^ will be greater 

 than the effect of the adjacent particles. Now the time of vibration 

 of a particle depends on the value of dj V, or — - — . 2 ——^ ; and there- 

 fore unless n be greater than unity, the parts of the medium which 

 are more remote will exert a greater influence upon the time of vi- 

 bration than those exert which are near. Now, Optical phenomena 

 seem to indicate that the adjacent particles exercise most influence ; 

 and therefore n must be greater than 1. 



19- It is probably not conformable to the simplicity of Nature, 

 that n should be fractional ; we have shewn that it must be greater 

 than 1 and cannot be equal to 2, consequently n is greater than 2. 



This result is important, as we are enabled to infer from it imme- 

 diately, by the aid of (16), that 



