456 



municated to me a result at which he has lately arrived, and 

 on referring to my note book I found that Mr. Jellett's theo- 

 rem gave a physical reason for the hypothesis 1 have alluded 

 to. So far as Mr. Jellett's investigation relates to this subject, 

 it may be thus stated : 



" ' If in a system of molecules the forces developed by the 

 displacement of any two molecules be functions of their rela- 

 tive displacements only, and tend to restore them to their ori- 

 ginal positions ; the function Ffor such a system will contain 

 thirty-six coefficients, the coefficients of S (ai/Bg) being equal 

 in pairs.' 



" This theorem evidently supplies the link which was 

 wanting in my equations, which, perhaps, may not now be 

 deemed unworthy of notice, as they may be shown to rest on 

 a definite physical hypothesis. 



" The note from which the following abstract is taken is 

 dated December 26, 1848. I have slightly altered the no- 

 tation, and prefixed two theorems which facilitate the under- 

 standing of what follows. 



Theorem I. 



" Let (M], M2j &c.) be functions of {x, y, z), defined by the 

 following equations : 



«i = i3273 - jSaya V\ = 7203 - 73a3 «^i = ai^z - as/Sg 



M2 = jSsyi - jSiya v^ = 7301 - 7103 W3 = as/Bi - ai^s 



«3 = /3i73 - ^271 ^^3 = 7ia2 - 72ai Wz = a\^2 - 02^1 



(ai,a2,/3i,&c.) denoting (l,^,^,&c.) 



" If the co-ordinates be changed into x, y\ z, by changing 

 the direction, without changing the origin, then the functions 

 (mi, U2, W3, V3 + w^, wi + Ma, M2 + Vi) will reproduce them- 

 selves by means of the following equations : 



