1 98 The Rev. J. H. Jellett on the Equilibrium and Motion of an Elastic Solid. 



\dy dz dz dy 



Similar conclusions will be obtained for all terms of this form. These terms 

 are distinguished by the technical rule, that, in the products which they seve- 

 rally contain, the same letter does not occur twice. Thus the conclusion at 

 which we have arrived does not apply to terms of the form 



dx dy ' 

 where the same letter ^ occurs twice ; nor to terms of the form 



dx dx' 



in which the letter x occurs twice. The preceding discussion gives us, there- 

 fore, the following general theorem : 



If the constitution of a body, whose particles act independently, and whose ori- 

 qinal position is one of free equilibrium, be such, that the sum of the internal ino- 

 ments may be represented by the variation of a single function, this function must 

 be of the form 



\ dd'-J \ dx dyj \ dx dx 



Each of the sums denoted by 2 will contain nine terms, thus giving thirty-six 

 for the total number of distinct constants in V. 



11. Previously to proceeding further, it may be well to compare this result 

 with the investigations of Professor Mac Cullagh and Mr. Gkeen, in the un- 

 dulatory theory of light. Both these writers assume the original state of the 

 supposed luminous ether to be one of free equiUbrium.* Both suppose also, 

 that the sum of the internal moments may be represented by the variation of a 



• Mr. Green has also investigated the problem under the supposition that the original posi- 

 tion is not one of free equilibrium. The remarks in the text are, of course, only meant to apply 

 to the first supposition. 



