The Rev. J. H. Jellett on the Equilibrium and Motion of an Elastic Solid. 201 



If these conditions be introduced into the general equations (N), it is easily seen 

 that the number of distinct constants will be reduced to thirty, sc, 



A^., A^., yl,3, 4^.„ ^1,,^, A.,,^, .4,,,, A^.^, A^,^, A^^, 

 -B^3, &c. 

 C„3, &c. 



The equations so reduced will refer to a system of attracting or repelling 

 molecules, in the more enlarged sense of the term attraction or repulsion, the 

 force being defined solely by its direction, without any hypothesis as to its in- 

 tensity. Using the words in this sense, we may state the conclusion at which 

 we have arrived as follows : 



The equations of equilibrium or motion in a system of attracting or repelling 

 molecules, will in general contain thirty distinct constants. 



13. We shall next proceed to consider what further simplification is intro- 

 duced into these equations by the supposition that the sum of the internal 

 moments may be represented by the variation of a single function. Making 



a'^a, ^'=ji, y'=y, 



in the equations of condition (R), we shall find that their number will be re- 

 duced to fifteen, the nine equations 



A.,'ff. ~ i>,!.„., C^,,. = ^ftr" -^ai7' = C*,,^/, 



being obviously equivalent to but six. Hence we infer that 



The equations of equilibrium or motion of a body in which the molecular force 



acts in the line joining the molecules, and is represented hy a function of the distance, 



will contain fifteen distinct constants. 



This agrees with the result obtained by Mr. Haughton, to whose Memoir 



the reader is referred for the further discussion of this case.* 



• Vid. note at the conclusion of this Memoir. 



