The Rev. J. H. Jellett on the Equilibrium and Motion of an Elastic Solid. 215 



Hence, in general, 



S,m = e,«. 



Now wo have seen that the error involved in the supposition from which 

 this equation is derived, is for each element represented by an expression of 

 the form 



The order of the total error will be found by multiplying this expression by 

 the number of the elements. Now 



Number of elements = ^"^'^^ "^^^^ = l!^ ,-■• 



V k" 



Hence the order of the total error will be 



i-i". 

 The equation 



2im = f|U 

 will, therefore, be free from sensible error if 



i > i". 



(3.) Lastly, it is easily shown, by reasoning similar to that of (1) and (2), 

 that the error in the equation 



Swez; = \\\uedv, 



is at most of the order i". The method here employed will, therefore, be free 

 from sensible error if the three following equations hold: 



*" - ^■' > 0, i- i" > 0, i" > 0. 

 Hence we infer that 



The methods of the integral calculus are applicable to questions of molecular 

 mechanics, provided that the molecular force varies continuously within its sphere of 

 action; and provided also that the sphere of molecular action is of such a magni- 

 tude as to admit of being subdivided into an indefinite Jiumber of elements, each 

 element containing an indefinite number of molecules. 



ill 



