614 PROFESSOR KELLAND ON GENERAL DIFFERENTIATION. 



1 



1 

 -^ira ['* dQd>{e) 



'Jo 



if {&) =/(^) p2, and = — ; therefore also z = — . 

 By applying the formula, this gives 



dz-^ 



p 

 But, according to the hypothesis, the attraction equals — ^ : 



^ d-^ (h (z) 

 27ra r_L£_ 



I 



dz a" 

 d_ 



dz 





or -^P^"+i = 27r0(;£) 



p 



0(^)= 9^(^ + 1)^" 

 Z TT 



or (i( — )=- — (w + 1) — 



•^^^^ 2-77 >«+2 • 



Cor. If «=0, /(p)=:--j the law of nature: hence an infinite plane attracts 



all points equally, provided they are not in its mass. 



From this corollary, it appears that, if a particle of the infinite ether which 

 pervades space (in equilibrium) be moved from its position, the only series of 

 particles by which it will be affected, is that which lies in that plane perpendicular 

 to its line of motion which passes through its position of rest. 



Let us next solve a few of the more simple inverse problems of Mechanics. 

 We desire to confine our attention to the more simple, from a wish not to intro- 

 duce any formula other than that which commences our memoir ; and likewise, 

 from a fear of otherwise distracting the attention which we desire to draw to the 

 subject of differentiation itself. 



Prob. 1. To find the curve which synchronizes all straight lines drawn 

 through the origin of motion. 



