Mathematical computation for law of force 125 



or may be represented thereby, but 



be* = (d - x) 2 + x (2a + 2d - x) = d* + 2ax, 

 therefore the fluxion of the repulsion is 



*(*-*) 



n+l' 



(d* + 2ax) 2 

 the variable part of the fluent of which is 



- 2ad - d 2 d* 



zax) 





but when x is nothing, d 2 + 2ax, or be 2 = d 2 , and when x = af, or s + d, it = s 2 , 

 therefore the whole fluent generated while b moves from a to f is 



2ad + d 2 / i i \ d 3 ~ n s 3 ~" 



2a* (n - i) W"- 1 s"- 1 / 2 2 (3 - ) ' 

 but the repulsion of all the fluid collected in the center on b 



_s + d 

 a" ' 



and a = 



2 



and 2rf + d 2 = ds, 



therefore the repulsion of the surface of the globe is to that of the same quantity 

 of fluid collected in the center as 



ds s"- 1 - d"- 1 d 3 -" s 3 -" 2 (s + d) 



x - 



s n-l_<fn-l d 3 -"-S 3 -" (S + d) 2"-l 



(n - i) (ds)"~ 2 + 3 - n ' (s- d) n ~* 



n i (ds) n ~ l 3~ n a n ~ 2 ' 



W- 



or dividing by s 3 - 11 , as 



n - 1 S-M ' ^ P' 2 -P) 



supposing - to be called p. 



