ATTRACTION. SPHEK: KLL. l!-7 



Expand ^r (e + r) and ^r (c - r) in power- .en uiing 



(c) for j! i &c., we hire 



{q *"<' 



whatever r may be ; therefore 

 -0, 



But t'W 



therefore * N (')-/+(<0<fc + *(c); 



fore t fw W -#()+ *'W- 



fore, by the first of the above equations of condition 

 for*(e), 



3^1 for this constant ; multiply both sidea of the equa- 



niul into-ratr ; thufl 



n 



^(c)^c-f 



This value satisfies all the other equations of condition for 

 4r (c) ; therefore the required laws of attraction arc those of 

 the direct distance, the inverse square, and a law compounded 



frfirifar ukat lawi AeiktU attract* an internal 

 particU equally in every direction* 



