286 ATTRACTION. SPIN! 



Tin- attraction on an int ; :iclc 



= 27rpr8r , [- 2 + 2^4r} = 0, (Art. 213). 



Let </> (r) = r ; 



therefore & (r) = r c + ^1, ^ (r) = Jr 4 + %Ar* + #. 

 The attraction on an external particle 



- rf - f (C + *)'-(<'-) + ^ (c + r)' - 4 A (c - r)'l 

 dc \ 8c j 



^ (c'r + t- 3 + 2Ar] 



= 47rpr*c3r = mass x c. 



The attraction therefore is the same as if the shell were 

 llrcted at its centre. This property we discovered for the 

 la\v of the inverse square. AVc shall now ascertain wl; 

 are any other laws which give the same property. 



224. To find what laws of attraction allow us to suppose 

 a spherical shell condensed into its centre when attracting an 

 external particle. 



Let <f> (r) be the law of force; then, if c be the distance of 

 the centre of the shell from the attracted particle, r the ra- 

 dius of the shell, and >/r (r) = /{r/< (r) dr} dr, the attraction of 

 icll 



But if the shell be condensed into its centre, the attraction 

 = 4 7rpr*Sr<f> (c) ; 



tll , rcfore 



