224 Of the SOLIDS 



fan ** 



and 



tan? 3 ' tang* „ tan? 3 tan? ? , 



-f , &c. tan p— ? = L-f, & c . 



3 5 3 5 



__ 4?r« / tan 9 3 tan?? tanp 7 \ i 



~* 7~ y tan? 3 " 



cof? 



\ 3 5 



iIi^^+^\ When ? = o, F = ±l» 5 

 cof ^t V3 5 7 J 3 



and fince « ~ m . i/J-, F = ^ !/ J- = m i/HZU = 



v 4^ 3^4* y 27.4t 



^ ^ — fl, which is the attraction at the furface of a fphere of 



the folidity m*, as was already fhewn. This laft is the con- 

 clulion we had to expect, the fpheroid, when it ceafes to have 

 any oblatenefs, becoming of neceffity a fphere. 



It is evident alfo, that the variations of <p will but little af- 

 fect the magnitude of F, while <p and tan <p are fmall, as the 

 leaft power of tan <p that enters into the value of F is the 

 fquare. 



For, inftead of cof . <p i , we may, when $ is very fmall, write 



i 4- - tan 6~ ; fo that F = 4 «■ « . (i -j — tan q? ) ( I — 

 3 \ 3 s \3 



+ 



tan <p* 

 \ 3 s \3 



tan <p* 



7 



-, &c. J. 



If the oblatenefs of a fpheroid diminifh, while its quantity 

 of matter remains the fame, its attraction will increafe till the 

 oblatenefs vanifh, and the fpheroid become a fphere, when 

 the attraction at its poles, as we have feen, becomes a maxi- 

 mum. If the polar axis continue to increafe, the fphe- 

 roid 



