3i8 On the FIGURE of the EARTH. 



4- "'-''' ^^ . x'sS'--^ — iSc* d'' + ^c^ d* — sci'^ and when ■n = ^ die 

 feries becomes 



,5 ^ 3-2^5 ^ 5.8 Z-s ^ ^ 7-i6i' 



+ ^Tlft^^35^^-'5^^^^+9^^^*-5<^° but . = ^ + ^^-^;- 



XIT^M- 15 a^d' + ga'd* + 5 d'. 



From a comparlfon of thefe two equations, it will be 

 feen that the law of continuation is the fame in both, 

 excepting that in the value of v, the figns of the odd 

 powers of J' are negative, whereas in the value of z all 

 the figns are affirmative. The powers and coefficients of 

 ^, c, and d, in the correfponding terms are the fame ; 

 and to whatever number of terms the feries may be car- 

 ried, it is evident that this will ftill be the cafe. Hence 

 if a be greater than c every term, except the fecond, of 

 the equation of the value of z, will be greater than the 

 correfponding term of the equation of the value of v ; 

 confequently the fum of the feries rr z will be greater 

 than the fum of the feries =z v : that is, if a be greater 

 than c, z will be greater than v. Converfely if z be 

 «Treater than v, a will be greater than c. If a — c, d'' 

 will vanilh and the two feries will be equal to each other. 

 If <: be greater than «, d^ will be negative, and the odd 

 powers of d^ in the feries zi z, will in this cafe be nega- 

 tive, but in the feries ■=. v the odd powers of i' will be- 

 come affirmative, and v will be greater than z; con- 

 verfely if V be greater than .s, c will be greater than a. 



Hence, 



