Relating to the F IGU RE of the EAR^T H. \i 



fame, computed for any other arch, be = /, the equations of 

 § 6. will become, 



ma — «f + ^ = /, and 



m'a — n'c + ^ - I'. 



a 



10. Here if we put d for the value of «, as given by the for- 

 mula ■ "!~"^.' : arid h for the value of c, as given by the for- 



mn — mn ' , 



jxiula "*', ~'" — , alfo V for the corredion to be made on d, and u 



for the corredlion to be made on b, fo that a z^ d -{- v, and 

 ^ = /& + a, by fubftituting thefe values of a and c in the two 



laft equations we have mv — n« + ^ ^ + 1 = o> and 



Hence, rejedling all the terms that involve •«% //•, or uv, we 

 have dmv — dnu + <f A* + 2ghv = o, 

 and ^zs'i* — dn'u + ^A* + 2g'hv = o. 



Therefore, . = ^^^_i"f;7,7jf..^.J .^ ^ -'^ 



g'P (dm + igh) — gh^ (dni + 'J-f^'h) 



'' rfo' (dm + 2^AJ — (/n (dm ' + 2^'AJ ' 



And, again, by rejedling thofe terms that are fmall in compari^ 

 fon of the reft, v = ^"^/-Jflj , and 



„ _ A' (gm—gm') 

 "— d(n'm — nm'/ 



Thus v and u are found, and of confequence d+v and b-\-u, 

 that is rt and/-, without neglediing any terms that are not 



of an order lefs than ^ ; and when it is confidered that 

 - js lefs than-^— , it will readily be allowed that it is quite un- 



a 22300 ' 



neceflary to carry the approximation farther. 



Be II. The 



