Relating to the FIGURE of the EARTH. n 



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

 § 6. will become, 



ma — nc -\- ^— zz /, and 

 rta — dc + ZL = l, 



1 a 



so. Here if we put d for the value of a, as given by the for- 

 mula " r~ n '; ■' ; and h for the value of c. as given by the for- 



mn — mn * o j 



mula — r— — 7U aHb v for the correction to be made on d. and u 



mn — ws' » 



for the correction to be made on h, fo that a ~ \d -f- <y, and 

 £ =: A -f- a, by fubftituting thefe values of a and c in the two 



laft equations we have mv — nu -f- g d " zz o, and 



' a -J- v 



Hence, rejecting all the terms that involve v % 9 «*, or Ui), we 

 have dmv — dnu -f- ^* -f- zghv zz o, 

 and ^''y — dn'u -f- y^ a -f- 2g'hv zz o. 



Therefore, v ±s £4 ^"XtJP? . 1 ,i , alfo 



_ /&* f<fo; + 2^ J — ^* (dm + 2ff '£J 



<&?' f <£?j + 2^J — rf« (dm ' + 2g'hj' 



And, again, by rejecting thofe terms that are fmall in compari- 

 fon of the reft, v zzz ,yf ~~* % -r» and 



' a ( act — »«r ^ ' 



d (n'm — nm' )' 



Thus <y and w are found, and of confequence d-\- v and h -\-u^ 

 that is a and c, without neglecting any terms that are not 



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



a ' 



•- is lefs than 2a r o , it will readily be allowed that it is quite un- 



neceffary to carry the approximation farther. 



B 2 ii. The 



