JYO INVESTIGATION OF CERTAIN THEOREMS. 



To determine 26. Hence, alfo, the comparifon of the degree of the mcri- 



the figure of the (Jlan, and of the perpendicular to it, in the fouth of England, is 

 fares of the per- better than if a degree of the perpendicular meafured in that 

 pendicular in latitude were compared with a degree at tiie equator. For if, 

 tif«r'^''^" "' ^^'^ equation cof ^'^ rz (cof (?') X x/ 3, we make (p' ZZ 

 50^ 4-Vi (or any thing lefs than 54® 4V,) <p'^ will come out 

 impoflible. 



27. It may be (liewn, too, nearly in the fame manner, that 

 if a degree of the perpendicular to the meridian were meafured 

 in Siberia, as far north as the latitude of 7<.®, fuppofing that to 

 be podible, and compared vvith a degree in latitude 45°, or even 

 conliderably farther fouth, it would not give a refult fo exa6l as 

 , the degree of the meridian and perpendicular meafured in the 

 fouth of England. This fliews, that the method of afcertaining 

 ' the figure of the earth, propofed by the authors of the Trigono- 

 metrical Survey, (Phil. Tranf, ibid. p. 529) as a fubjed of 

 future inquiry, is lefs exad than that which is founded on their 

 own obfervations. 

 Whether the 28. We may alfo afcertain, by the fame means, the relative 



corf:parifon of a accuracy of the method of finding the figure of the earth, from 

 roe^/id! and perp. ^he comparifon of a degree of the meridian with a degree of 

 in famelat. be the perpendicular in the fame latitude, and of the method of 

 than t^hatTf^ refolving the fame problem by the comparifon of two degrees 

 jnerid. degs. in of (he meridian in different latitudes. 



different lats. j^- ^j^^j,^ D be a degree of the meridian, and D' of the per- 

 pendicular, in latitude ^, and if A be a degree of the meridian 

 in a ditfercnt latitude <?', it is required to find whether the moft 



accurate value of - will be found, by comparing D and-D', or 



D and A. 



Since we hav^, by what has been already flated, J 4. 



mX) = a — 2c -f- 3c fin *??, and 



mA =.a — '2c -\- oc fin *?', we have alfo 



D 3c 



— = 1 -{ (fin *?> — fin *$') and thcreforci 



A a 



r D ~ A 



a 3a (fin ^?>- fin^^')* 

 Now, it has been already fiiewn, that, by comparing D and 



D' we have — = — r-r — ttt-* Suppofing, therefore, equal er- 

 a 2D' col *(f> « « o 1 



rors to be committed in the determination of D — Aj and of 



