RELATING TO THE FIGURE OF THE EARTH, 'JQS 



Hence, rejecling all the terms that involve v*, w*, or uv, we Farther approxi- 



have dmv - dnu + W/* + 2ehv = 0, "P""'" ^\ ^^ ^ 



, , , ' * , ' * then employed, 



and dmv — dn u '^gh -\- 2g'hv ZI 0. 



^. r. (ns!~ n*g) h^ ^ 



I herelore, v rr ~r~, ■ s u i ^ — 7 , ^1 * ^^^^ 



* (wm — iim ) d -\- (gn''- g n) '2n* 



— g'^^* (dm -h '2gh) - gh^ (dm' -f 2g^A; 



'^"TTi. *] , dn' (dm + '2gh) — dn (dm' + 2g'h) 



And again> by rejeding thofe terms that are fmall in corapari- 



on of the reil, v =z --— — ^, and 



d(nm~-nm ) 



^ W^ (g'm — gm) 



d(n'm — nm'y 



Thus 27 and m are found, and of confequence d-^-v and h-^-u, 



that is a and c, without negleding any terms that aie not 



of an order lefs than ; and when it is conlidered that 



a 



£l 

 a 



— is lefs than , it will readily be allowed that it is quite 



a 22500 ^ ^ 



unneceflary to carry the approximation farther. 4 



Jl.The fame thing that renders the comparifon of large The errors of 



arches of the meridian ufeful for leflening the effeft of errors obferyation ire 

 • ^ r ■ ,....,. ^. r •, 1 .lefs the larger 



arifing from irregularities m the direction of gravity, makes it t^g grcg, 



ferve to diminifti the effe6l of all the errors of the aftronomical 

 obfervalions at the extremities of the arches, from whatever 

 caufe they arife. They are all difFufed over a greater interval/ 

 and have an effefl proportionally lefs in diminifhing the accu- 

 racy of the laft conclufion. 



12. The meafurement therefore of large arches of the meri- Extenfive fur- 

 dian, efpecially if performed in diftant countries, is likely to ^^ys particularly 

 furnilh the bell data for afcertaining the true figure of the 

 earth ; and on this account extenfive and accurate furveys, 

 fuch as that above mentioned, are no lefs interefting to fcience, 

 in general, than conducive to national utility. The furvey of 

 this ifland, when completed, will furniQi an arch of the meri- 

 dian, beginning at the fame parallel where that meafured in 

 France terminates, and nearly of the fame extent, fo that the 

 length of an arch of more than 16**, or almoft a twentieth of 

 the earth's circumference, will become known. Theditferent 

 portions of this arch compared with one another, or with the 

 V - arch 



