264 



Archdeacon Pratt on the effect of 



8. I will now apply the formulae just obtained to determine the Mean 

 Figure of the Earth from the *data afforded by the eight arcs. For conve- 

 nience I shall use the well-known symbol (2-6961987) to mean the number 

 of which 2*6961987 is the logarithm ; and so of other numbers. By sub- 

 stitution from the Table, the formulae give 



(2-6961 987) + (2-7323262)U-(2-0404588)V+ (1 -4873505)^, 

 -f(l-7363431)^,-(0-1996455)#3 4-(T7556462)^,-}-(r-8579353)^5 

 + (0-0501090)^6 + (l-8610562)^, + (r7413092)f3=0,; 



(3-24694l7) + (3-0309997)U-(2-5186555)V-|-(2-6515733)#, 

 -f-(2-2115282)#2+(l-7938874)^3 + (l-0599608)#,-f(l-5898592)^s 

 H-(0-6093596)#e + (l-4249273)^, + (l-4176941)^3=0. 



Multiplying by the coefficients of V crosswise, and subtracting so as to 

 eliminate V, we have 



(5-2148542)-f(5-2509817)U + (4-0060060)#, + (4-2549986)^3 

 -(2-7183010)^3 

 -(5-2874005)- (5-0714585)U-(4-6920321)^i-(4-2519870)^a 

 -(3-834362)^3 



+ (2-2743017)^, + (2-2765908)^5 + (2-5687645)j?e-f(2-3797il7)^, 

 -i- (2-2599647)^8 



*-(3-1004196)^,— (3-6303180)^5— (2-6498184)^g—(3-4653861)^, 

 -(3-4581529)^8=0. 



Putting numbers in the place of logarithms, 



164004-M78230U-1- 10139^1+ 17989^2- 523^3 

 — 1 9382 1 — 11 7885U— 49208^, — 1 7864^, - 6829^3 

 29817-f 60345U- 39069^^+ 125^^-7352^3 



4-188^,-1- 238^5 -f 370^6+ 240f,+ 182^8 

 -1260^,— 4269^5— 446^e— 2920^^,-2872^3 

 - 1072^,-403 Ug- 76?^,-2680?f,-2690^3=0. 



Putting logarithms in the place of numbers, 



- (4-4744639) -f- (4-7806413)U- (4-59 18323)#,-f (2-0969 100) 



-(3-8664055)^3-(3-0301948)if,-(3-6054128)^5-(l-8808136)^6 

 — '(3-4281348)#,-(3-4297523)^g=0. 

 Transposing and dividing by the coefficient of tJ, 



U=(r-6938226)-l-(r-8lll910)^,-(3-3162687)^2+("l-0857642)^3 



■f(2-2495535)#,+(2-8247715)^5 -f (3-1001 723)^, + (2-6474933)^, 

 + (2-6491 110)^. 



