“ 
GP ap, 
g30 . AN ACCOUNT OF THE . 
Pour L = the latitude of B, andi. that of A, L being = Litid Doss 
- Let » be the distance from the meridian in feet, and 5 the value of it in 
deg grees, and = ‘A B Pihe difference of longitude, and a b = - 90 
—dz We have, (Bownveastu’ s Trigonometry, p: 0% Jee 
} 
Tang. +d See 22 hea Zs! +L). EC) 
Bur the arc of 1 is the same as the tangent to 8 places of firures, and 
dE can never exceed i, we may therefore As tangent 4 d EL substitute 
its equivalent ies a ~, multiplying by 2 R we get, 
dL=2R “tang. 3 3, tang. 2 £ a ft ep alg (2) 
Now tang. 2 (L + iL) — tang. Loe d L, and tang. L+ ae 
(Bonnycastie’s Trigonometry, p. 409). tang. By apg Selkiaits on 
Cos L, Cos: Cos (L440) aL), | 
account of the extr eme smallness of value of the second member, it is equi- 
Sine 3d L 
valent to —3- 
Tus expression 2 becomes then, ir 
uray *L 5 @R, tang, 12 13, site} d Te 
d-L=2 R, iang. , tang. L + Bees ase Ra a (3) 
. Surstirutine for sine $.d.Lit’s approximate value. 
Tang. *55 ee a beeginks : Ae ke ON 
Tus second member is ‘evidently equal io the Ist multiplication by 
Se The formula may therefore be written, putting — f- 
A = first-term; d L = Q RF, Be 21 3, tang. + A pa dee 
