[ 2 73 ] 
through L and a , L/ as the fine, and at as the 
verfe-fine of the arch L a ; and confequently <2 t 
equal to the fquare of L t divided by 2 L T. But, 
the triangle Lr/ being right-angled in t, the fquare 
ot is equal to the difference of the fquares of 
L r and r t> and confequently to the product of their 
fum and difference ; that is to fay, at = 
2 L TP 
or (becaufe the tangent T L is equal to the fquare 
of the radius C S divided by the cotangent of L S) 
= LHT 7 ? Now fup- 
2 x lquare ot Cb V 
pofe the fpaces Lr, rt to be expreffed in minutes, 
which will be mod: convenient in practice, then the 
radius of the iphere C S muff be taken equal to 
3437 t> f° r man y minutes are contained in an arch 
of a cir cle equ al to its radius : and at will be - — 
L r + rt -f- L r — rt x cotan. of L S ^ , 
~ • But > the eontan - 
gents of nmilar arches of circles of different radii 
being diredtly as the radii, therefore the cotangent 
of L S to the radius CS or 34372., is to the cotan- 
gent of the fame arch to 10000000000, which is 
the radius to which the logarithmic tables are adapt- 
ed, its logarithm being io; as 34374 to 10000000000. 
Therefore the cotangent of L S — tabular cotangent 
of L S x 34.37 i ... 
10000000W wlllch > bein S fubftituted in the value 
of at a bove, gives at> expreffed in minutes = 
Lr + rZ + Lr - r t x tabular cotangent L S . . 
T5 ; or, multi- 
oo 755 °°°oooooo 
plying by 60, the value of at will come cut in fe- 
Vol, LIV. N n conds 
