188 Bond, Graham, and Peirce, on the Latitude of Cambridge. 
tan. L, = tan. D sec. h,, 
tan. L, = tan. D sec. h,; 
or, when the star passes near the zenith, as it always should do in 
these observations, these equations give 
tan. D 
cos, h, = 
tan. L,’ 
1 — cos. h, __ tan. fT, — tan. D 
1+ cos.h, tan. L,-+ tan. D’ 
sin. (L,, — D) 
tani h,= sin. (L, + Dy’ 
sin. (L, — D) = tan.? $h,. sin. (L, + D), 
and, in the same way, 
sin. (LZ, — D) = tan.? $h,. sin. (L,-+ D); 
and these two formulas are, in this case, to be preferred in com- 
puting the values of Z, and LZ, When the star passes very near 
the zenith, they are reduced to 
L, — D = +hi sin. 1” sin. (L,+ D) 
L, — D= th? sin. 1” sin. (ZL, + D). 
In order to determine the declination of the point Z, which will 
be denoted by J, let 
oi = the distance of the wire from the axis of collimation ; produce ZP to 
the horizon at H, so that ZH may be a quadrant. The right triangles H.2S 
and P.1S give, by Bowditch’s rules for the solution of oblique spherical 
triangles, cos. HA cos. HS 
cos. 4P~ cos. PS’ 
cos. (90° — di) __ cos. (90° — L, + L) 
or 
cos. (90°— D)~ ~— cos. (90° — L,) ” 
sin. dt sin. (Z,— L) 
2 Sine) sin. L,, : 
In the same way, the right triangles HBS’ and P BS’ give 
sin. d¢__ sin. (Z—L,) , 
sin. D™ einem 
sin. (Z,—L) _ sin. (L— L,) 
hence sin. L, = sin. L, 
> 
