Bond, Graham, and Peirce, on the Latitude of Cambridge. 189 
sin. (Z, — L) sin. D, . 
and (hi) an D, 
sin. (Z, — L) —sin. (L—L,) © sin. L, — sin. L, 
sin. (LZ, — L) + sin. (LZ — Z,) ~ sin. L, + sin. L, 
tan. [3 (Z, + L,) —L] _ tan. 4 (L, — L,) 
tan.3(L,—L,) ~ tan. 4 (L,+ L,)’ 
and tan. [3 (L, + L,) — LZ] = tan? 3 (L,— L,) cot. 3 (Z, + L,). 
But L,, differs very little from Z,; and ZL is so near a mean be- 
tween L,, and L,, that it may be substituted for this mean, in the 
whence 
or 
second member of this equation; whence 
3 (L, + L,) —L = 3 (L,—L,)? sin. 1” cot. L, 
or L=3(L,+4 £,) —34(L,—L,) sin. 1” cot. L. 
The term + (Z,,— L,) sin. 1” cot. LZ, which may be denoted by 
dL, is then a small correction to be subtracted from the mean of 
the declinations of S and S’, in order to obtain that of Z. It 
needs to be computed but once for each wire and star; for no 
changes in the place of the star and no errors of observation can 
perceptibly affect its value. The same remark is applicable with 
regard to the values of L,—Z and L—L,, that they need to 
be determined only once, and their values are given by the formule, 
Big ei (Tey tlh A ae, 
L—UL,=3(L,—L,)—61L; 
and they have been determined for each of the stars, except « 
Lyre, by the mean of all the observations in which both the east 
and west transits of the star have been observed. The determination 
of these values is given in Table VI. The letters n and s, which 
are annexed in this table to LZ, denote the direction of the illu- 
minated axis of the telescope, and their use differs, therefore, slight- 
ly from that of this explanation. 
A different method of computation, and one which is more rapid 
in practice, has been applied to the reduction of the observations 
of « Lyre. 
