Bond, Graham, and Peirce, on the Latitude of Cambridge. 191 
This equation, divided by the value of cos. h, becomes 
DL 2DL 
= = or ? 
sin. L.cos. LZ sin.2L 
tan.h. Dh — 
and will also answer well enough, for a star so high as @ Lyre, 
in computing the change of h, corresponding to a change — D L of 
the declination. 
When the value of A is found, that of L is readily determined 
by the formula 
sin. (LZ — D) — tan” shsin. (L-4- D), 
which it will be convenient to compute for a mean value of h, and 
determine the corrections of Z for another value of h, by the pre- 
ceding formule between DZ and Df, in which sin. 2 LZ and tan. h 
may be regarded as constant. 
This method of reduction, although exceedingly expeditious, 
cannot be applied to those stars which pass very near the zenith, 
because the observation of the time of transit of such a star over 
one of the wires is much more uncertain when the wire is south 
of the axis of collimation, than when it is north; that is, the value 
of h, is less accurate than that of h,. The values of h, therefore, 
and those of LZ, computed from h,, will be less accurate than those 
computed from h,, although the contrary should be the case; for it is 
obvious that the southern observations ought to have rather the ad- 
vantage over the northern ones in the determination of the latitude. 
The observer will find, in fact, that if he undertake to reduce, by this 
method, his observations of a star which passes so near the zenith 
as not to make a transit over his most southern wires, which is the 
case with « Urs Majoris and 8 Canum Venaticorum in this series, 
he will obtain most unsatisfactory results. 
The value of L is, finally, the latitude of the place of observation, 
if the telescope is exactly in the prime vertical. But if the plane 
