exactly in the Meridian. — 283 
must make (R"—R) = dR and (T"—Ts) =dT; and the 
formula for finding A will, agreeably to the principles laid down 
by MM. Delambre and Biot, be 
rf = ; cos N. cos S 
: A= (7 —d®) * sin (N+5S) cos L * 
If the quantity (dT —d®) be positive, the deviation of the tran- 
sit instrument will be to the east of the meridian: on the con- 
trary, if it be negative, the deviation will be to the west. When 
it is = 0, the instrument is exactly in the plane of the meridian, 
and consequently does not require any correction. 
By the help of a table expressing, for any given latitude, the 
cos N. cos § 
sin (N+S) cos L 
declinations (or the difference of the polar distances) of the two 
stars observed, we may, almost by inspection, obtain, in every 
case, the value of A, or the deviation of the transit instrument 
required; and consequently bring it afterwards exactly in the me- 
ridian, so as to be enabled to adjust it at any time to a meridian 
mark. The table, which I have here given, is calculated for the 
latitude of Greenwich (= 51°. 28’. 40”): but since it is not 
necessary to be very exact in the declination of the star, it 
will suit any other place not very distant from that parallel of 
latitude. I might have constructed the table so as to have 
been general, for all latitudes, by merely taking the value of 
cos N. cos § 
sin (N-+S) 
cosine of the latitude of the place where the observer might be 
situated. But, I have preferred, in the present instance, con- 
fining the table to. the latitude of Greenwich; subjoining, how- 
ever, a correction for the use of it in any other part of England. 
The first perpendicular column of the table denotes the sum 
of the declinations (or the difference of the polar distances) * 
of the two stars, for every degree from 42° to 72°: and op- 
posite thereto is set down, in separate columns, the value 
for finding the deviation of the instrument in azimuth, ac~ 
cording to the value of N, or the northern star, from 24° to 
40°; those limits being sufficient for the purposes alluded to in 
the preceding part of this paper. The proportional part for any 
intermediate difference may be readily seen, on inspection. These 
values, multiplied by (dT — dR) or the difference between the ° 
difference of the apparent right ascensions of the two stars, and 
the difference of their observed transits, will show the value of 
A, or the total deviation of the instrument in ¢ime; which, mul- 
tiplied by 15, will give the deviation in arc: and when the de- 
viation of the instrument has been thus determined, it may be 
eorrected in the usual manner. An example or two will best 
Nn2 explain 
in numbers, according to the sum of the 
value of 
3 which value must then have been divided by the 
