1831 .] 
Method of finding the Meridian. 
329 
XI — Method of finding the Meridian. Bij R. S. 
The following method of finding the meridian is not, so far as I know, commonly 
to be found in books, though it be very simple, and sufficiently correct for ordinary 
purposes. 
Direct the central wire of the transit instrument to the pole star, and note the 
time and altitude. We thus have the approximate meridian without any trouble ; in 
this position ot the instrument, observe the transit of some star near the zenith : 
"<? thus have the approximate time of the stars’ transit, and if the star be within 10 u 
ol the zenith, the time so found will be within about one minute of the truth, in 
Indian latitudes ; and the error will never amount to so much, if the pole star be not 
at its greatest elongation. It diminishes also as the star is near the zenith. Hut 
for the present purpose the time so found is sufficiently accurate ; assuming then the 
time so tound to be correct, find how far the pole star was distant from the meri- 
dian at the time of observation, or its horary angle — H A ; then with the hour 
angle, and zenith and polar distances of Polaris, the deviation of the transit from 
the true meridian is thus found : sin deviation = ^ ^ ^ \ this will be gc- 
sm Z D 
nerally within two or three seconds of the truth. The right ascension of Polaris is 
within a few seconds of lh. ; and its polar distance is very nearly 1° 36’ ; these 
raa y be used in ordinary cases. If the zenith distance of the star by which the 
approximate time is found, do not exceed 5°, the error of the meridian so found 
will scarcely in this country ever exceed 5", so that this method, besides being sim- 
ple, is sufficiently correct for almost any purpose. By taking 1 0 36 as the polar 
distance, and one hour as the AR of Polaris, the result will never err beyond one 
minute. 
f'here is another very simple and strictly correct mode of finding the deviation 
r >f the transit instrument in azimuth, from the observed error in AR of the transit 
of two Stars. Let P Z p (PI. XIX. fig. 8 ) be the meridian, Z the zenith, and I) Z d 
^ ie position of the transit instrument out of the meridian. D and d the observed 
Positions of the stars, and Z D and Z d their zenith distances : DPrf the observed 
error in A R. It is required to find P Z D, the error in azimuth, or the angle 
w bi°h the instrument makes with the meridian. By the principles of spherics, we 
havp . „ . „ sin DPrf sin Prf__sin err ARjinjgj 
sin P> d: sin DPd:: sin P d : sin D = -. u ^ — s i n I) d 
alsosinP 7 • ^ sin D sin PD sin err AR sinJ ^inJV 
>nPZ: sin D sin PD : sinPZD^=- sin pz ~~ — sinPZ sin D d 
in words, add together the log. sine of error in AR, and the log. sines of the 
e $pective polar distances, and from the sum substract the log. sine of the co 
ibide and log. sine of the observed difference in the polar distances of the two 
^ le remainder is the log. sine of the error in azimuth. I he same forum a 
V ,S "°°d, Avhether the stars be on the same or opposite sides ot the /a nith. 
jn U a11 ordinary cases ft d will be obtained correctly enough, by taking the tabular 
of the observed difference in polar distance. 
an , err °r in azimuth is NE, when the observed difference in AR i> too great, 
W, when the difference is too small — both stars being abous the pole. 
