the Differences of Latitude. 355 



to deduce the results by means of the watch ; which I effect 

 in the following manner. 



I place a transit instrument (whose axis is horizontal, and 

 whose line of coll imation is correctly adjusted) so that the mid- 

 dle wire should describe a vertical circle. Its axis should lie 

 nearly in the meridian, so that the vertical circle should stand 

 nearly east and west, and thus twice traverse the parallels of all 

 the stars which culminate between the equator and zenith. 



The observation of the two times T and T' in which the 

 star passes the wire of the telescope will give the altitude of 

 the pole as well as the zenith distance of the star on the 

 meridian; and by repeating this observation in another place 

 we shall obtain the difference in the altitude of the pole, or 

 zenith distance, almost independently of the assumed declina- 

 tion of the star. However, the times T and T' must be taken 

 from a watch or clock which shows sidereal time : but it is 

 not necessary that the correction of the clock, for the purpose 

 of reducing it to the sidereal time, need be known. 



In order to show the peculiarity of this method in a general 

 view, I shall not take into account, at first, that the vertical 

 circle described by the instrument is directed exactly east 

 and west, but point out the results of) and the errors which 

 might arise from, some elements of calculation, independently 

 of that supposition. 



I denote the correction of the clock by t and t', taking them 

 (as well as the observed times) in degrees, minutes and seconds ; 

 the right ascension and declination of the star by « and 8 ; and 

 the polar height by </5. According to these designations the 

 two hour angles of the star (negative if easterly) will be 



t = T + T - a. . r=T' + T'-« 



and the cotangent of the azimuth will be 



cos t. COS S . sin ^ — sin S . cos ip cos t'. cos J . sin p — sin S . cos ^ 



cos S . sin t cos S . sin l' 



If we eliminate the azimuth from these two equations, we 

 obtain cos(ili--') 



tan <p = tan 8 x 



or, by introducing the values of t and t', 



/ T + c> + T+ t _ \ 



tan (p = lan 8 x 



(- 



T ^i' ^T-t 



1 y 



If we now assume that 8, a, t', t are incorrectly known, and 

 require the corrections r/8, r/«, di\ dr, we obtain thereby the 

 correction of ^ deduced from the formuhi just given, as under: 



Yy2 d<f 



