90 BULLETIN OF THE UNIVERSITY OF WISCONSIN 



value li^^ assumed in the computation of x^ and A'^o The ob- 

 servations should be so arranged as to secure at least a 

 rough approximation to this interval between the observa- 

 tion of Polaris and the clock star, but a deviation of even 

 several minutes from the prescribed amount may be very 

 simply corrected. 



Since the interval S — 6" affects TJ, m' and «' precisely as 

 does a^ — ag whose effect is represented in the term EGy 

 we apply to >S' and K the corrections 



i2 -j S - (S" + 4»0 I i2' I 5f - (S' + 4"i) 



and the reduction of the observations takes the very sim- 

 ple form: 



'' = lUo ] ^' - ^^' + '^"^^ 



S^ = S -\- R^r ■\- Bh - Ch ^T ± Cc = ^ - So 



Ko = K -^ R\r + B'b - C'h M t Cc = A'o - a' 



The level corrections Bb, B'b are most conveniently taken 

 from a table of multiples of 



-— sec Q) = Bv 5 tan qi -- Br 



where r represents the angular value of one division of 

 the level scale. The factor i?o equals 100 R and its value 

 together with that of the coUimation factors C, C are to be 

 derived from the data given with each star in the ephemeris 



^0 == P"o + Xo G ^^ pCi + Co 



R'o = P>o C' = p'Cj 



These values when once computed should be preserved for 

 future use. 



The reduction to the middle thread of transits of a clock 

 star observed over the side threads must not be made, as 

 in the meridian, by the use of the factor C, but by a special 

 factor F whose logarithm is given in the ephemeris and 

 among the general constants for each star. 



F = sec So sec n sec r 



