90 BULLETIN OP THE UNIVERSITY OF WISCONSIN 



value 4 m assumed in the computation of X Q and N Q 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 



f 



several minutes from the prescribed amount may be very 

 simply corrected. 



Since the interval S S' affects U, m' and a' precisely as 

 does ^ a 2 whose effect is represented in the term EG, 

 we apply to S and K the corrections 



R J S - (S' + 4) ^' j S - (S' -f 4m) 



and the reduction of the observations takes the very sim- 

 ple form : 



r 



8 = S + R r + 6 - CH AT Cc = 6 - S 



K = K -f- R' Q r + B'b - C'x M T C'c = # - a' 



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

 from a table of multiples of 



- sec <p = Br - tan CD -- B'r 



do 2 



where r represents the angular value of one division of 

 the level scale. The factor E Q equals 100 R and its value 

 together with that of the collimation factors (7, C' are to be 

 derived from the data given with each star in the ephemeris 



I?' l^\' I I /"V /v-k'/^V 



JK Q P // Q U = P O I 



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 (7, but by a special 

 factor F whose logarithm is given in the ephemeris and 

 among the general constants for each star. 

 F = sec d sec n sec r 



