30 CARPMAEL AND McLKOD ON TIIR 



the two positions of the instrument on each night, bnt those values "u-ere assumed to be 

 constant in each position. 



Let qj = Lalituilo of the place of observation. 

 Ô = declination of an observed star. 

 « = I'ight ascension correotcd for dimnal abcrralion. 

 A = sin (<p — (J) sec 6. 

 B = cos {qj — 6) sec ô. 

 C! ^ sec 6. 



a = approximate azimnlli before reversal. 

 a'= " " after " 



h ^= level error at time of obsej'vation covrcctod when necossaiy for inequality of pivots. 

 c = approximate collimation error (the values obtained from the micrometer measurements 



were always used for this quantity.) 

 7= mean of observed times, reduced when necessaiy to the mean wiie, (sidereal lime). 

 fi = reduction to 21 hours for clock rate. 



t = approximate clock error at 21 hours, sidereal time. This was generally taken as the 

 arithmetrical mean of a- — (T + Aa + Bh + Cr ± H) for all the stars observed in 

 one night. 

 da, da', dc, dt ^= corrections to a, a', c and t, obtained In- least squares. 



Then a=T + A {a+da) + Bh+0 (c+dc) + (t+df) ± 8, or if R=n-— (T+Art+B/j + CV+C±(9). 



Ada-\-Cdc+dt—R=() 



In this form the equations of condition are entered in the folloAving tables. 

 Prof. G H. Chandler has shared with me the work of these reductions. 



