The Laws Observatory. 507 
A is the azimuth factor, and 47, and a, are the clock correction 
and azimuth constant circle west uncorrected for error in the 
assumed collimation. Taking the means of the quantities 
and 4 for all the time stars circle west we have the equation. 
In like manner 
4T,, = — a, A, +, in which 4, and J, are the means of 
the quantities 4 and ¥ for the circumpolar stars circle west. 
From equations of this form representing the group of stars 
observed circle west, were deduced the quantities 47, and a, 
The observations circle east were treated in the same way, 
giving 47, and a, which are the clock correction and azimuth 
circle east uncorrected for the error of the assumed 
collimation. 
Then, for the observations circle west was written an equa- 
tion of this form — 
AT=4T,+4cK, (A.) 
in which 4c is the correction to the assumed collimation 
and X,, is the differential co-efficient of 4 7 with respect to c. 
The numerical value of 4, was computed by the formula 
K, =A pia ce C; 
Asal I 
in which C, is the mean of the collimation factors of the time 
stars circle west and C,, the mean of the collimation factors of 
the polar stars. For the observations circle east was written 
the equation 
AT=4T,— Ack, (B.) 
in which K, is found by a formula strictly analogous to that 
for X,. From the equations (A) and (B) formed from the 
observations circle west and circle east were computed 47 and 
4c. The mean of the right ascensions of the time-stars 
was taken as the epoch of 47. 
In this preliminary reduction the time-stars were all 
