446 



MEMOIRS OF THE AMERICAN ACADEMY. 



The local time and azimuth are obtained thus: Assume an approximate 

 the clock correction = 6 for the arbitrary time T , and make (o> ) — 



of 



For each star, At-\- Aa 



a> 



o 



CO 



o 



' + <* 



If Jt 







J 6 we have A a -\- J 6 



CO 



> 



a>Q being a small residual. 



Following the method of 



squares, multiply this equation for each star by the 



coefficients of the unknown quantities, and we obtain the normal equations 



(1.) 

 (2.) 



2Aa + 2Jd = 

 ZA 2 a + 2AJd 



2 



to) 







XA 



CO 







From these two equations, we can compute the values of a, J 6, and hence derive 

 the value of Jt for the time T . 



When the collimation constant has not been determined by reversals, but enters 

 into the equations as one of the unknown quantities, we have for each star 





Aa± Cc + Jd 



CO 



> 



(&)' being equal to (©) 



In this case the normal equations are 



(1.) 



(2.) 

 (3.) 



2A 2 a±I l ACc + 2AJe 



ZA 



In the computations for Brest and Duxbury, only two normal* equations were used 



the value of (c) being assumed from the result of the 



In the computation 



for Cambridge, the value of (c) was assumed from reversals, for December 17 and 31, 

 for January 3, and for February 1. On January 4 the value of (c) was taken from 

 January 3. On January 12, the values calculated for January 11 and 16 were 

 adopted. On January 19, the values calculated for January 18 and 26 were adopted. 

 On February 11, the value calculated for February 10 was adopted. On the other 

 nights (c) was calculated by means of the three normal equations. 



