CATALOGUE OF POLAR STARS. 



283 



dable errors in 



arithmic computation of 



*y 



pen that it will be a positive disad 



- 



beyond a certain limit. 



Th 



limit appears, in the 



V 



ic initial functions. Hence, 

 to extend the development 



esent case, to be near the 



seventh term when 



IV 



16 and 







Development of the Functions a and d bxj M.ch<niic<d Quadrature*. 



The differential coefficients already computed hold true only for the instant of 

 time at which the initial functions a and S are assumed to be true. In the series 

 of differences obtained from these functions, the differentia] coefficients all fall 

 upon the same horizontal line. 



In order to obtain the summed series which will represent the valu< of a and 

 S at any assumed epoch of the constants of the precession, it will be necessary i<> 

 find the values of the differential coefficients which correspond to the instant t -f- I 

 or t 



2 



If the series does not extend beyond 24 years, the fourth term may be taken 

 as a constant. The coefficients may be converted into differences from which the 

 summation may be directly made by the following relations: 



Functions for the Instant t . 



Equivalent Functions for the Instant f ± 1- 



A 



A 



A 



*i 



dUt 



dt 



d 



a 



dt 



d' 



a 



dt' 2 



da 



dt 



A 



IV 



A 11 



A 1 



A 4 = A 



A 



A 



i 



IV 



a constant 



A 8 = A 1 " 



A* + t>t A 



IV 



I 



A 1 + i A 



III 



A, + i = A, + i A 2 



From the example given on 



247 we have the following data: 



Epoch. 



da 



dt 



1875.0 



h. m. s. 



7 29 5.631000 



*. 



73.51432400 



<f2 



fit* 



.<? 



0.30-237888 



dfi 



9. 



0.0020374G 



d*_a 



$. 



+ 0.00 OS 34 



Whence for the instant t ± > 



2 



