Astro-Photographio Catalogue Plates. Ill 



Feom the Declinatioks. 



I + 15 i? + 37 '■ + c — is'.'is = o 



2 



— 



2 



P 



+ 



33 



r 



+ 



e — 



14,46 



=^ 







3 



+ 



13 



P 



+ 



24 



r 



1 



c — 



15-44 



= 







4 



+ 



II 



P 



+ 



19 



»• 



+ 



c — 



13.08 



= 







5 



+ 



16 



P 



+ 



16 



r 



+ 



c — 



14.62 



= 







6 



— 



3 



P 



+ 



I 



r 



+ 



c — 



13-41 



= 







7 



— 



27 



P 



— 



2 



r 



+ 



e — 



14-77 



= 







8 



— 



I 



P 



— 



2 



r 



+ 



c — 



14.09 



= 







9 









P 



— 



24 



r 



+ 



c — 



14.46 



= 







10 



+ 



33 



P 



— 



32 



r 



+ 



c — 



13-19 



= 







II 



+ 



17 



P 



— 



34 



r 



+ 



c — 



13-73 



= 







The combined solution of all these equations hy least squares 

 gives the following values of the unknowns, in which p and r 

 have been multiplied by .01 to restore their original units. The 

 sum of the squares of the 22 residuals is 10.3179, so that the 



' one equation 



is 



±o."76. 



2) = — .000089, 





mean error ± .000081 



r ^ -\- .000145, 





" " ± .000081 



k = — 2. "64, 





" " ± o."24 



c= + 14. "24, 





" " ±o."24 



The total corrections required hy the measured co-ordinates of 

 the unknown stars are now found b}' means of the expressions (3) 

 to be : 



+ .000137 XsecfJ + .000011 Y — 0.193, for XsecfJ 



— .00209 Xsecf^ + ,000256 Y + 14. "24, " Y 



Having thus arrived at the constants required for the reduction 

 of the plate, we now come to the computation of the places of the 

 unknown stars from their measured co-ordinates. This is of 

 course the most important part of the subject, since the process 

 must be applied a very large number of times for each plate ; 

 while the foregoing computations need only be made for the com- 

 paratively small number of known stars. 



As an example of this part of the work I take the first star of 

 the above series, treating it now as an unknown star. We have : 



