248 Prsesepe Group; Measurement and Reduction 



Residuals from the Declination Equations : 



Plate. Star 4. Star 5. Star 15. Star 40. Star 44. 



I — 0.13 -(-0.20 +0.01 +° IO — O.18 



II 



— -03 



+ .20 



— -15 



4- -ii 



— -13 



III 



— .07 



4- .13 



— .06 



+ .16 



— .16 



IV 



— .00 



4- .23 



— .04 



4- .07 



— .26 



V 



— .09 



4- .34 



.00 



— .or 



— -24 



VII 



— .10 



4- .22 



— .04 



4- .08 



— .16 



VIII 



— .08 



4- -25 



4- .01 



4- -04 



— .22 



IX 



— .02 



4- .23 



— .01 



+ .03 



— -23 



Means, — .06 + -22 — .03 + -°7 — -20 



Employing the constants in the manner described at length in 

 the last section, we obtain the quantities a t and S which have 

 been tabulated in the following pages. It will be remembered 

 that a x arid d 1 are the projected right ascension and declination of 

 a star respectively ; the transformation correction being the same 

 for all the plates, may just as well be applied to the means; 

 and it is evident that this procedure does not affect in any way 

 the comparison of the right ascensions or declinations of a star 

 as derived from different plates. The columns headed " At Epoch 

 of Plate " give the coordinates uncorrected for proper motion. 

 The calculation of the latter is very simple in this case as the 

 plates were taken at practically only two dates, 1870.3 and 1877.3 ; 

 hence the annual proper motion is obtained hy subtracting the 

 mean of the places on plates of the earlier date from the mean for 

 the later date, and dividing the difference by 7. The columns 

 marked " P. M." give the correction for proper motion necessary 

 to reduce the place of the star to the epoch 1875.0. 



Probable errors are given for the right ascension and the dec- 

 lination of each star, and also for the proper motions ; they were 

 calculated thus : 



Let m = the number of plates of date 1870.3 on which the star 

 was measured. 

 n = the number of date 1877.3. 

 [uu] = the sum of the squares of the residuals obtained by 

 subtracting the mean from the separate observations 

 reduced to the epoch 1875.0. 



Then the probable error of a quantitj- having the weight unity 

 is : 



