STARS IN COMA BERENICES. 427 



to the measured ^ 7ns. They refer respectively to the first 

 and to the second half of the morning's work. One point 

 regarding the use of these tables deserves mention : It some- 

 times happens that the reading on the scale corresponding to 

 one image of a star is less, and that corresponding to the other 

 image is greater than i iR. In such cases the correction must 

 be found from the table separately for each reading, and then 

 the mean of the two taken. This is evident if we remember the 

 way in which ^;// is obtained. 



Measured Coordinates and Rotation Errors. — Having 

 applied the corrections described above, we are in position to 

 obtain the measured coordinates. These are the differences of 

 the readings on a star and the readings on the central star, /'. c, 

 star No. 14. As the x is to be positive when the star has a 

 greater right ascension, and the y is to be positive when it has 

 a greater declination (algebraically) than the central, we must 

 apply the following rule : Subtract the position of the star from 

 that of the central for x direct, and subtract the central from the 

 star for y direct. For the opposite positions of the plate these 

 operations must, of course, be reversed. The reasons for this 

 rule are plain, when we remember that the numbers on the scale 

 increase towards the right. 



The coordinates thus obtained are not yet free from error, 

 however. For it is evident that, unless the plate were always 

 rotated exactly 90° from its previous position, the axes of ref- 

 erence would not be rectangular. This was, however, found to 

 be impossible of accomplishment. The best that could be done 

 was to turn the plate approximately 90°, and then to measure 

 exactly the angle through which it had been rotated. In order 

 to obtain formulae to reduce the measured coordinates to what 

 they should have been, 1-et us call 



x' , y' the coordinates referred to the central star as measured; 



X, y the same coordinates as they should be ; 



OX' OY' the position the axes actually had on the plate ; 



OX, V the position they should have had ; 



(87) 



