of the Rutherfurd Photographs. 281 



changed in the interval, the refraction-coefficients will also be 

 changed. Denoting by M ' and N y ' what these coefficients be 

 come for the trails, we have the correction to the offset, 



W ■ z + {My — MJ) Xsec 6 Q -f (N y — N/) Y 



The first term is constant for all four stars, and the two remain- 

 ing terms are small. To calculate M ' and N ' we must know how 



a y y 



much the hour angle has changed in the interval between the ex- 

 posures for the principal images and that for the trail. As each 

 of the former lasted six minutes and as the exposure for the trail 

 was much shorter, we may safely adopt seven minutes of time as 

 the change in the hour-angle. M ' and N/ may then be calculated 

 with sufficient accuracy by interpolating in Table VII. 



After these corrections have been applied it will be convenient 

 to transform the offsets into position angles, which may be done 

 by the formula 



_.. . -if offset ) 



p = 270 -f- sin < r r 



[z- cos o j 



Precession, Nutation and Aberration. Formulas for correct- 

 ing position angles for these were deduced in convenient form by 



Bessel* ; let 



a' = 20" sec cJ sin a Q 

 ji' = sec <J cos % 

 y / = tan (5 cos a 

 8' = tan d sin a 

 A, B, C, D = Bessel' s star-numbers, tabulated for eacb day 

 in tbe year in the ephemerides. 



The true position angle at the beginning of the same year is 

 found by adding to the observed position angle the correction, 



(— Aa' + BP' + Of + B&') 



Then to reduce this to beginning of another year we add 



-j- 20 // .o6 sec tf sin a - t 



where t is the integer corresponding to the difference of the years, 

 and must be considered positive if we are reducing an observation 

 to a later year than that in which it was made. 



As an example of the reduction of trail measurements, I have 

 set down the calculations in detail for the trail of Star 23, Plate I. 



* " Astronomiscbe Untersucbungen " Vol. I., pg. 202. 



