212 Rutherfurd Photographic Measures. 



VI. 



ZERO CORRECTIONS. 



The first correction required by the position angles given in the 

 observation books is one of -f- 270 . This makes them agree with 

 the usual method of counting position angles from the North point 

 towards the East. The correction is of course due to the use of the 

 last impression of the central star as a starting point for position 

 angle measurements on the plate. The further correction is then 

 as follows:* 



Let v = the correction which must be added to all the observed 



position angles of any plate. 

 x = precession to reduce position angles to 1873.0 (See IV.). 

 y = refraction (re — p) for position angle 270 (See tables at 



end of III.). 

 k = approximate scale value in seconds of arc = 28". 01. 

 z = distance of last impression of the central star (See table at 



end of I.). 

 8 = declination of central star. 



Then 



v = 1 k z tan 8 — y -f- x. 



The following table contains the zero corrections computed by 

 this formula for the various plates :f 



* For a demonstration of the formula here given, see Astronomical Journal, 

 1891, No. 17, p. 131. 



f It is perhaps worth while to note that these zero corrections do not include 

 a certain special correction required by the position angles derived from the 

 Western impressions. This special correction, which will he fully explained 

 later (see VII.), might have been included in the zero corrections for the 

 Western impressions, as it is a constant for each plate. But I have preferred 

 to apply it directly to the final results, as will be seen in the next section. 



