460 KRETZ. 



Then it is evident, from the method by which the constants 

 are derived (/. c, by comparison with catalogue positions) that, 

 but for errors of observation, 



^=:52'^87(I+/). (I) 



But evidently, n is too great by the amount of the aberration, 

 being the measured distance on the plate. Hence, if we let 



7 = — (tan e sin 6^ -(- sin a^ cos cIq) • sin !■'■' 

 6 = cos ttfl cos £$0 • sin l'^, 



where e is the obliquity of the ecliptic, and a^ and o^ are the 

 coordinates of the central star, roughly corrected to the time of 

 exposure of the plate, then will (cf Chauvenet, Astronomy, Vol. 

 II, p. 467) 



a(i + C7 + i?d) 



be the measured distance on the plate in seconds of arc. (Tand 

 D in this formula represent the Besselian day numbers, and may 

 be obtained from the Ephemeris. We find, then, evidently 



True Scale-Value =S = '^i^ + fi' + ^'^) (3) 



n 



or, remembering equation (i), and neglecting small terms 



5=52^^.87(1 +/+C7+Z)rf). (3) 



A correction for the temperature at which the plate was 

 measured might also be applied, using for this purpose the co- 

 efficient of expansion determined by Dr. Schlesinger ("Pr^esepe," 

 p. 223). But as that quantity is not very reliable, and as the 

 corrections are necessarily veiy small, being in no case as large 

 as 0.0007 if ^^'^ ^se the value of v as given in the place referred 

 to, while, on the other hand, the mean uncertaint}^ of / is more 

 than 0.0013, I have felt justified in neglecting the same. 



We obtain then the following table : 



(120) 



