STARS IN COMA BERENICES. 447 



dk' da' 



~-~ = 8^' y\' ~ ^^ (Cf. Chauvenet, Vol. I, p. 171) 



with sufficient accuracy, as both A' and // are practically con- 

 stant, and /5 and y do not vary with the zenith distance. But 

 this is only 0.00002 at the limit selected ; and since the 



dk' 

 tangent of 70° is 2.7, the term -^- tan C^ will be inappreciable 



when Cy is less than 70°. Hence we can write 



or 



K tan2 (To = k' tan2 i:,^ 



with sufficient accuracy for photographic work, where s is not 

 large. 



Let us then substitute in the original formulae for J(a^ — «) 

 and J(o' — o) from the following equations : 



K=zk' 



J sin / =: X 



J cos / = F 

 tan Co sin q =^ H 

 tan Co cos q ^^ G 



and they become 



^{a' — a) = k' X i^z (\{\ +zr2)+i^y(G' — tan 6^)H s^c 6^ 

 A((5^ — rf) = /J^ X( CP + tan (Jq) ^ + /[-^ F(i + 6^^) 



where /^' is expressed in parts of the radius. These formulae 

 are evidently identical with Professor Jacoby's except for the fac- 

 tor 66/65 by which k' must be multiplied in order to obtain /9. 

 It should be observed that in the above equations terms in the 

 second and higher powers of s are neglected ; for we take ac- 

 count neither of transformation corrections, nor of the fact that 

 in Bessel's original formulae the quantities C^ and 0^ are intended 

 to apply to the middle point between the two stars, whereas we 

 transfer them to the end of the arc. This is, however, entirely 

 legitimate for most photographic plates. 



I subjoin Table VII which shows the values of the four 

 factors iJ/ , iV , J/, N^ for all of my plates. 



(107) 



