Parallaxes of n and e Cassiopeise. 3 



2. The "tangent correction," due to the photograph being taken 

 on a plane surface. This correction is derived from table 

 IV. A, given in my paper on the Rutherfurd photographic 

 measures of the stars about j3 Cygni.* 



3 Correction for refraction, computed according to the method 

 given in my paper on the Pleiades.f Whenever necessary, 

 the higher terms of the refraction were approximately taken 

 into account. 



4. Correction for aberration, computed according to the customary 

 Besselian formulae. J 



5- Correction for the proper motion of ^ Cassiopeiae. The obser- 

 vations have been reduced to the epoch 1872.0, using Auwers' 

 proper motion, which is : 



Aa = + 0^3860 AS = _ i."58o, 



corresponding to a motion of 3". 7 29 upon a great circle whose 



position angle is 115° 4'. Now, in general, if we let: 



P = the annual proper motion of the principal star on a great 



circle, 

 X = the position angle of that great circle at the time t^, 

 t = the time of observation, expressed in years and fractions 



of a year. And put : 



S, = cos ix — p) 



S, = — ^ sin^ (x — p) 



P, = rp 





P. — -'-' 



then we must add to the observed distances the correction : 



AS = S,P, + S,P,. 



The values of S^, S^, P^, and P^ used in the present paper are 

 given in table III. (p. 13), the unit of measure for p being one 

 division of the glass scale, as already explained. The distances 

 thus completely corrected, are set down in the second and third 

 columns of table lY. (p. 15). The fourth and fifih columns of the 

 same table contain the sum of the distances of the two comparison 



* Ann. N. Y. Acad. Sci., vol. vi, p. 340. f Ibid., pp. 253, et seq. 



X Astron. Untersuch., vol. i, p. 202, et seq. 



