302 Ratherfard Photographic lleasures. 



The numerical values of these quantities as applicable to the 

 present purpose are given in Table III., pages 308-9, and the cor- 

 rection for proper motion is 



to be added to the observed distance s. 



The distances thus completely corrected are to be found in the 

 second and thii'd columns of Table IV., pages 310-15. The fourth 

 and fifth columns respectively of the same table contain the suvi of 

 the distances of the two comparison stars from r^ Cassiopeia and 

 the ditferenee of that sum from the mean given at the foot of the 

 fourth column. In the sixth, seventh, and eighth columns are 

 placed the difference of the distances as given in the second and 

 third columns; the scale correction, which is simply a propor- 

 tional part of the quantity given in the column "mean minus 

 sum ;" and finally the corrected difference to be used in forming 

 the parallax equations. The latter equations, together with their 

 solutions, are in Table Y., pages 316-21, where the absolute terms 

 are expressed in units of the second decimal place equivalent to 

 o."28oi as the value of one division of the glass scale. 



Using AuwERs' values of the coordinates of r^ Cassiopeioe 

 reduced to 1872.0 



a = d" 41™ 22. '108 



0^ = 57= 8' 10. "50 



and the almanac values of r and O, the radius vector and longi- 

 tude of the sun respectivel}', the values of S3, S^, P^ and P^ were 

 computed by the formulae* 



g sin G = sin cos a h sin H= sin o sin a 



g cos G = siu a h cos H = — cos 



f sin F = h sin {H + z) 

 f cos F = — cos a cos a 



S3=/sin(p+ F) 

 S^ = g sin (2? -f G) 

 P3 ^ — r sin O 

 P4 ^ — r cos 



*Annals N. Y. Acad. Sci., Vol. VIII., p. 4. 



