66 Rutherfurd Photographic Measures of 



ing measures of distance in Table Y. The first column is a repeti- 

 tion of the number of the plate. In columns two and three are 

 given the observed angles for the eastern and western impressions. 

 The number of degrees for the west column are the same as 

 printed in the east column, except where there is an obvious 

 change of ± i° indicated by a difference of nearly 6o' in the min- 

 utes of the two columns. 



In column four are placed the zero-corrections of paragraph 7 

 plus the special corrections due to the precession, etc., mentioned 

 in the same paragraph. This quantity is taken from the last col- 

 umn of Table III. The correction for refraction from Table II 

 is in column five. The mean of the east and west impressions 

 thus corrected is placed in column six. 



17. In column seven of Table VI is the correction due to 

 proper motion of the central star. This has been computed from 

 the following formulae : * 



Let t, t, S 1 , P x , P 2 , p and % have the same'meaning as in para- 

 graph it; also let 



8 5 ^sin{x— p) 



S 1 = s 5 s 6 



P b =r p cosec 1" 



K = — I P 1 smx tan 6 -f- J P 2 sin i // sin x cos x ( 1 + 2 tan 2 6) \ 



Then will the correction for proper motion, additive to observed 

 angles, be 



Ap = 8,P 5 (i + S 1 P 1 -S 6 )+K. 



Throughout these formulae p and <r are to be expressed in divi- 

 sions of the scale, whereas K and Ap are in seconds of arc. The 

 convenience of expressing Ap in this form is more noticeable 

 when it is remembered that S^P-^ has already been computed for 

 use in correcting the distances; see paragraph 11. Here <r is to 

 represent the value of s after being corrected for scale variation 

 and proper motion. 



18. As K is obviously a constant for all stars on the same 

 plate, being only that part of the variation in (/ — p) due to the 



*Handbuch der Vermessungskunde von Dr. W. Jordan, Bd. III. S. 359. 

 Vierte Auflage. 



