276 Permanence of the Rutherfurd Photographic Plates. 



9. From the final adopted values of the coordinates given in 

 the last column of the preceding Table, the position angle and dis- 

 tance of each star with respect to the central star were computed. 

 The computation was made by means of the following formulae, 

 in which s andp designate distance and position angle: 



ssmp=:x 

 scosp = y 



The results of the new measures obtained in this way are set 

 down in the next Table, side by side with the corresponding re- 

 sults of the measures obtained under Mr. Rutherfurd's direction, 

 soon after the plates were made. These values were taken from 

 my paper on the Pleiades without the application of any correc- 

 tion whatever. For the position angles the Table gives the direct 

 discordance of the old and new measures, the same quantities 

 corrected by the addition of a constant, and finally in the last 

 column, the discordance expressed in arc of a great circle. These 

 final values are obtained from the numbers in the preceding col- 

 umn by multiplying each by the sine of the distance of the star 

 in question from the central star. 



In the case of the distances, the old measures are expressed in 

 terms of the glass scale of Rutherfurd's machine, while the new 

 measures are in millimetres. It was therefore necessary to find 

 the ratio of the space of the Rutherfurd scale to the millimetre of 

 the scale of the Repsold machine. In the case of each plate the 

 ratio adopted was obtained by dividing the sum of the old meas- 

 ures by the sum of the new ones. The sums used in this way are 

 set down in the Table. The fifth column gives the new measures 

 reduced to the old Rutherfurd scale by means of the ratio so ob- 

 tained. The diiferences in the next to the last column are there- 

 fore also expressed in terms of the Rutherfurd scale. In the final 

 column they are given in seconds of arc, using for the ratio of the 

 Rutherfurd scale to the second of arc the value : 



1 division of the Rutherfurd scale = 28". 01. 



