of the Ruther furd Photographs. 



239 



not involve errors of orientation, scale-value, etc., such as would 

 be incurred through the use of the measured X and Fin the sec- 

 ond members. I have therefore used the latter expressions for 

 computing the transformation corrections given in Table VI, em- 

 ploying the heliometer values of Aa and Ad given by Professor 

 Schur. It will be remembered that Rutherfurd was careful to 

 make the central star 15 coincide with the foot of the perpendicu- 

 lar let fall from the optical centre of the object glass upon the 

 plane of the plate. As our measured coordinates are referred to 

 this star as origin, Table VI applies equally to all the plates. 



Table VI. — Transformation Corrections. 



Star. 



Aa — Xsec 6 



As—y 



Star. 



Aa — X sec & 



As— Y 



1 



— 2.83 



ti 



—3.01 



24 



-0% 



— 0.22 



2 



+0.66 



—2.80 



25 



—0.34 



— 0.26 



3 



+3-15 



—2.58 



26 



— 1.60 



—0.23 



4 



+5-75 



—2.23 



27 



—041 



—0.28 



5 



—3-33 



— 1.22 



28 



+0.23 



— 0.29 



6 



— 1.31 



—O.77 



29 



4-1.68 



-0.36 



7 



+1-49 



—O.52 



31 



— 1. 01 



— °-35 



7A 



+0.21 



— O.27 



32 



— 2.92 



—o.39 



8 



—0.84 



— O.29 



33 



—3.08 



— o-53 



10 



+0.36 



—O.23 



34 



— o-34 



—0.65 



. 11 



+0.60 



— O.I9 



35 



+3-24 



-0.89 



14 



— 0.02 



— O.O I 



36 



+1-13 



—0.98 



15 



0.00 



O.OO 



37 



—1. 41 



—0.97 



16 



—0.16 



+O.O5 



38 



+0.45 



-1.38 



17 



— 0.20 



— O.O I 



39 



+1.28 



—1.47 



18 



—0.31 



—O.03 



40 



—4.84 



—1-59 



19 



+0-54 



— O.06 



4i 



— 1.24 



— 2.24 ! | 



20 



—0.36 



— O.O4 



42 



—1-35 



—2.54 



22 



+0.51 



O.IO 



43 



4-1. 19 



—2.89 ,; 



23 



+0.53 



—0.15 



44 



+4 79 



—3-05 



23 A 



+0.67 



— 0.18 



45 



—5-12 



-3.66 



II. Corrections for Refraction. 



Formulas for clearing rectangular coordinates of the effects of 

 refraction were first published by Dr. Rambaut in the " Astro- 

 nomische Nachrichten," No. 3125. Professor Turner has shown 

 how these may be much simplified by employing the coordinates 

 of the zenith as projected upon the plate.* His formulas, how- 

 ever, will not serve in the transformation of rectangular coordi- 

 nates into right ascensions and declinations unless we apply an 



* Monthly Notices, E.A.S., November, 1893. . 



