Astro-PhotograpMc Catalogue Plates. 107 



tal correction has been applied, we have only to turn the result- 

 ing X sec <5 into Aa, and y into A^, by means of the tables con 

 structed with the expansions given above. 



When it is desired to base the determination of the orientation 

 constant r on measures of " trails," we can proceed as follows : 

 We can regard the end of the trail simply as the image of a sec- 

 ond star, having the same declination as the first impression of 

 that star. If we calculate Uy for each impression of the star, us- 

 ing an approximate value of d\ or the declination of the star, the 

 values of iiy will differ from the truth by a constant onl}^ This 

 constant will of course be the error of the approximate declina- 

 tion we have used for the star, and will be the same for both riyS,. 

 With the two w^^'s we get two equations like the second of equa- 

 tions (i). By subtraction of these equations, the above constant 

 will disappear, and we shall have an equation involving r as the 

 only unknown quantity. 



As an example of the above methods of reduction, I shall take 

 the plate discussed by M. Prosper Henr}'- (Bull. Com. Perm. 

 Tome II., deux™® fasc.) This plate was taken at Paris (latitude 

 48° 50') 1891., December 2, at an hour-angle of — o'' 9"", the de- 

 clination of the centre being 24°, and the right ascension i*" 4™. 

 The first step is the preparation of the tables for the reduction of 

 the 24° belt of the astrophotographic catalogue. These tables 

 are appended to the present paper. Table I gives the refraction 

 coefficients If^, etc., the numbers obtained for the auxiliaries be- 

 ing 



Wj = .000225 w-i = .00000000212 w-^ = .00000000115 



w^ = .0000112 W5 = .0C0345 Wg = .00000000151 



Table II gives the quantities necessary for transforming Aa 

 into X sec 8, and x sec 8 into Aa, by the aid of the expansions al- 

 ready given. Finally, Table III gives the corresponding quan- 

 tities for a8 and y. In both tables it was found sufficient at de- 

 clination 24° to include terms of the third order. The actual 

 numbers tabulated are as follows : 



Table II A gives value of ^1 {x sec 6) X lO'', with argument x sec 8 



or " " — Ji' A a X 10^ " " Aa 



" 11 B " " J./Aa3 " " Aa 



" II C " " A.,'y2X10^ " " y 



" II Z> " " —J3 (a; sec (5)3 " " x see 6 



