90 UNIVEBSITT OF VIRGINIA PUBLICATIONS 



In order to obtain comparisons between mj' results and those of former 

 observers, all the positions were reduced for precession and proper motion 

 to 1910.0. The proper motion of ® was taken from JSTewcomb's Funda- 

 mental Catalogue. In computing his precession coefiBeients Professor Bond 

 used Madler's proper motion of ®, which is erroneous by at least 2" a 

 century, so that the use of his coefficients for reducing observations sepa- 

 rated by any considerable period of time will result in a large error. 



The precessions for Part V were computed by means of the formulEe, 



77 = n {sin a' (tan 8' — tan S)+ 2 sin |(a' — a) cos ^ (a' + a) tan 8 [ , 



d(8' — 8) 



dt 



= n{cOS a cos a). 



These may be written, 



d(a' a) r sin a 



dt i COS 8 COS 8" ^*iii(S-S)+2sin^(a'-a)cosi(a' + a)tan8}, 



d(8' — 8) ., . ,, , , , • 1, , , 

 , — ^=2resin^(a -t-a)sm^(a a). 



Taking into consideration the small relative distances of the stars, we 

 may simplify the formulae by putting sin a' = sin a, 



-|(a' -|- a) = a, and cos 8 = cos 8', whence 



'^^"^j^"'' =™{Psi^(8' — 8)+Qsiii4(a' — a)}, (A) 



d(8' — 8) 



dt 



+ P - 



cos- 8 



E sin^(a' — a). 



where we have put P = - — ^-r-, Q = 2 cos a tan 8. and E = 2w sin a. 



Newcomb's value of n, 20."069, was used, and the position of © for 

 18830, the mean of the epoch of Professor Bond's observations and my 

 own, was taken from N"ewcomb's Fundamental Catalogue. The following 

 tables of precessions were thus computed: 



