LONGITUDE OF McGILL OBSERVATORY. 117 



The observed times of transit were corrected for level aud for approximate values of the 

 azimuth, collimatioii aud clock error. These values were obtained somewhat after the 

 method of equations between a aud c, discussed by Professor Rogers. Corrections to these 

 values were then obtained by the method of least squares. In forming the normals, the 



equations of conditions have been multiplied by the weight factor »«, = \/ w+^'H^zsi^o 



The values oîw, for Montreal and Cambridge are given in Table I. This formula- is due 

 to Professor C. A. Young, and is a modification — taking into account the zenith distance 

 of the star — of those proposed by Struve and Satibrd. Where stars were not fully observed 



the equations were also multiplied by the factor ?", = y^ — ^ where N is the number 



n 



of wires in the reticule and n the number observed. (See Chauvenet's Astronomy, Vol. 

 IL p. 198.) The collimation is assumed to have been constant throughout the work of a 

 single night, and on no night do the residuals appear to throw any doubt on the validity 

 of this assumption. The azimuth error was assumed to have been different in each posi- 

 tion of the instrument, but to have been constant while in any one po.sition. 



Let ij) = latitude of the place of observation. 

 Ô = declination of an observed star. 



a ^= tabular right ascension, corrected for diurnal aberration. 

 A = sin {(J) — a) sec â. 

 B =r COS {(j) — Ô) sec Ô. 

 C ^ sec Ô. 



a, a', a" = approximate values of azimuth. 

 h = level error at time of observation, 

 c = approximate collimation error. 

 T = mean of observed times, reduced to mean wire. 

 t) = redaction for clock rate. 

 t = approximate clock error. This was generally taken as the arithmetical moan of 



a — (T + Ja + Bb + Cc ± H) 

 for all the stars observed in one night. 

 da, da', da", dc, dt ^= corrections to a, a', a", c and t. 



Then, 



a=:T + A(a + da) + Bb + C (_c + do) + (t + dt) ± W 



or, if:D = a — (T+ Aa + Bb + Cc + t ± H), 



A da + dc + dt — J» = 0. 



The equations of condition are entered in Table III. in this form. In this table the 

 last column gives the residuals from the ec[uation of condition after weighting. 



Professor Gr. H. Chandler, M.A., has shared with me the work of these reductions 



