LONGITUDE OF McGlLL OBSERVATOEY. 137 



Proiessor Safford has given (U.S. Surveys west of the 100th meridian, Vol. II, p. 346), 



the form 



ic sec c>" :^ / ^••'^ 



"^ cos' d" + 0.3' 



or 



"^ 10 + 3 sec» 8 

 Struve's formula, reduced to this form, becomes : 



/ 13 



■^ 9 + 4 sec- Ô 



Professor Young ("Washington 01)servations for IST-*!," p. 2<S) has properly introduced 

 a factor which takes into account the effect of atmospheric disturbance depending upon 

 the zenith distance of the star obser\ed. The form given by him is : 



/ 12.35 



10 + 2 sec z sec â 



The values of the weight-factor employed in the longitude operations between 

 Washington and Princeton are supposed to belong to the Princeton instrument, but they 

 were applied to the Washington observations as Avell. 



In the present series of observations, there is no need of introducing the factor which 

 depends on the number of threads observed, since, with a few exceptions, all the tallies 

 were observed. The weight-factors were taken from the last formula given. The general 

 equation (2) now becomes : 



(8) = w (J„+ Aa + Cc + JT) 



On account of the great labor invoh'ed in a complete solution by least squares, and 

 especially because an error of observation at any point can only be detected after the 

 complete solution has been effected, the writer has generally preferred, at least in a provi- 

 sional solution, to deal with equations (4) in the following way. By sirbtracting the time 

 equations from the polar equations, we have equations (9) as follows : 



= -Jo' - ^o' + (-4, -A,) a+ (C, - C) c = A^- - z/; -f {A^~A') a+ ((7, - C) c 



= j; - J/ + (^, _ A^) a + (a - C3) c = a: - J/ + {A, - A") a + (C, - C") c 



= j; - J„' + (A, -A') a + (C, -C')c = J„^ - J„^ + {A,- A') a + (C3 - C) c 



= j; - j; -f {A, - A") a + (C, - 6-) c = J/ - J; + (^ - A") a+{C,~ 0") c 



Dividing these equations by the co-efficients of c, we have equations (10) as follows : 



a-\-c 

 a -\- c 



J 1 Â^ A A' ~~ 



[3] 0=-» ^ + ^^LZli-a + c 



C, — C C — C 



TAT n -V-^o^ , A, - A " 



[4] = + a-\- c 



Sec. III., 1885. 18. 



