LONGITUDE OF McGILL OBSERVATORY. 1^5 



always remain iiuless the value of r can be found as often as required by a mechanical 

 process. 



It is generally assumed that the value of c remains constant during the series of 

 observations in one position of the instrument. Under this supposition, any change in 

 the value of a can be detected by the derivation of this constant from time and polar stars 

 having nearly the same right ascension compared with the value derived in a similar way 

 at a later time in the series. On the supposition that the azimuth either varies uniformly 

 or is constant for all the observations in one position of the instrument, and, after reversal 

 takes another value which also varies uniformly, c being taken as a constant for the entire 

 series, the equations will take the form : 



,g. \ For L.\mp East. = Ô\ + Aâa + O.OOrfa' + Câc + âsr. 

 \ For Lamp West. = as,, + Aâa' + O.OOÔa — Câc + âsT. 



in which dsT, 6a, etc., represent the corrections to assumed approximate values of the 

 unknown quantities. 



If both a and c are considered as variables, the equations will take the lorm : 



.^. \ For L.AMP E.AST. = (>\ -f .-Id'a + O.OOdV + fWc + O.OOo'c' + rfAT. 

 I For L.wii» West. = rS\ + ASa' + O.OOÔa — Câc' + O.OOâc -f as t. 



It is doubtful, however, if there will ever be any real gain in increasing the number 

 of the unknown quantities from three to five. In the Washington-Princeton series, âc is 

 made ecj^ual to zero and the corrections, Aa, were applied throughout the groups before 

 and after reversal by interpolating in a straight line between the two outside values 

 of a. The ecjuations then take the very simple form : 



(7) = â\+ Ada + âsr. 



Thus far it has been assumed that all stars of a given series of observations have been 

 observed with equal precision. Struve has shown [" Struve : Sur l'Emploi de l'Instru- 

 ment des Passages," p. 17], that the relative precision of transit observations is a function 

 of the secant of the declination of the star observed. The expression for the weight factor 

 given by him is : 



y{0.0T2y + (^y(o!oi6)=sec= â. 



where u = the magnifying power of the telescope compared with a standard power of 180. 

 For a power of 30, he found : 



w = ^ (o'.072)= + ((K096)= sec^ Ô. 



These formulae are also given in the " Recueil de Mémoires," p. 30. 



Sawitch (" Praktischeu Astronomie," p. 140) has given the more complete formula 



.= /^ 



: y a' + (^b' + ~c') sec^ Ô sec' q. 

 in which : 



a ^ & constant dependent upon the sense of hearing, which for a given observer is constant 

 for all stars. 



