LONGITUDE OF McGILL OBSERVATORY. 139 



It needs to be said, however, that these conclusions only hold when the following- 

 conditions are at least approximately fulfilled : 



(a) When the observations are properly distributed in declination. 



{b') "When they are sufficiently good and sufficiently numerous to insure a substantial 

 freedom from accidental errors. 



(c) When there is a freedom from systematic errors in the system of fundamental stars 

 employed. 



(d) When the hourly rate of the clock is known. 



(e') When allowance has been made for changes in the instrumental constants which 

 occur during the observations. 



(/') When the line of collimation of the telescope moves in an invariable plane. 



{g') When the personal equation of the observer remains constant for stars at dififerent 

 declinations. 



Conditions (/ ) and (g) relate to a particular instrument only, and to one observer 

 with that instrument. It often happens that after an exhaustive discussion of the errors 

 of a transit instrument in a given series of observations extending over a long period of 

 time, different values of the azimuth constant are required for different zenith distances. 

 It may be assumed, at least as a working hypothesis, that this resixlt may be due to either 

 one or both of the causes expressed under conditions (/') and {g'). No method has been 

 tried which seems adequate to a proper discussion of the variation of the instrumental 

 constants due to the deviation of the line of collimation from an invariable plane during 

 the revolution of the telescope. If the residuals due to this cause are of the nature of 

 systematic errors, they could probably be expressed by some empirical formula. At 

 present this source of error must be considered as not proven. On the other hand, if these 

 residuals are due to a variable personal equation on the part of the observer for stars at 

 different declinations, it seems quite possible to determine the law of their formation. 

 They can be expressed by a term Ee, added to the fundamental equation. 



Equation (2) will then become 



= J„ + Aa + Cc + JT + Ee. 



in which e must be determined by some mechanical method, and E may be assumed 

 empirically, probably as some function of the secant of the zenith distance. 



The value of e may be determined mechanically by observing transits of an artificial 

 star at the focus of a collimator. In this way the two essential requirements of a personal 

 equation machine would be fulfilled, since the observations Avoiild be made with the same 

 instrument as that employed in the regular observations and the velocity of motion could 

 be easily made equal to the apparent velocity of a star at any given declination. 



Since both E and e are to be determined, e could not be obtained from a solution of 

 the equations. Even if the form of the coefficient E were known, it is doubtftil if the 

 solution would be sufficiently exact, on account of the probable slow change in the value 

 of this co-efficient up to 60" or 70° north declination. 



There are at least two independent sources of evidence that this variable personal 

 equation really exists, and that it affects not only the determination of the instrumental 

 constants, but the clock errors also. 



In the meridian observations at Harvard College Observatory, the collimation is deter- 



