Section III., 1894. [ 43 ] Trans. Roy. Soc. Canada. 



IV. — Notes on Errors in Merldinn Transit Ohserrations. 



Bij Professor C. H.^^McLeod. 



(Read May 25th, 1834.) 



The following notes are intended to refer more especially to the conditions which ohtain 

 in longitude work, in which the portable astronomical transit is chiefly used. Defective 

 instrumental construction will be considered only in so far as concerns the special errors 

 under discussion. 



Putting aside instrumental flexure, which, in a properly conducted series of observa- 

 tions, need not be considered, the corrections to be applied to the observed times of transit 

 are those for azimuth, inclination of axis and collimation, and it is the errors which occur in 

 the determination of these which have mainly to be considered. 



Azimuth. — The German and the usual American method of determining the azimuth 

 constant is to observe, in addition to the time stars, one or more stars of al)out the declina- 

 tion 70^, in each position of the instrument, and from the erpuxtions of condition arising 

 from all the stars oliserved to compute the constant. In this method, the stars of high 

 declination enter, with such weights as are assigned to them, into the value of the clock error. 

 In the best French and English works, on the other hand, stars in the neighbourhood of 70" 

 are never observed. The observing list is divided into time stars and polar stars. The 

 time stars lie mostly between 20° south and 40° north and the polars are north of 80°. The 

 polars are used solely to determine the azimuth constant and do not directly enter into the 

 clock correction. The essential difierehce in the methods lies in the position of the polar 

 stars observed. In an ideal set of observations under the German method, the sum of the 

 coefficients of a should be zero or nearly so, and when this condition is reached, any out- 

 standing error in the constant a has no apparent efiect upon the resulting value of dt. The 

 elimination of azimuth error is however — apart from the unavoidable errors of observation — 

 not usually fully accomplished, owing to the personal equation curve which, up to and some- 

 what beyond 70° declination, is of the form 



E=K&Qc. "' d 



where m usually lies between ^ and f . This law, however, fails for very close polar stars, 

 and some recent experiments, conducted by the Geographical Service of the French Armj', 

 have shown that for very close polars E is equal to K. This being accepted, there is no 

 doubt that the French and English method of determining azimuth is the true one. There is 

 also a decided increase in accuracy in limiting the time stars to close equatorial stars since 

 in the observation of these stars the personal equation is substantially constant. 



