GOULD — REDUCTION OF d'aGELEt's OBSERVATIONS. 17 



Instrumental errors affecting the right-ascensions. 



The first attempts ai determining the clock correction, Jl, disclosed large discordances 

 between the indications of the different stars, as well as the fact that these were not due to 

 any error of adjustment, but must arise from a distortion of the limb of the quadrant. The 

 only course open was to determine the clock-rate by observations of the same stars made on 

 different nights, and then to investigate the nearly constant differences between the values of 

 Jt, as given by different stars. By means of a table of these differences, the transit of each 

 star may be reduced to an arbitrarily assumed plane parallel with the meridian ; and from their 

 discussion a first approximation was obtained to the amount and character of the distortion of 

 the quadrant. The locus of these special constant corrections, arranged according to the zenith 

 distances of stars, indicated some great indentation or flexure in the vicinity of 37° 20' of zenith 

 distance, corresponding to about 11|° of declination, and a decided distortion of the limb of 

 the quadrant in the same direction both above and below. The inference is irresistible to my 

 mind that the limb, along which the eye-end of the telescope moved, and to which it seems to 

 have been confined by clamp-rollers, had experienced some severe blow, and that this not only 

 injured its figure in the region above named, but had really bent the whole limb. 



To determine the precise amount and law of this deviation from a plane, in the path 

 described by the line of collimation, no direct means are available. Only the assumption of au 

 approximately correct value for the transit-error due to this cause, in the case of each standard 

 star, can guide to a knowledge of the azimuthal deviation of the plane of the quadrant. But 

 without some determination of the azimuth it is uncertain what portion of the discordances 

 between the results given by different stars is due to error of adjustment, and what to irregu- 

 larity of form. Furthermore, some plane must be arbitrarily assumed to represent the normal 

 plane of the quadrant ; and to this the corrections to be deduced for the several standard stars 

 must reduce them. 



The best plane for adoption, as that of the quadrant, seems to be that one for which the 

 sum of the squares of the constant errors is a minimum. And this, although not absolutely 

 attained, is nearly approximated by the indirect process to which I have had recourse. 



After applying the best attainable values of the corrections due the time of transit of the 

 several standard stars, which correction is denoted by q, so that 



a— T=M + m + ntgd + q 

 where T represents the sidereal time of transit, reduced by the use of the clock-rate to a fixed 

 epoch; At being the clock-correction at that epoch, and m = m — q; the equations of condition 



a — T — q = (Jt + m) + n tg 3 

 were solved, by the method of least squares, for every date. 



The several outstanding residuals thus afford new values of q for each star, which being 

 then combined by weights, depending on the apparent accuracy of the observations, and 

 upon the total number of determining stars on the respective nights, afforded a means of 

 repeating the process with advantage. Thus each successive series of solutions gave a closer 



3 



(17) 



