18 OOITLD REDUCTION OF d'aGELET'S OBSERVATIONS. 



approach to the true values of q, and to a determination of the azimuth of that normal plane 

 to which the employment of these values reduced the observed transits. And this plane being 

 inferred from the entire series of dates, and by the use of least squares on each individual date, 

 cannot be far from the truth. This process was repeated so long as the individual values of 

 the residuals, and the various determinations of n, were found to be rendered more accordant; 

 and the present reduction is based upon the results of the sixth successive series of solutions. 

 The accordance of the values of n thus attained yields a strong corroboration of the trustworthi- 

 ness of the result. 



After various attempts to deduce a correction proportionate to the secant of the declina- 

 tion, I have concluded that this is impracticable, and that any error due to the motion of the 

 lino of collimation in a small circle is thoroughly merged with the values of q. 



The values of the correction q for each standard star being carefully charted, a curve was 

 obtained by graphical means which represents the observations within the limit of probable 

 error in the whole range of observations, excepting for the zone contained between 9° and 

 13° of north declination. For this region the distortion appears to have been so great, and the 

 errors of observation so large, as to render the results less trustworthy than the rest. 



Only after the work of reduction and the construction of the catalogue had been entirely 

 completed in all other respects, was the investigation of the distortion within these limits 

 resumed. The success of this special research has been greater than I had anticipated, and 

 the results have now been modified to conform to the new determination. 



For this special investigation the best attainable places were deduced for every star 

 observed by d'Agelet within the above-named limits. For stars whose proper motion was 

 found capable of approximate determination, this has been used to refer the right-ascensions 

 to the date of d'Agelet' s observations. Some of the stars occur in Argelander's catalogue, 

 but for the great majority of them Piazzi, and Baily's reduction of Lalande, furnished the 

 places, and a comparison of these with later observations, the proper motion. All these adopted 

 places were of course referred to the fundamental equinoctial points by special tables, originally 

 deduced for the construction of the standard lists. 



These residuals, when charted, soon made manifest the existence of two independent curves; 

 one belonging to observations made by d'Agelet previous to some date in May, 1783, and the 

 other, for which the corrections were decidedly smaller, holding good for subsequent observa- 

 tions. No note or memorandum exists by which the date may be indicated, but from internal 

 evidence I am inclined to believe that it must have been on the 9th, and have accordingly 

 assumed the change to have taken place on that day. 



Observations before this date give reasonably accordant results, as also do those subsequent; 

 and I cannot resist the strong conviction that d'Agelet, being aware of the great defect in the 

 limb, employed some mechanical means on the 9th May to remedy it. The attempt was suc- 

 cessful, in so far as the errors were decidedly reduced in magnitude within the region of their 

 greatest influence ; but was by no means successful in removing them, or indeed in diminishing 

 tliem outside of the limits already named, for which they remain essentially the same through- 

 out the period of d'Agelet' s observations. 



The accompanying chart I. shows the value of q for different declinations ; the dotted line 

 (18) 



