2IO REPORTS ON INVESTIGATIONS AND PROJECTS. 



only, and too frequently there is no attempt at all to determine these correc- 

 tions. In the present instance the following facts have been made clear : 



(i) That the systematic errors of our graduation, though not abnormally 

 large, are important, and could not have been neglected without disaster to 

 the principal aim of observations with this instrument — essential accuracy in 

 the systematic sense. 



(2) It is found that, when the corrections due to the circle-readings for 

 each interval of 10' are actually determined, those for intermediate divisions 

 can be interpolated from these with the greatest confidence. The faithful 

 periodic repetition of errors from one lo-minute interval to another is a 

 remarkable characteristic of these circles. This fact is of great importance 

 in its bearing upon the sufiiciency of our investigation. 



(3) Including the foregoing considerations, but of distinct value as a 

 voucher for accuracy both in marking the lines by the maker and in deter- 

 mining their errors here, is the extraordinary similarity in the trend of errors 

 found for corresponding subdivisions of the two circles, as well as the exceed- 

 ingly minute errors found in the length of successive arcs of 10'. 



I would not so dwell upon a point of technical detail like this but for the 

 fact that it offers some assurance in advance that the execution of our pro- 

 posed task is likely to be successful in one particular of primary importance, 

 and that, too, without an undue expenditure of time and effort. 



The second point relates also to a technical detail. In my report of last 

 year allusion was made to the results of a new method applied to determine 

 the motion of the mathematical axis of the meridian circle during rotation. 

 As previously explained, if the observations of star-transits can be reduced 

 to a true plane as described by the line of instrumental coUimation, then the 

 observations in the two hemispheres will offer a valuable indication of the 

 systematic errors of each. Usually the question whether the instrumental 

 line of collimation describes a true plane (and, if not, what are the deviations 

 from the plane) is left most obscure as to that part of the error which may 

 arise from minute irregularities in the form of the pivots upon which the 

 instrument revolves. 



Since the date of my last report this point has been again investigated, and 

 in two ways. The first method employed was that to which allusion has 

 already been made. The second did not involve any special observations, 

 but simply treatment of observations already made in great abundance for 

 another purpose — determination of error of graduation. The second method 

 would have been too costly in observations if error of pivots had been the 

 only result sought. The gratifying feature in our determinations b)^ the two 

 methods of this error is that the two sets of results closely agree. 



These particulars as to our experience in the instrumental investigations 

 are the only ones in that line calling for special remark at present, and these 



