156 



REPORTS OF INVESTIGATIONS AIS'D PROJECTS. 



In November, 1908, we determined the errors of the surface of revolution 

 of the instrument from the meridian plane, due to slight errors of the pivots. 

 Three vears previously we had determined the correction on account of 

 minute errors of graduation for every 10' of the circles Avith most pains- 

 taking care and with what is believed to have been very great precision. 



We now repeated these researches at San Luis. The investigation of the 

 corrections due to slight errors in the forms of the pivots first received atten- 

 tion. The result agreed remarkably with the results previously obtained in 

 Albany. The probable error of the differences in the two determinations, 

 Albany and San Luis, respectively, at each point (points 15° apart) was: 



Component. 



Vertical component... 

 Horizontal component. 



Extreme accuracy is required in order to obtain probable errors of the 

 differences between two determinations as small as the foregoing, even when 

 there is no disturbance of the instrument between the two series. When 

 dismounting, transportation over 76° of latitude (with three transhipments), 

 and remounting intervene, it was very refreshing to find that the pivots, 

 protected as they were with extraordinary care in packing, received no injury 

 whatever. Moreover, the largest error found was only o.02^ a quantity 

 which is sometimes neglected in the correction of instrumental results for 

 this class of errors. Yet this error is about 8 times the probable error of 

 determination and is thus essentially real. In linear measurement the 

 largest observed relative displacement of the pivots due to inequalities of the 

 pivots was not more than one sixteen-thousandth of an inch (0.00006). The 

 pivots are slightly elliptical. The fact that this small ellipticity could be 

 detected is confirmatory of the accuracy of the observations themselves. 



The determination of horizontal flexure was next investigated. The dif- 

 ference of the two determinations — one at Albany in November, 1908, and 

 the other in San Luis in March, 1909 — was 0.13". This extremely small 

 quantity includes the result of any slight defect in putting the instrument 

 together, so that its parts will be under the same relative strains as at Albany. 

 It also includes the inherent uncertainties in the two determinations them- 

 selves, which are always difficult. Discordances much larger than the 

 difference between our two determinations have been developed in successive 

 determinations of this quantity when the instrument has remained unaltered 

 during the interval between determinations. It is quite evident that the mean 



