192 



EEPORT — 1882. 



othera are available. It seems, tberefore, unreasonable to entrust the cor- 

 rection entirely to the initial point curve up to the point where the first 

 upper point curve overlaps it, and then suddenly to regard it as of equal 

 value to this, which is itself only one out of ten carves which are used to 

 determine the correction in the centre of the scale. 



Experiment fully confirms this view. In no case, either of examples 

 worked out by members of the Committee or of those given by von 

 Oettingen, do the corrections given by the initial point-curve differ on a 

 first approximation from the values they ultimately assume so much as 

 do many of those given by the upper point curves. 



(32) In calibrating their thermometers, therefore. Professors Thorpe 

 and Riicker thought it better to weight the initial point curve 10, the 

 upper point curves being weighted 1, to introduce the additional measures 

 in the first approximation, and to determine the initial point of any 

 additional measure with full accuracy before using it to determine the 

 error of its upper point. 



For this purpose the calculations were carried on exactly as in the 

 previous method up to and including Table XXIV., and the upper point 

 and initial point curves were drawn. The mean ordinates of the upper 

 point curves were calculated from the highest initial point (116°) up to 

 the point where the first upper point curve ended (123°). The means of 

 the lower parts of the upper point curves and of the initial point curve 

 were then taken, giving the latter the weight 10, and thus the fii-st mean 

 curve was formed from 98° to 123°. It is given in fig. 1, Plate III. 



The additional observations were now at once introduced, and the 

 calculations required the gradual building up of five Tables at the same 

 time. The highest point given by Thread I. is at 123°-9 ; hence the 

 corrections for the initial points and for all the upper points on Thread I. 

 were taken out from the first mean curve and entered in Table XXXVII., 

 in the columns headed f {{) and I. respectively. 



Table XXXVII. 



Corrections of U^per and Initial Points from Mean Curve I, Jiff- 1, Plate III., 

 expressed in terms of(i°QQ\. 



The mean of the ^ (i)'s subtracted from the mean of the numbers in 

 Column I. gives the correction on the mean value of Thread I. given m 



