METHODS EMPLOYED IN CALIBRATION OF MERCURIAL THERMOMETERS. 189 



for its initial points (both taken from Table XXXI.), be subtracted, the 

 corrected thread-length is obtained. These are exhibited in Table XXXII. 



The errors of tlie additional measures (given iu Table XXXIII.) are 

 obtained by subtracting the corrected thread-lengths from the uncorrected 

 lengths given in Table XX. 



If now the corrections for the lower ends of the additional measures 

 f .2(1',.) be taken out from the second mean curve, the corrections for the 

 upper ends can be calculated. 



Table XXXIV. 

 Correctians for Initial and Upper Points of Additional 3feasicres, in terms o/0°-001. 



The values of ^o (^-) ^^'^ entered in Column I., Table XXXIV., and 

 by subtracting from these the numbers in Table XXXIII., the upper 

 point corrections are obtained. 



The corrections given by each thread are plotted down in fig. 4, Plate 

 II. ; and the curve shown in fig. 5 is obtained by taking the mean of their 

 ordinates. 



It agrees closely with the second mean curve. Where they diverge, 

 as in the neighbourhood of 134° and 140°, the mean is taken and plotted 

 down in fig. 2, Plate II., in the curve drawn thus : : 



The curve thus finally attained must next (for purposes of comparison) 

 be converted into a standard curve. 



The corrections for 100° and 140° are : - 0-223 and 

 respectively. 



Hence, in accordance with the formula given in Part I., p 

 following quantity must be added to the corrected readings : — 



- 0-022 

 147, the» 



0-223 



201 r . . / N , a.ooQ 0'201 



Now 



•^ {x) + 0-223 - 



0-201 

 40 



■] 



only amounts to 0-001 if the quantity inside the brackets = "2. 



The values of </> («) 4- 0-223 are given in Column III. of the following 

 Table XXXV. They exceed •! when a; is > 2. As x increases, however^ 



the quantity — - — x becomes greater, and at about 125° it reduces the 

 expression below -1. On the other hand, the last significant figure of the 



numerator in the fraction — —— introduces a term >-0005 when x 



40 



is >20. 



