METHODS EMPLOYED IN CALIBRATION OF MERCURIAL THERMOMETERS. 165 



In Column IV., therefore, are the means of the readings in Columns 

 I. and II., or the points to which the corrections are to be applied («). 

 In Column V. are the values of c(u) obtained by subtracting each of the 

 numbers in III. from their mean. 



In Column VI. are the values of ^(«) obtained by taking the sum of 

 all the c's up to c(n). 



Table VII. 



In order to obtain a standard curve from the numbers given in the 

 above Table, a few points were plotted down in the neighbourhood of 

 100° and 140°, and the curve drawn through them. 



The corrections at these points were 0°-069 and 0°-028 respectively, 

 i.e. in the notation used above (p. 147) 



f (i) = 0-069, a = - 0-041, - = - 0-001025. 



N 



The largest value of ^(a;) = 0-216. Hence the largest value of 

 -i0(*) - fO)} is - 0-001 X 0-188 = - 0-0002, 



N 



which is negligible, as is the largest value of —^ x. 

 Hence the formula reduces to 



X + </>(.-0 - 0(i) - - .-c = .?; + ^(a;) - 0-069 + "001025 x. 



N 



