494 Prof. A. Schuster on tlie Scale-Value of 



the actual temperature on the French hard-glass mercury 

 scale as determined by the Tonnelot. The second column 

 gives the corresponding readings of " Joule A." As Joule, 

 in his work, assumed a fixed zero of his thermometer, we 

 must reduce the observations here also in the same way. 



Any convenient position may be assumed as zero, as the 

 scale-value which is to be deduced from the observations will 

 only depend on the differences of readings, so that the zero 

 is really eliminated. But it is convenient to take as zero that 

 corresponding to the average temperature of the air, which 

 in our case was about 23 "33. The third column gives, there- 

 fore, the numbers obtained by subtracting 23*33 from the 

 readings given in the second column. If Joule's scale-value 

 is correct these figures should, when multiplied by his factor, 

 give the temperature as determined by a thermometer made of 

 glass having the composition of these thermometers. Joule's 

 reducing factor is 0*077214, which for the Centigrade scale 

 becomes '042897. For convenience of calculation I have 

 taken it as '0429. The fourth column gives the numbers so 

 reduced. Columns V. and VI. give the corrections to the 

 vertical position and the corrected readings. The last column 

 gives the differences between the temperatures as determined 

 by the Tonnelot and Joule's thermometer respectively. These 

 numbers show no very marked increase or diminution between 

 the temperatures of 10° and 30°. If the numbers in column VI. 

 were constant throughout, it would mean that the two ther- 

 mometers read alike as regards differences of temperature. 



In order to obtain the greatest possible informatioiji from 

 the numbers obtained they were reduced by the method of 

 least squares, all comparisons below 13° and above 22° being 

 left out of account as lying outside the range within which 

 Joule worked. If Ty represents the reading on the Joule 

 thermometer, T T that on the Tonnelot, and we wish to form 

 an equation 



T T -Tj=a + bT T 



we may do so, substituting for T T — T, the number in column VI., 

 and for T T those in column I. The constants a and b were 

 thus found to be 



a= 0*0081, b = 0-000933 + '00068. 



If we denote by £ T and tj intervals on the two thermometers 

 we finally find 



*,=£ T (l-0-0009&). 



