Dr. Mills's Researches on Thermometry. 3 



and 3 will be equal when (using an obvious notation) 



(« 2 +AN 2 )N 2 =(a3 + AN 3 )N 3 , 



If we put N 3 =166 and use the coefficients given in the paper, 

 we get a quadratic in N 2 , viz. 



(•00014148 + -000000037880 N 2 )N 2 



= ('00013197 + -000000057030 x 166)166. 



Solving this by approximation, we find that N 2 is (neglecting 

 fractions) 159. Instead, therefore, of the correction being 

 the same (as the unfortunate slip with respect to the substitu- 

 tion of y for x might easily lead an unwary reader to believe) 

 when the number of exposed degrees differed by 166, it was 

 the same when they were 159 and 166 respectively and there- 

 fore differed only by seven. 



We have not thought it worth while to find the correspond- 

 ing values of y for the other two thermometers employed, as 

 the following method of comparing the results appears to us 

 to be more satisfactory than that given above. 



The interval between the freezing- and boiling-points was 

 apparently divided into 400 divisions. If, in order to make 

 the differences large, we make the very favourable suppositions 

 that the whole scale was in each case exposed so that N = 400 

 and that T — £ = 100° C, we obtain for the values of the cor- 

 rections for the thermometers 6*2652, 6*2312, 5*9443, and 

 6*3076. As each division was about a millimetre long, it 

 must have been impossible to read with certainty to less than 

 a tenth; and thus the first place of decimals only is significant. 

 So far, therefore, from proving that each thermometer " has 

 its own independent equation for exposure correction," these 

 results seem to us to show that the exposure corrections below 

 100° C. are, in the case of three out of four similar thermo- 

 meters, practically identical. If the formulas are intended to 

 apply to the measurement of temperatures higher than 100°, 

 in which case the differences between the corrections would 

 be greater, experiments ought surely to have been made above 

 that temperature. 



The second point we have to notice is a mistake in trans- 

 forming the expression for the correction from scale-divisions 

 of the thermometers to degrees Centigrade. It is evident, if 

 we consider the case of the same thermometer having two dif- 

 ferent scales engraved upon it, that the value of the correction 

 in terms of a scale-division must be inversely proportional to 

 the length of a division, and therefore directly proportional to 

 N, or the number of divisions exposed. Hence the factor 



B2 



