186 Messrs. Thorpe and Riicker's Remarks on 



thermometer 2, A =0*11 when N=273. In the case of ther^ 

 mometer 3, A = 0*01 when ]ST = 156; 8 vanishes when ]N~=312, 

 and is O01 when N" = 400. Finally, in the case of thermo- 

 meter 6, the largest value of 8 is 0*13, which occurs when 

 N = 400. 



Of these quantities, the value of A for thermometer 4 is 

 considerably in excess of the error of reading. It is not in 

 this case, however, a question of the error of reading only. 

 An experiment conducted with an exposed scale is in that 

 respect conducted under unfavourable circumstances ; and the 

 other errors thus introduced are far more important. This 

 can readily be shown from Dr. Mills's own paper. 



He says (Trans. Roy. Soc. Edinb. 1880, p. 570) that there 

 appeared to be in the experiments some source of variation 

 which I could not detect." Thus the value of the correction- 

 factor varied between 0-000113 and 0*000164 in the first of 

 the three series of observations of which details are given, 

 between 0*000136 and 0*000165 in the second, and between 

 0*000140 and 0*000166 in the third. On the other hand, the 

 mean correction-factor for all the thermometers, and that 

 for thermometer 4, both calculated forN =400 div. (for which 

 in this case 8 has its largest value), are 0*000155 and 0*000149 

 respectively. The difference between these numbers is evi- 

 dently well within the above limits of error, and is in fact 

 exactly equal to the probable error of a single determination 

 as calculated by Prof. Mills. 



On the whole, then, we are disposed to extend rather than to 

 withdraw our previous statement, and to say that Dr. Mills's 

 experiments go far to prove that the exposure correction below 

 100° C. is practically the same for all similar thermometers. 

 Nor is this a matter of slight importance. Dr. Mills's inves- 

 tigation of the exposure correction of one of his thermometers 

 involved 2160 readings. Had his conclusion that " each ther- 

 mometer is proved to have its own independent equation for 

 exposure correction " been correct in the sense that the differ- 

 ences were important, every observer working with exposed 

 thermometers, who wished to attain the highest possible 

 degree of accuracy, would in like manner have been compelled 

 to make hundreds or even thousands of observations on each 

 instrument. He would have had either to repeat Dr. Mills's 

 research, or to undertake some not less difficult and laborious 

 comparison with a standard for which the correction was 

 known. Dr. Mills cannot, therefore, be surprised if, before 

 consenting to accept such a yoke, we closely examine the 

 grounds upon which it is imposed. We believe that he has 

 rendered a greater service to his fellow-workers than he him- 



