8 



Messrs. Thorpe and Riicker's Remarks on 



and that the relation between?/ and the position of the zero, as 

 gathered from the table given above, is 



Z=-2+y, 

 we are at a loss to understand this remark. The depression 

 of the zero Z becomes greater as y becomes less ; and this is 

 no way affected by the passage of y through the value 0. For 

 numerically increasing negative values of y we get increasing 

 depressions. It seems, therefore, that the statement that the 

 formulae point to a change in the direction of the motion of the 

 zero is due to a confusion between Dr. Mills's y and our Z, 

 and that, as a matter of fact, no such change is indicated. If 

 we are wrong in this conclusion, we can only apologize to Dr. 

 Mills and ask him to state what y really means. If we should 

 turn out to be right, we are afraid this error upsets all the 

 inferences drawn by him from his formula?. But even if we 

 have misunderstood the meaning of Dr. Mills's y, the deduc- 

 tions in question appear to be open to grave criticism. 



The conclusion drawn from the experiments is, that " the 

 zero of an ordinary vacuous mercurial thermometer undergoes 

 three distinct movements under the influence of heat. It is 

 at first depressed under the action of temperature, varying 



with each particular case The further application of 



heat causes the zero to ascend , after which it again 



descends." 



If we call the temperatures at which these changes take 

 place turning-points, the following table fairly sets forth the 

 grounds on which the conclusions are based. 



Table I. 



Thermometer. Henrici's. 



Dr. Mills's. 



455. 



3. 



c. 



Lowest temperature to which 1 -aco 

 the thermometer was heated J 1 



Corresponding value of y ■ 2000 



Highest temperature to which 1 ; , AO o.n 

 the thermometer was heated J ; 



Corresponding value of y j 1*400 



Motion of zero after heating ... descent 



Turning-points calculated by] 1 ^qo- 



Dr. Mills ../ i4d ° 



168°-6 

 2-726 

 296°-8 



0-554 



ascent 



306°-5 



40°-0 



4-000 

 120° -0 



3-356 



descent 



256°-7 



48°-l 



1-000 



239°-2 



0-686 

 ascent 



379°-8 



It will be noticed that in no case is a " turning-point " in- 

 cluded within the range of temperatures actually observed; 

 and that in all, therefore, the existence of the upper point is a 

 theoretical deduction from the formulas. We cannot, how- 

 ever, allow that such a deduction, even if algebraically cor- 



