4 Messrs. Thorpe and Rucker's Remarks on 



ct + /SN in the expression 



must be independent of the scale. Thus, if we change from a 

 scale in which the length of the exposed column is measured 



by N scale-divisions to another in which it is measured by — , 



we must change ft to n/3. As, therefore, a scale-division of 

 the thermometers used corresponded to a quarter of a degree, 



N . . . • 

 N divisions on this scale correspond to -j divisions when de- 

 grees Centigrade are employed; and thus we must multiply /3 

 by 4. 



The mean expression for x in terms of scale-divisions ob- 

 tained from the observations on the four thermometers is 



#=•00013321 + -000000053046 N. 



Dr. Mills writes (p. 571), as the equivalent of this when the 

 degree Centigrade is the unit, 



#=•00013321 + -000000013261 H. 



He has therefore divided the coefficient of N by 4 instead of 

 multiplying it by that number, and has thus not only allowed 

 a serious error to creep into what is perhaps the most import- 

 ant formula in his paper, but has done himself the great injus- 

 tice of making his own correction appear sixteen times less 

 than it really is. 



If the above expression for as is taken as it stands, the second 

 term in the expression for y is 



•000000013261 (T- ON 2 ; 

 and if 



T-* = N=100, 

 this becomes '013261. 



JSTow a thermometer graduated for 100°, and on which it was 

 possible to read to the hundredth of a degree, would be of inor- 

 dinate length ; and as the millimetre divisions on Dr. Mills's 

 thermometers corresponded to o, 25, he could not possibly 

 have read to less than o, 02. In other words, if the formula 

 as given is correct, the term added by Dr. Mills to the expres- 

 sion for y may not only be neglected for all ordinary instru- 

 ments, but would have been absolutely inappreciable on those 

 he used. 



The correct value of y in terms of the Centigrade scale, as 

 deduced from Dr. Mills's experiments, is 



t/= (-00013321 + -000000212184N)(T-0N. 



