Dr. Mills's Researches on Thermometry. 185 



admit; but, on the other hand, at the lower temperatures both 

 N and T— t must be less than at 100°. They, too, are factors 

 of the correction; and if their variations are taken into account, 

 our statements that the example worked out by us was favour- 

 able to Dr. Mills's views,, and that the corrections for three of 

 the thermometers were practically identical below 100°, are 

 strictly correct. Let us investigate this point a little more 

 fully. 



The corrections may be considered as practically identical 

 if, in the case of any thermometer, we may substitute for the 

 correction peculiar to it the mean of the corrections obtained 

 from all the thermometers. 



For the thermometers referred to by us (2, 3, and 6) the 

 expression for the mean correction is 



y = (-00013591 + -000000051152N)N(T-0. 



Subtracting this from the correction for thermometer 2, we 

 get the difference 



6 = (-00000557 - -000000013272 N)IN T (T- 1). 



If N varies, the maximum value of this expression occurs when 

 K = 210 scale-divisions (each of which on Dr. Mills's thermo- 

 meters was a millimetre in length, and corresponded approxi- 

 mately to o, 25 C). Making the same liberal assumption as in 

 our last communication, that T — 1= 100, we obtain, if we write 

 A for the maximum difference from the mean correction, 

 A = 0*06 division. 



For thermometer 3 we get (neglecting signs) A= 0*07 div. 

 when N = 335 div. In the case of thermometer 6 the two 

 curves intersect below 400 div. The correction-difference is a 

 maximum and = 0*01 div. when N= 111 div., is zero when N = 

 222 div., and is =0*05 div. when N=400 div. The largest of 

 the above values of A is a little above the error of reading; and 

 we may for a moment digress to say that we do not think 

 there is any difference of opinion between ourselves and Dr. 

 Mills as to the value of this quantity. We said it is " impos- 

 sible to read with certainty to less than a tenth" of a milli- 

 metre. Dr. Mills can read " fairly " (L e. not with certainty) 

 to a twentieth. We have frequently had occasion to read the 

 same thermometer independently. We invariably agree to 

 C, 01 (?'. e. on our thermometers to a tenth of a millimetre), 

 thus showing that the error of reading is +0*05 millim. 



To return, however, to our argument. If, instead of taking 

 the three thermometers with respect to which our statement 

 was made, we take all four, we find for thermometer 4 (that 

 previously excluded) A = 0*23 div. when N = 400 div. For 



