188 Remarks on Dr. Mills's Researches on Thermometry. 



zero is thus given by the formula as unchangeable in direction. 

 It is not reversed when ?/ = 0; and the evidence, if of any value 

 outside the range of the experiments, is directly opposed to 

 the theory of the three movements of the zero of a thermo- 

 meter. 



To make the matter clearer, we reproduce Dr. Mills's table 

 with three additional rows, which are separated from the rest 

 by a line, and with some additions to the headings of the 

 columns. 



so. 



Zero observed. 

 Z. 



y 



=2+Z. 



y calculated from 

 formula (1). 





 1 

 3 



4 

 5 



o-oo 



-0-10 

 -0-25 

 -0-40 

 -0-60 



2-00 

 1-90 

 1-75 

 1-60 

 1-40 



1-92 

 1-73 

 1-61 



1-45 



9 



9-35 

 10 



-1-81 

 -2-00 

 -2-41 



...... 



0-19 



o-oo 



-041 



The last three numbers in the second column are calculated 

 from the formula y = 2 + Z. The Table shows that the zero 

 continues to descend though y becomes negative. The same 

 considerations may, mutatis mutandis, be applied to Dr. Mills's 

 own thermometers. The only one for which there is a critical 

 value is thermometer 3 ; and that corresponds to a negative 

 value of A\ There is, we believe, no flaw in this argument, 

 and it certainly is not abstruse ; but, in view of the ambiguity 

 of the term " total remaining ascent," we assumed, when 

 writing before, that Dr. Mills might be able to explain the 

 difficulty. We therefore reminded him of certain canons for 

 the use of empirical formulae, which, if his conclusions were 

 not invalidated by the previous objection, were applicable to 

 the case under discussion. His admission that these were not 

 novel does not explain his disregard of them. 



In concluding his reply to our paper, Dr. Mills seeks to 

 reduce our criticisms to " an obvious misprint, a slip in arith- 

 metic, a question of mere nomenclature, and the like/'' 



The misprint was only incidentally noticed in a discussion as 

 to whether his method of exposition did not exaggerate the 

 importance of the variations of the exposure correction — a dis- 

 cussion which, as we have seen, involves the whole scope and 

 meaning of this portion of his work. 



The slip in arithmetic occurred in the formula which, 

 though Dr. Mills has never employed it himself, is the first to 

 which any one desirous to make use of his results would turn. 



