6 Messrs. Thorpe and Riicker's Remarks on 



zero, the total ascent one would naturally suppose would be 

 equal to the total depression ; or, if the secular elevation of 

 the zero could not be neglected, the " total ascent/' however 

 it might be compounded of this and of the temporary effect due 

 to heating, would at all events increase with the temporary 

 depression. 



The table, however, shows that y grows less as the depres- 

 sion of the zero increases ; and it is only from it that we are 

 able to gather the relation between y and the position of the 

 zero. If 



y — ka. x — B/3% 



and Z be the change in the position of the zero (depressions 

 being taken as negative), then 



Z=-{A=B-^ = -2 + </ 

 in the example given. 



But though this expression is algebraically similar to that 

 obtained for the secular movement of the zero, the meaning 

 of the quantity y is quite different. In the first case it is the 

 amount by which the reading for the zero falls short of a posi- 

 tion which may be attained at some future time. In the 

 second case it is the amount by which the depression of the 

 zero falls short of that which may be produced by some future 

 heating. If therefore any such name is to be applied, it should 

 here be the total remaining descent. Even with this modifi- 

 cation, however, the nomenclature is very misleading, as there 

 is nothing to show that the points from which the "remaining" 

 ascent or descent is measured are really limits to the motions 

 of the zero. 



The experiments on three other thermometers (455, 3, and c) 

 are then described: — 



" The results for thermometer 3 are given in terms of its 

 scale, one division of which was equal to o, 280. The equa- 

 tions are — 



yaw = 2-869 (-998)* -•143(1-324)*, 



3/ 3 =4-723(l-006)*--723(ri964)*, 



y c =l-112(-9986)*--112(l-299)*. 



the values of a unit of x being respectively 13°, 20°, 38°." 



It will be observed that all these expressions are similar to 

 that given above for Henrici's thermometer. In all y is posi- 

 tive for small values of x ; in all it diminishes as x increases. 

 The three formulae are illustrated by a table ; and for all three 

 the tabulated values of y are of the same sign. Both formulae 

 and table would therefore lead us to expect that, as in the case 



