162 REPOET— 1892. 



than the calculated. The difference between the real and apparent 

 temperature of the case would be too small sensibly to affect the result 

 until the absolute excess u became comparatively small. We are not, 

 however, concerned with such small excesses u in the actual use of the 

 instrument. The lagging time deduced came out 5'6 minutes. 



The reciprocal of this was then introduced into equation (2), which 

 was then applied to the reduction of the first portion of the observation, 

 that portion, namely, which was concerned with the rise of D consequent 

 on exposure. As and T are observed and q deemed to be known, the 

 equation contains only two unknown quantities, namely, r, which depends 

 on the radiation, and the ai'bitrary constant c. These might be deter- 

 mined by any two not unfavourably selected observations of the series, 

 and then the observed and calculated values of u ought to agree for the 

 rest. This, however, was found to be by no means the case, and the 

 differences between theory and observation wei'e far too methodical to ba 

 attributable to errors of observation. Equation (2) was then tried as a 

 mere formula of interpolation, q being taken as a disposable constant as 

 well as r and c. Any three observations would of course theoretically 

 suffice for the determination of the three constants, and then the formula 

 would give the calculated final excess, to which r is theoretically propor- 

 tional, or the calculated value of u for any other observation of the series. 



The numerical calculation is much facilitated by choosing for the 

 determination of the constants three observations equidistant in time. 

 If t„ be the time of the first of the three and Ai the chosen interval, we 

 have from (2) 



1*0=- + ce '" ; 



These equations give 



1 

 Atto=— ce-'^'°(l — e-'^') ; 



A2«o=ce-'"°(l-e-«^')"- 



which determines q, and then 



2-"*° ~A^«T' 



which gives the calculated final excess. 



A rough calculation showed that four minutes was a very suitable 

 interval A^ to choose, which also agreed with the result of actual trials. 

 When various trios were taken from different parts of the series not too 

 near the end, as there the differences became small, and consequently 

 errors of observation would be telling, the calculated final excesses came 

 out remarkably accordant. It thus appeared that equation (2) was no 

 mere formula of interpolation, but that it was very well satisfied, pro- 

 vided, at least, the higher part of the series were not included. The 

 limit to which the excess tended when it had become nearly stationary 

 was evidently a little, though only a little, lower than the calculated 

 limit. This is not to be wondered at, because in the calculation it was 

 assumed that the cooling followed Newton's lavv, which it is known is 

 not sufficiently accurate when the excess of temperature is as great as 

 40° or 50°, the cooling in such a case being more rapid than if Newton's 

 law had been followed exactly, the constant involved in it being determined 

 by observations taken with more moderate excesses of temperature. 



