130 Prof. H. F. Weber on Electromagnetic and 



In this equation, M denotes the sum of the water-worths of the 

 substances filling the calorimeter, t a the constant temperature 

 of the environment of the calorimeter ; c a the specific heat of 

 water, and w a the absolute resistance of the platinum wire, at 

 the temperature t a ; 7 the coefficient of the increase of the 

 specific heat of water, and q the coefficient of the increase of 

 the absolute resistance of the platinum wire, for 1° rise of tem- 

 perature ; and h the heat which the calorimeter would part 

 with to the outside if its temperature were 1° higher than that 

 of its environment. 



T p , A v* w a i -d Jh — (q—y)i 2 iu a , 



It we put A= -..-■■ and B = VW and assume 



r J Mc fl JMc a 



that at the time z = the temperature of the calorimeter is 

 equal to t , the integration of the above differential equation 

 gives the following connexion between the variable temperature 

 t of the calorimeter and the time z : — 



<-«o=(g-«o + 4)(l-e- B 0; • • . . (1) 



or if the notion " mean temperature of the calorimeter during 

 the time z = to z—z " be introduced with the symbol 7, 



jm a [t-t + B(t-t a )z = i 2 w a z. .... (2) 



The quantity B(t—t a )z represents the temperature-correction 

 which must be applied to the direct reading of the rise of tem- 

 perature of the calorimeter on account of the heat-exchange 

 with the environment, and on account of the variability of the 

 resistance as well as that of the specific heat of water with 

 rising temperature. This correction can be made as small as 

 we please, by a suitable selection of the quantity t— t a . In 

 all the measurements executed, care was taken so that this 

 difference only amounted to so small a fraction of a degree 

 that the correction, B(£ — t a )z, to be added to t— 1 amounted to 

 only from s ^q to 20Q °f t ~ i o- The period z was chosen so 

 great that the rise of temperature amounted to about 15°. For 

 the determination of the mean temperature t of the calori- 

 meter, and of the constant B, the temperature of the calori- 

 meter was read off, from the commencement onwards, every 

 five minutes ; in this way a series of equations of the form (1) 

 were obtained, from which B could be ascertained. The ther- 

 mometer of the calorimeter was most carefully compared, within 

 its entire scale, with the air thermometer ; all readings taken 

 from it were always reduced to the indications of the latter 

 instrument. 



