Calometric Absolute Measurements. 129 



development cannot be unhesitatingly made use of for the 

 absolute determination of resistance. 



In order to procure the means to enable me to carry out an 

 entirely unexceptionable determination of the absolute value 

 of the S. M. U. by the heat-evolution of stationary galvanic 

 currents, I undertook, in a very extensive and in many ways 

 varied third experimental investigation, as rigorously exact a 

 solution as possible of the question : — In a stationary galvanic 

 current in which evolution of heat appears as the only action, 

 is the heat generated in a certain time the exact equivalent of 

 the mechanical work consumed by the current during that 

 time ? 



In the path of a current maintained constant, of which the 

 absolute intensity i was carefully measured electromagnetieally, 

 was placed a thin platinum wire of about 15 S. M. U. resist- 

 ance, wound in zigzag upon a numerously perforated frame 

 of hardgum. Thick copper wires conducted the current to 

 and from the platinum wire. The frame carrying the wire 

 was suspended in a water calorimeter of the thinnest sheet 

 copper, which was in an environment of constant temperature. 

 The water filling the calorimeter amounted to about 250 grams ; 

 the water-worth of the calorimeter-vessel, the frame, and the 

 thermometer amounted to about 3 grams. 



The constant current with the intensity i was conducted, 

 during the time z, through the resistance w in the calorimeter. 

 The mechanical work consumed by the current during this 

 time, within the conductor with the resistance w, was then 

 Pwz. On the other hand, a certain amount of heat Q was 

 generated in the resistance iv, was given up to the calorimeter, 

 and was to be calculated from the rises of temperature in the 

 calorimeter, the water-worths of the substances filling the 

 calorimeter, and the losses of heat of the calorimeter by radia- 

 tion outwards or the gain of heat by the calorimeter from 

 without. The mechanical value of this amount of heat, JQ, 

 would necessarily, if the total work of the current were con- 

 verted into heat, be equal to rwz. 



On the hypotheses that the entire work of the current is 

 converted into heat, that the exchange of heat between the 

 calorimeter and its surrounding is governed by Xewton's law, 

 that the specific heat of water increases linearly with the tem- 

 perature, and that the resistance of the platinum wire used in- 

 creases proportionally with the temperature, the following 

 differential equation holds for the dependence of the variable 

 temperature t of the calorimeter on the time z: — 



Mcll + y(t-t a )yt=^[l + q(t-tJ]dz-h(t-t a )dz. 

 Phil. Mag. S. 5. Vol. 5. No. 29. Feb. 1878. K 



