Degrees of Heat in Absolute Measure. 71 



showed such small agreement among each other that they must 

 be left out of consideration. 



As the average of twenty-eight experiments with water, we 

 obtain 



a = 2-543xl0- 10 ; 



and of ten experiments with oil of turpentine, 



a = 2-652xl0- 10 . 



There is no greater difference between these two values of a than 

 might have been expected from the greater conductivity of water ; 

 hence the latter number must be taken as that which follows 

 with the greatest probability from Quintus Icilius's experiments. 

 With this value of a we obtain 



S = 2-720A = l-16xl0 10 ; 



that is, exactly the same value for Siemens's unit of resistance in 

 absolute measure which we have deduced above from the thermal 

 conductivity of the metals. That it is exactly the same value 

 must, of course, be regarded as accidental. 



In another way also we obtain a confirmation of the accuracy 

 of the law here propounded, since we shall find that in this law 

 there is the closest agreement between the laws for the propa- 

 gation of energy in metals, no matter whether this transmission 

 is effected by the motion of heat or of electricity. 



By energy we understand any magnitude which can be mea- 

 sured by units of work. We will consider only the propaga- 

 tion of heat and of electricity so far as it is effected in both 

 cases by conduction ; so that we may waive any considerations as 

 to the propagation of heat in the interior of a body by radiation 

 and by thermoelectric currents, just as in the case of electricity we 

 neglect the propagation by induction and by therm oelectrical 

 currents. 



If by Q we denote the energy present in a body in the 



unit of volume, the increase -rrdt, which Q experiences by ther- 

 mal conduction in the form of heat in the element of time dt } is 

 expressed by 



dQ_± ^dT d_ dT d dT 



dt dx dx dy dy dz dz } ^ 



where T is the temperature and k the thermal conductivity, 

 which may in general be regarded as a function of the tempe- 

 rature. 



If we substitute in this, in accordance with the law propounded 

 above, 



K = kT, 



