72 Prof. L. Lorenz on the Determination of 



where k is the electrical conductivity, we obtain 



2 Q = d_ k *r ± k m d_ k sp # _ (3) 



dt dx dx dy dy dz dz ' 



in which equation all the magnitudes may be considered to be 

 expressed in absolute units. 



As the increase of energy here only occurs in the form of heat, 

 it stands in a known relation to the increase of temperature, 

 dependent on the specific gravity and the specific heat ; and the 

 equation gives therefore completely the law for the propagation 

 of heat by conduction. 



If in any point x, y, z of a body the components of the inten- 

 sity of the current are u, v, w, and if k is the electrical conduc- 

 tivity, the quantity of heat received by the element of volume 

 dx dy dz in the element of time dt is, according to Joule's law, 



U -J- q)" -4- yj" 



T dx dy dz dt. 



If this element of volume contains at the same time the quantity 

 of electricity e dx dy dz, and if the electrical tension (potential) 

 there is P, the element acquires at the same time the energy 



¥ -j- dx dy dz dt 



in the form of electricity. If, then, as before, Q denotes the 

 energy present in the unit of volume, the increase arising from 

 the motion of electricity, and which occurs both as heat and as 

 electricity, is 



-df~ V dt+ I (6) 



In like manner, if we disregard the electricity which results 

 from induction, from Ohm's law we have 



y=s -*3P "=-*-*> w =- k HP ' * (4) 



in addition to which we have Kirchhoff's equation 



de _ (du dv dw\ 



dt~ ~\dx + dy + di) p ' 



Thus 



dt " \dx dy dz J \ dx dy dz r 



from which there follows 



dQ (du? dv? dw? \ 



dt ~ \dx + dy + dz I 9 ' * ' ( ' 



