74 Prof. L. Lorenz on the Determination of 



this equation in combination with the given limiting con- 

 ditions. 



The motion of electricity is here looked on as permanent ; 

 that this may completely be the case, the heat developed (which 

 in this case represents the total increase in energy) must be 

 conducted away. In order now to develop further the ana- 

 logy between electrical tension and temperature, we will imagine 

 the corresponding suppositions applied to the motion of heat in 

 a body ; that these suppositions cannot in fact be fulfilled may 

 in this case be disregarded. 



We consider a body in which the motion of heat is kept per- 

 manent, and in which the entire energy which heat can produce 

 in the form of work in passing from a higher to a lower tempe- 

 rature is conducted away from every point of the body. 



If, now, the quantity of heat W at the absolute temperature T 

 is added to a body in every second, and simultaneously and con- 

 tinuously therewith the quantity of heat W, at a lower tempe- 

 rature Tj passes away by conduction, the condition remains un- 

 changed if the entire difference W— W x is converted into work ; 

 and, in accordance with the mechanical theory of heat, the entire 

 amount of work which the quantity of heat W can produce in 

 the change of temperature T to T l is obtained if we have 



W_ W 



If we put for the three coincident surfaces of an infinitely 

 small rectangular parallelepiped 



W 



TfT = f dy dz + rjdxdz + ^dx dy, 



we have for the other three surfaces 



T&-( f+ J*)** + (' + 'S)** + & + S**' 



and equation (9) will then give 



dx dy dz ' •'•-{) 



In this case Tf dy dz is the quantity of heat transmitted 

 through the surface dy dz in the unit of time; but this is also 



defined by — k— -dy dz if k is the thermal conductivity; then 



^~ T X dx~ k dx> 

 and in the same manner 



, dT y .dT 



