488 Mr. 0. Heaviside on Resistance 



of uniform strength can produce no flux whatever. This is 

 instructively shown by the equation of activity, 



2er = Q + U + t, (31) 



indicating that the sum of the activities of the impressed 

 forces, or the energy added to the system per second, equals 

 the total dissipativity Q, plus the rate of increase of the stored 

 energies, electric and mngnetic, throughout the system. Now 

 here F consists of closed tubes ; if, therefore, the distribution 

 of e be polar, or e be the vector space-variation of a single- 

 valued scalar potential, of which a simple closed shell of 

 impressed force is an example, the left member of (31) 

 vanishes, so that the dissipation, if any, is derived entirely 

 from the stored energy. Start, then, with no electric or 

 magnetic energy in the system ; then the positivity of Q, U, 

 and T ensures that there never can be any, under the influence 

 of polar impressed force. Hence two shells of impressed 

 force of equal uniform strength produce the same fluxes 

 if their edges be the same ; not merely the steady fluxes 

 possible, but the variable fluxes anywhere at corresponding 

 moments after commencing action. The only difference made 

 when one shell is substituted for the other is in the manner of 

 the transfer of energy at the places of impressed force ; for 

 we have to remember that the effective force producing a 

 flux, or the " force of the flux/' equals the sum of the impressed 

 force and the " force of the field ;" whereas the transfer of 

 energy is determined by the vector product of the two forces 

 of the field, electric and magnetic respectively. In (31) no 

 count is taken of energy transferred from one seat of impressed 

 force to another, reversibly, all such actions being eliminated 

 by the summation. 



It is well to bear in mind, when considering the consequences 

 of this transferability of impressed force, especially in cases of 

 electrolysis or the Volta force, not only that the three physical 

 properties of conductivity, permittivity, and inductivity, though 

 sufficient for the statement of the main facts of electro- 

 magnetism, are yet not comprehensive, but also that they 

 have no reference to molecules and molecular actions ; for 

 the equations of the electromagnetic field are constructed on 

 the hypothesis of the ultimate homogeneity of matter, or, in 

 another form, only relate to elements of volume large enough 

 to allow us to get rid of the heterogeneity. 



As the three fluxes are determined solely by the vorticity 

 (to borrow from liquid motion) of the vector impressed force, 

 we cannot know the distribution of the latter from that of the 

 former, but have to find where energy transformations are 



