100 Dr. 0. V. Burton on a 



example, let us trace the consequences of supposing that the 

 negative electrons alone possess sufficient mobility to enable 

 them to mi orate through unrestricted distances within the 

 mass of a solid conducting substance; the negative electrons 

 thus serving to convey the whole of any current which may 

 be flowing in the substance. In a cylindrical conductor 

 whose axis is vertical, let a current be flowing upward ; 

 consider what happens when negative electrons whose aggre- 

 gate charge is — e% pass downward through the cylinder, 

 and in particular through a certain stratum of the cylinder, 

 bounded above and below by horizontal planes, whose distance 

 apart is h. According to our notation, — e^is the aggregate 

 charge of the negative electrons which are comprised in one 

 gram of neutral matter, and which have collectively the mass 

 /x 2 , experiencing in a gravitational field of intensity g the 

 force yu^Ys^? measured downward, so that the work done 

 by gravity while the quantity — e% moves downward through 

 the stratum h is ptfiigh. There is thus virtually, correspond- 

 ing to a height h of the conductor, an electromotive force 



~~ /W2 9^ l l e X (measured downward) ; . . (65) 



the quasi-electromotive-intensity due to the action of gravity 

 being therefore 



— fJL 2 y-2<// 6 X (measured downward). . . . (66) 



53. If, in place of gravity acting, an acceleration / is 

 impressed on an isolated conductor, then the negative elec- 

 trons of total charge — e^;, having an aggregate mass fi 2 . 

 must experience, when there is electrical equilibrium, a re- 

 sultant force fjL 2 f, and in virtue of the assumed mobility of 

 the negative electrons, this resultant force fi 2 f must be due 

 to an electrical distiibution on the conductor in question. 

 But an electrical distribution which would exert the force 

 ^2/ <?n certain electrons is precisely that distribution which 

 would arise from such an external field as would by itself 

 exert the force — /j, 2 f on the same electrons. In other words, 

 the conducting body caused to move with acceleration /', 

 becomes electrified precisely as if it were placed in an 

 electrostatic field of intensity 



fhfl*X- (67) 



If we take / to be vertically downward, and identical in 

 value with g, we find by combining (66) and (67) an ex- 

 pression for the virtual electrostatic field clue to the action of 



