Properties of the Electric Field. 167 



motion of the positive tubes is the same as that given by 

 Prof. Poynting in the Philosophical Transactions, 1884, 

 part 1, p. 350. 



In those parts of the field where there is no resultant 

 electromotive intensity there will be as many positive as 

 negative tubes in the field, and when the field is steady the 

 positive ones will flow as fast in one direction as the negative 

 ones in the opposite. Let us consider a region close to the 

 circuit which we may here consider straight ; let h be the 

 sum of the strengths of the positive tubes in a unit of the 

 area at right angles to the current, u their radial velocity, ti 

 the sum of the strengths of the negative tubes, u l their radial 

 velocity. Then in unit time the number of positive tubes 

 flowing in plus the number of negative ones flowing out of any 

 cylinder coaxial with the wire, must equal t the intensity of 

 the current. If r is the radius of such a cylinder, the number 

 of positive tubes flowing in in unit time is hux2irr, the 

 number of negative ones flowing out h'u'x27rr; hence we 

 have 



(hu 4- h , u)27rr=i. 



But by equations (5) 



4w(Aw + A'w)=/3, 



if /3 is the magnetic force at the surface of the cylinder; as 

 this is at right angles both to the direction of the tubes and 

 also to their velocity, it will be tangential to the cylinder 

 and at right angles to the current. From these equations we 

 find 



„ 2i 



the usual expression for the magnetic force close to a 

 current. 



The radial momentum inwards =%h/3 = @Sh y hence the 

 radial momentum carried across unit area of the cylinder in 

 unit time 



47T* 



The electromotive intensity due to the motion of the tubes of 

 electrostatic induction is 



-2qft 



and is at right angles both to the magnetic force and the 

 direction of motion of the tubes, so that in the neighbourhood 

 of the current it will be parallel to the current. When the 



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