142 Mr. A. B. Basset on the Induction of Electric Currents, 

 whence equation (4) becomes 



„^(P + F)=o* (5) 



The value of the electric potential yjr may be obtained as 

 follows. From Maxwell, art 600, 



^^'-F^-G^-H'i ; .... (6) 



where ty is the quantity which appears in art. 658, and which 

 is therefore zero ; ^ is the quantity which appears in art. 668*; 

 and F', G', H 7 are the components parallel to moving axes 

 x, y, z of the total vector potential due to the influencing 

 system and the currents. In the present case, 



x = — toy, y = eox, 2=0 ; 



H4 + *l) (p+F) 



=°>»| (P+F) • • & 



at the surface. 



If we change the signs of P and P', it will be seen that (5) 

 and (7) agree with Prof. C. Niven's results t. 



4. Another result, which is more convenient for practical 

 purposes, may be obtained as follows. - 



Taking account of (3), equation (2) may be written 



p =f(f- <B |) dT+/( ^^ ); 



and since /(^ + Rt, p, </) + wt) vanishes when t=qo, 



P=-w| -ndi, 

 Jo # 



Differentiating with respect to z, we obtain 



°— fw* 1 .' ••••• (8) 



where IV is the magnetic potential at the instant under con- 

 sideration of the currents which were instantaneously generated 

 at time r ago. 



5. Let us now suppose that we have a long thin bar-magnet 



* It should be noticed that the two ^'s in Maxwell's investigation do 

 ; the same quantit 

 ans. 1881, p. 342. 



not represent the same quantity 

 f Phil. Tin 



