Action of a Galvanic Coil on an external small Magnet. 355 



p — l p + l 



Z _ Q-Q 8 + 9*)* Q + Q' + g')* 



x l g g 



the origin of the coordinates being the middle point of the axis. 

 This ratio determines the direction of the magnetic current at 

 the point P, and, according to our theory, gives also the direc- 

 tion of the current which would be produced at the same point 

 if the magnet were replaced by a galvanic coil having an axis of 

 the same length, so far, at least, as the current is due to what 

 I have named the indirect action. If r L\ and X ; x represent the 

 directive forces in the same rectangular directions due to the 

 direct action of the coil, it follows from tbe results obtained in 

 arts. 46 and 47 that 



Z i_ \g-«i 9 + fli/ _ J \q-a l q + aj 



X'j n l — n 2 — n 3 -j-n /i 



Substituting now for n 1} % w 3 , n 4 the expressions given in art. 

 46, after putting a x for #, and supposing that #j is small com- 

 pared with the distance of the point P from the extremity of the 

 axis, which distance is C{p — J) 8 4-£ s )*j it will be found, by ex- 

 panding the right-hand side of the above equation so as to in- 

 clude only the first power of a v that 



* >, £i (A)V- (■+ (MLl 



x,-x.,- (l + (£fi)r ,_ (l+(£f , )T .- 



Since, as it is easy to see, the right-hand side of this equality 



Z 

 is a positive quantity, it follows that ~ is greater than 



Z' * 



^-i The meaning of this result is that the lines of motion 



pertaining either to the current of a magnet or to the current 

 indirectly produced by a galvanic coil, supposing the current to 

 issue in the positive direction, are less bent from the axis than 

 the lines of motion directly due to the circular motions about 

 the axis of the coil. Hence it appears that the lines of motion 

 due to the streams compounded of those resulting both from the 

 indirect and the direct actions will be more bent from the axis 

 than those of the magnet. These lines, therefore, supposing 

 them to pass through all the points P of the circumference of a 

 circle, the centre of which is on the axis of z and its plane per- 



2 A2 



