210 Dr. Ritchie's Remarks on Mr. Christie's 



to the lengths of L', L" of the conducting wire on each side, 

 from the helix to the galvanometer, and to the arcs A', A"; 

 and suppose that the intensity varies inversely as L" ; 



then ^= l - = ^1^.» 

 I/» I" sin±A" 



This principle requires to be carefully examined. It is well 

 known that the velocity of a pendulum at the lowest point is 

 proportional to the chord of the arc (or to the sine of half the 

 arc) through which it has descended, and that the same law 

 holds with terrestrial magnetism acting on a horizontal needle. 

 " En general, le parallelisme de direction des forces magne- 

 tiques terrestres qui sollicitent les divers points d'une aiguille 

 aimante permet d'appliquer a tous ces phenomenes les consi- 

 derations usitees dans la theorie de la pesanteur*." Now 

 Mr. Christie has assumed, without a shadow of proof, that a 

 needle placed directly above a wire, and acted upon by a series 

 of successive impulses so as to deflect it a certain number of 

 degrees, will have the same velocity at the commencement of 

 its motion as if it had descended from that point by the force 

 of terrestrial magnetism. 



It is a well known principle that a body at rest being put 

 in motion must pass through all the degrees of velocity from 

 up to the maximum velocity, and that it cannot gain this 

 velocity till the end of a definite portion of time after the com- 

 mencement of the motion. This definite portion of time may 

 be longer or shorter according to the nature of the action. 

 If the action be instantaneous, the time may be neglected, as 

 being indefinitely small ; but this is far from being the case in 

 the present instance. The needle, instead of acquiring its 

 maximum velocity at the commencement of the motion, may 

 not reach that velocity till it has moved through several de- 

 grees from its position above the conducting wire. 



This conclusion is in perfect accordance with the curious 

 properties of electro-magnets which I communicated to the 

 Editors of the Lond. anrl Edinb. Phil. Mag. last summer, and 

 which are published in vol. iii. p. 122. I there showed that 

 magnetic induction on soft iron is not instantaneously pro- 

 duced, nor does the induced magnetic state cease as soon as 

 the inducing power is removed ; but that it depends on the 

 length of the soft iron magnet employed. By employing soft 

 iron lifters of different lengths, the point at which the needle ac- 

 quires its maximum velocity may be made to vary at pleasure 

 from the zero of the scale. By employing needles of different 

 weights, the point at which the needle gains its greatest velocity 



* Biot, Traile de Physique, torn. iii. p. 20. 



