318 Intelligence and Miscellaneous Articles. 



the values of t and H that t would be expressed by VH; and as, 



besides, the value of the intensity of the current is -o ■ -u - (R being 



the resistance of the exterior circuit, E the electromotive force of 

 the source of electricity), the magnetic moment F of the needle 

 would be 



p = EVH ...... 



E + H' 

 an expression susceptible of a maximum for B=H. 



But in reality the value of t is far from being expressed by VH ; 

 and if we amend the preceding formula by inserting the true quan- 

 tities, we arrive at altogether different conditions. g 



In fact, let a be the thickness of the layers of spires, b the width 

 of the galvanometric framework, c the diameter of the circular part 

 which terminates it on each side, d the length of the framework 

 between these two circular portions, and g the diameter of the wire 

 (including its insulating covering) ; the number of the turns t will 



be expressed by — , and the length H of the helix by 



consequently the magnetic moment F of the needle will be 

 -p__ ccEab 



g 2 R -f db\_{a -j~ c)tv + 2cV 



a denoting the constant of the instrument. Now the conditions of 

 a maximum for this formula, taking a for variable, which is the sole 

 quantity proportional to t, lead to the relation 



Eirba* 



which shows that the resistance of the galvanoineter-wire must be 

 greater than that of the exterior circuit by a quantity represented 



We can, moreover, easily assure ourselves of the truth of this de- 

 duction by supposing the framework of the galvanometer repre- 

 sented by a simple coil, as in the Thomson galvanometer, and 

 taking the magnetic moments of the needle with the two lengths of 

 the wire of the helix corresponding to the two conditions for a 

 maximum given by Mr. Schwendler and me. For greater simpli- 

 city, we will represent the diameter c by 2r. In these conditions 

 the length H of the helix, instead of being greater than the resist- 

 ance B by a quantity represented by — (vc+ 2d), will be greater 



7 (J 



only by a quantity —ttc, or will be, in proportion to K ? as a+2r is 

 to a, "We shall therefore have :— - 



