to be employed in Testing with Wheatstone's Diagram. 33 

 or after some simple reductions we arrive at last at the equation 



^^k^ l Lx 3 -2kx^k 2 = (3) 



w 



* The above equation of the fourth degree has only two real 

 roots, which are both positive. One of these two roots is always 

 larger than Vk, and the other smaller than Vk ; but as only 



%< Vk 



dY 2 

 makes -r-j negative, only this one corresponds to a maximum of 



Y and answers our question*. Thus 



x' 2 =g<k, 

 or 



Considering the insulating covering of wires, the resistance of 

 the space, which shall produce the maximum magnetic effect, must 

 be always smaller than the external resistance, and may be calcu- 

 lated numerically by equation (3) . 



If we substitute in equation (3) 



^5=0, i.e. 8=0 

 w 



(no insulating covering), we have again our former expression, 



x 2 =g = k; 



and therefore the difference between k and g depends in every 

 case on the coefficient 



m= 



w 



i. e. increasing with this coefficient. An inquiry into the nature 

 of this coefficient will therefore be of interest . 

 We had before 



and 



* The other root, a? > s/ k or x 2 =g > Jc, gives the maximum for Y, if the 

 positive sign of the square root in Y is adopted ; and the reason that equa- 

 tion (3) contains both these maxima is, that -—=0 is identical for both 



ax 



the Y, we may adopt the — or the + sign of the square root. 

 Phil. Mag. S. 4. Vol. 33. No. 220. Jan. 1867. D 



V 



v'c 



IT 



B 



AXir 



,c. 



w 



B 



! 





