98 The Radio-Micrometer. [Apr. 19, 



These expressions give the proportions which will produce the 

 greatest deflection. But in case of a strong magnet the resistance 

 to the motion is so great as to be more than sufficient to make the 

 movement dead beat, and this is inconvenient. I have therefore 

 introduced the effect of this resistance into the equations, and found 

 expressions for the best circuit that is just dead beat. 



Calling H' the least magnetic field that will make the circuit dead 

 beat, 



G the conductivity of the whole circuit, 



K' the moment of inertia of the whole circuit, 



I have shown that — 



and that the greatest sensibility of a circuit that is just dead beat 

 is — 



" • *- Vr$ 



From these it is found that the best sectional area is reduced to about 

 three-fourths its previous value, but that the shorter the rectangle of 

 copper the better, until the greatest magnetic field that can be made 

 use of practically is reached. 



On considering variations of breadth in the circuit, it is found that 

 if the upper side of the rectangle — that which crosses the axis — is 

 neglected, the sensibility is independent of the breadth, and that the 

 following relations hold : — 



Best I = Jta/-. 



when b is the breadth, and that what I have called the greatest 

 efficacy E*, i.e., sensibility in a given field, is — 



¥ _ 1 



* ~~ 8n/(KCWT 



Since the cross wire becomes increasingly mischievous with an 

 increasing breadth of circuit, b cannot be made too small. 



Further, it appears that the copper wire should have the same 

 moment of inertia and resistance as the invariable parts of the 

 circuit. 



Other expressions are given, but it may be sufficient to state here 



