176 
MR. C. V. BOYS ON THE RADIO-MICROMETER. 
Making use of the same methods and symbols, but neglecting the now infinitesmial 
effect of the cross wire, the following equations will be found to hold :— 
best 
I fYiv 
' & V . 
• (14). 
best 
1 /KC 
n V . 
• (15), 
greatest 
F ^ 
8^(KCioq. 
. (16). 
Further, it will be found that 
C = — and K = 2 lanh^, 
a 
and thus the copper hoop must be so proportioned that its resistance may be equal to 
the dead resistance, and its moment of inertia to the dead moment of inertia. It is 
also found that under the supposed circumstances, namely, that the cross wire is of no 
account, the efficacy is independent of the breadth, and the only effect of an increased 
breadth is to require a diminished sectional area of wire and a diminished length; 
thus, during variation of the breadth neither the resistance nor the moment of inertia 
of the copper wire is changed. 
The exjDression for the dead beat magnetic field, when the circuit of greatest efficacy 
is used, is, as before, 
H"=8y'^y«f.(17); 
and this seems to be very generally true. 
The sensibility under these conditions is 
. 
which shows that, no matter what the material of the hoop may be, if the dimensions 
which give the greatest sensibility in any given magnetic field are employed, and if the 
field is so strong that the motion is dead beat, the sensibility will always be the same, 
and this will only depend on the resistance and moment of inertia of the invariable 
part of the circuit. 
Since, as in the case of the wide circuit, the magnetic field that will make the 
motion of the best narrow circuit dead beat is far less than that which is available, 
it will, as before, be best to employ a circuit so much smaller than the best as will 
just make the motion dead beat. 
