MR. C. V. BOYS ON THE RADIO-MICROMETER, 
173 
if the field is more than strong enough, the extra resistance to the motion so increases 
the time of coming to the resting place that the loss of time more than counter¬ 
balances any advantage given by the increased ultimate sensibility. If the ultimate 
sensibility is required to be made a maximum, then the expressions found are the best, 
and, the stronger the field, the better; but, if the best combination which is dead beat 
(and no more than dead beat) is required—and this is what any one who has used 
both would require—then the lengdh and the sectional area already found are not the 
best, unless the strongest field which can conveniently be employed is not strong 
enough to make the motion dead beat. In the particular case it is more than strong 
enough. 
It is necessary, therefore, to introduce the effect of another variable, the strength of 
the field, the relation between it and the rest of the circuit being such that the 
motion is just dead beat. 
It is well known that motion ceases to be oscillatory when half the coefficient of 
resistance to the motion is equal to the square root of the acceleration when the 
angular displacement is unity. In the investigations depending on these relations the 
following symbols will have the meanings attached to them :— 
S. Sensibility, i.e., efficacy X enclosed magnetic field. 
A. Area enclosed by the circuit. 
oi. Angular velocity. 
T. Time of a complete undamped oscillation. 
G. Conductivity of the vdiole circuit. 
a. Angle included between the plane of the circuit and the direction of the lines 
of force, supposed parallel to one another. 
K. Moment of inertia of the whole circuit, i.e., K + Z:. 
H'. The minimum strength of magnetic field for which the motion is dead beat. 
This will hereafter be called the dead beat magnetic field. 
The resistance to the motion of the circuit 
= G X H" X A^ X ftj X cos^ a ; 
half the coefficient of resistance = GH^A^ cos^ a/2/c'. 
Since the magnetic field is radial and is everywhere cut normally by the side wires 
of the circuit, the factor cos^ a ought to be omitted. Owing to the small possible 
angular deflection, it could not in any case differ appreciably from 1. 
Stt 
-^(acceleration at unit angle) = — • 
Since, when the motion is just dead beat, half the coefficient of resistance is equal to 
-v/(acceleration at unit angle), 
27r 
2 k ' ' ~ T ’ 
