166 
MR. C. V. BOYS ON THE RADIO-MICROMETER. 
Considering, first, the case of a circuit of only one turn of wire, the variable 
resistance r and weight iv of the wire will be 
r = (2Z + ^ 5 ) V o, 
'll) = {2l p) u' X a. 
The conductivity G of the whole circuit will be 
^^ ^ 
(21 + _p) v + aC 
The efficacy of the circuit with respect to its weight, i.e., the moment which it 
can exert upon a unit field for every gramme that it weighs when unit E.M.F. is 
acting at the junction, is 
_ Z X G _ he 
~ W + w “ {{21 +p)v + «C}{W+ {21 + p)au'} ' 
Now, it is evident that there must be a maximum value for E,^./, both when I and 
when a is varied, for, if either is made very great or very small, more is lost than 
is gained. If, therefore, the expression for E,;.,,; is treated in the usual way to find the 
two maxima, the result will be found to be 
best a = 
(W + pavJ) {pv + «C) . 
4:vaio' 
( 1 ), 
or, substituting the value of a above, it will be found that 
( 2 ). 
If, further, the circuit is supposed to have n turns, the corresponding expressions 
will be 
/\Nv 
V.7c’ 
V ew 
u'v 
(3). 
Thus, the size of wire that is most suitable is independent of the length of the 
rectangle or of the number of turns. The numerical values of these quantities for 
1 . . . 5 turns are as follows:— 
