MR. C. V. BOYS ON THE RADIO-MICROMETER. 
165 
The circuit may be considered best from more than one point of view. It may be 
with respect to weight, or with respect to moment of inertia. 
The best circuit with respect to weiglit would be that which would give the greatest 
deflection when supported by a particular bifllar arrangement free from torsion. The 
strength of the field, the thermo-electric power of the junction, and the value of the 
radiation, being constant factors, may be omitted for the present. 
Let the following be the meanings of the several symbols that will be used :— 
The weight of the plate, mirror, and stem, the invariable or dead 
weight. 
The weight of the hoop of copper, the variable weight. 
The resistance of the plate, the invariable or dead resistance. 
The resistance of the hoop of copper, the variable resistance. 
The length of the rectangle. 
The number of turns of wire. 
The weight of a unit piece of copper (1 X ’1 X ’01 cm.). 
The resistance of a unit piece of copper (1 X ’1 X ‘01 cm.). 
The sectional area of the wire (T X '01 being considered unit 
area). 
The reason for taking 1/1000th of a square centimetre as the unit of sectional area 
for the wire is that this is not very difterent from the actual sizes that will be 
required, and that it avoids the absurdity of supposing a hoop of wire of such a size 
made of wire of 1 sq. cm. in sectional area. It is a matter of convenience, and 
nothing more. The mirror that I have used is 6 mm. in diameter, and weighs 
•04 grin. Tire glass stem may be taken as '005 grm. The weights and resis¬ 
tance of the three metals are taken from Lupton’s Tables, and the numerical 
values of the several cj[uantitles so calculated are enclosed in parentheses before their 
respective symbols. All the quantities, except when otherwise specified, are in 
C.G.S. units. 
It is necessary to bear in mind that a certain excess of wire may be required, over 
and above that actually necessary to reach the active bar. Though in the numerical 
examples which follow I have not allowed for any, I have taken care in the equations 
to introduce a symbol, p, which must be explained. Imagine a circuit made of one 
turn 1 cm. wide and I cm. long : then, if there is no excess, the amount of wire 
will be 2? 1 ; but, if there is an excess, then the amount will be 2Z -f- 1 -{- excess. 
I have used the symbol p in the following calculations for 1 -j- excess, and I have 
assumed that both the resistance and the weight vary with the total length. The 
only possible discrepancy can be due to the manner in which the current leaves the 
wire for the plate. 
(•1481) 
W. 
w. 
(6-742 X 106) 
C. 
/ • 
1 
n. 
(•00895) 
u'. 
(1-642 X 106) 
V. 
a. 
