172 
MR. C. V. BOYS ON THE RADIO-MICROMETER. 
n. 
Best 1. 
E^.. 
Best a. 
1 
2-3366 
7-1863 X 10-® 
2 
1-4183 
3-4222 
o 
o 
1-1122 
2-1208 
> 1-0174. 
4 
-9591 
1-5014 
5 
'8673 
1-1500 
Thus, tlie best length and the best sectional area with respect to moment of 
inertia are each just over half the values found with respect to weight. One turn, 
of course, gives a greater efficacy than any other number, just as it did before, and for 
the same reason, but in this case one turn is more than twice as good as two, whereas 
it was only about one-fifth in excess. 
The result at present obtained, then, is this : provided a torsion fibre of convenient 
length can be obtained which shall in every case produce a certain pre-determined 
period, say 10 seconds, which, with my process for quartz, is possible even when the 
banging body is far lighter and smaller than any galvanometer mirror, then the 
moment of torsion and the moment of inertia will always have the same ratio ; 
therefore, the circuit which produces the greatest couple for its moment of inertia will 
also produce the greatest couple compared with the torsion, and will, therefore, give 
the greatest deflection. This circuit has been found above to have a length of 
2'3366 cm., and to be made of copper, having a sectional area of '0010174 sq. cm. 
at the sides. 
Though this circuit has the best length and the best sectional area under certain 
magnetic conditions, it is not necessarily the best when these are varied. 
It has, of course, been understood that in the comparison between long and short 
circuits the magnetic field is in both cases the same, and is uniform throughout the 
whole of the area enclosed by the circuit. This may or may not be true when an 
internal pole piece is arranged as shown in figs. 2 and 3. There must be some 
clearance above and below ; thus, the internal drum is always less than the actual 
length. It is therefore probable that the effective area is proportional to the length, 
less a small constant quantity. If this defect is equal to the sum of the clearances 
above and below the drum, then the length of the drum must be called I in the 
preceding formulse, and four times the clearance added to p. It is not possible to say 
exactly what is the error thus introduced into the calculations, but in no case can it 
be important. This, however, is a mere detail compared with the effect of very strong 
magnetism. 
When a closed circuit oscillates under the conditions in which that in the instrument 
is placed, induced currents are formed which oppose the motion, and thus, if the field 
is strong enough, or the conductivity great enough, the oscillatory character ceases, 
and the circuit slowly moves towards its resting place, more slowdy as it approaches it. 
It is a great advantage in an instrument that it should in tliis way be dead beat; but. 
