164 
MR. C. V. BOYS OY THE RADIO-MICROMETER. 
large, the enclosed magnetic field will be increased; but, supposing the period of 
oscillation to remain invariable, the moment of torsion must be increased, and, further, 
the resistance may be increased. Both of these actions will reduce the sensibility. 
Let it be supposed that there are two instruments in all respects the same, except 
that the circuit of one is n times the length and is 7i times the width of that of the 
other, and let it be supposed that the thickness of the bar and of the wire of the circuit 
is the same in each case; the value of the enclosed magnetic fields will be as : 1 ; 
the moment of inertia, and therefore tlie moment of torsion, will be as : 1 ; and the 
resistance as n :1. Therefore, magnetic _ fi e l cl ^ ^ angle 
torsion X resistance 
of deflection will be times as great in the smaller as in the larger instrument. But 
there is a limit to the smallness, owing to two causes. The moment of inertia is made 
up of two parts, the circuit and the mirror, on which account, when the moment of 
inertia of the mirror becomes comparable with that of the circuit, the smaller instru¬ 
ment will have a greater moment of inertia, and, therefore, its sensibility on this 
account wfill be less than that given by the above rule. 
The second reason why there is a superior limit to the sensibility as the instrument 
is reduced in size is due to the fact that the sensitive plate conducts more heat from 
the hot to the cold junction in the case of the shorter plate, and thus, for a given rate 
of radiation, the junction will not be so hot; and, hence, the current will be less than 
it \vould be if the diminished resistance were the only cause of change. It is, there¬ 
fore, necessary to choose some length of plate or width of rectangle wdiich can 
conveniently be made in practice, and, assuming this as a constant, to find by 
calculation the best values of all the variables, and so, as it were, to fit to the plate 
the best possible instrument. Something must be assumed as a starting j^oint, and 
this seemed, on the whole, the most convenient. I have assumed the plate, then, to 
be composed of two squares of antimony and bismuth, each 5 mm. in the side and 
^ mm. thick, soldered edge to edge, thus forming a plate 10 X 5 X ^ mm. This 
assumption I have made simply for the sake of numerical calculation; any size may 
be equally wmll taken as the basis of operations, provided that in the equations which 
follow" the proper numerical values are assigned to the constants. 
Of the three dimensions of the plate, the length, the thickness, and the breadth, 
the first twm only need be considered as assumptions which can in any way aflect the 
result, for it matters not how the breadth be varied, provided that the sectional area 
of the wire and the moment of torsion are varied in the same proportion, i.e., if the 
whole breadth is exposed to the radiant energy. 
It w"ill first be convenient to see how the circuit can be formed, so as to give the 
best results Avhen the magnetic field is suj^posed constant; it w"ill be seen later that 
this best is not the ultimate best when the field and the circuit are adapted to one 
another. 
