184 
MR. C. V. BOYS ON THE RADIO-MICROMETER. 
But the point that requires special correction is the estimate formed of the greatest 
possible sensibility. This was calculated on the assumption that an instrument could 
be used practically when a particular circuit had a natural vibration period of 20 
seconds, and was suspended in a field of 10,000 units, produced by an electro-magnet. 
Without entering on the question whether an electro-magnet could be used, it is 
sufficient to say that the resistance to the motion would be so great, the instrument 
would be so much more than just dead beat, that the time of coming to rest would be 
enormously prolonged. Thus, though the figure given is correct, the conditions to 
which it refers would not practically be advantageous. 
It is, then, wfith some satisfaction that I turn to the result given by an instrument 
of the narrow form, having the best proportions. I have now taken quantities which 
can not only be separately obtained, but which can be used together, and which I 
have actually used with success. 
Under these conditions, the least difference of temperature that could be observed 
with certainty, that is, one giving a movement of the light of ^ mm. on the scale, 
would be due to a temperature difference of less than one two-millionth of a degree 
Centigrade. This figure is obtained by putting in the values of the quantities in the 
formula for temperature, which may be expressed in a variety of ways. The following- 
are convenient:— 
y/K.Cuv 
3TTO ’ 
Temperature difference = 
or, if the dead beat magnetic field for such a circuit be employed as well. 
Temperature difference = ^ ■s/KC. 
a! is the least observable angle of deflection (supposed lo.oo b )? 
d, the thermo-electric power (supposed 10,000), 
T, the natural vibration period (supposed 10 seconds), 
K, C, "14, and v as before. 
The temqjerature difierence 8’06 X 10“'^, found from the equation above, must be 
multiplied by y to give the corresponding figures for the circuit of reduced length. 
Tests made with an instrument of the narrow form, in which it was evident that 
tlie magnet still acted to a slight extent on the materials of the suspended portion, 
show it to be in practice exceedingly sensitive, and, what is of even more importance, 
the equilibrium of the moving parts remains perfectly stable. The surface which 
receives the radiant heat is in a particular case a disc only 2 mm. in diameter, and 
when the scale is 30 inches from the mirror, the hand held about a yard from the 
instrument produces at once a deflection of 16 cm. A candle flame at 9 feet produced 
