182 
MR. C. V. BOYS ON THE RADIO-MICROMETER. 
It is easy to show that this time is for the Peltier effect equal to where 
J is Joule’s ecjuivalent (4‘2 X 10’'), 
E, = 2C is the resistance of the whole circuit (67'42 X 10*^), 
s is the heat capacity of the two bars ('000798), 
t is the mean absolute temperature (taken as 290), 
9 the thermo-electric power (taken as 10,000). 
The time of ecjiialisation at a supposed constant rate is on this account 7 7'9 seconds. 
This is true of the circuit of greatest efficacy; if the circuit of reduced size is 
employed, that is, one with a length one-ISI‘'' of this, then the total resistance R and 
the time of equalisation will he (N -j- l)/2N times as great. This can never be less 
than 
The corresponding time for the equalisation by conduction may he taken as equal to 
s//Da, where 
I is the length of the bars, 
a their sectional area (separately), 
D the sum of the conductivities of antimony and bismuth, i.e., '0607, 
The value of this time is 2'63 seconds. 
Thus, conduction appears to be far more important than the Peltier effect, which, 
})ractically, may be left out of account. It can only become comparable when so 
much heat is lost by radiation that the rate of conduction at the cool end is-far less 
than at the hot end, but in this case they would neither be of any practical 
importance in comparison with the radiation. 
The data for finding tlie time for the escape of half the quantity of heat by 
radiation, contact of air, &c., are of doubtful value, on account of the very small 
size of the bars. But taping Professor Tait’s figure, given in Burton’s Tables, for a 
black surface, the time would be about 29 seconds. Though no great value must be 
attached to this figure, it would appear that conduction is the main cause of the 
equalisation of the temperature of the circuit. 
The Peltier effect is involved in another manner in the action of the instrument. 
It must make a difference in the value of the least magnetic field w'hich is necessary 
for the dead beat conditions. Thus, during motion of the circuit, currents are 
induced which oppose the motion ; but these currents set up difierences of tempera¬ 
ture, which oppose the currents. Therefore, a stronger field may be employed before 
the dead beat conditions are reached. It is hardly necessary to do more than state 
that, as the result of calculation, no appreciable change is made in the value of the 
dead beat magnetic field on this account. 
I nmst here mention the only difficulty which is apt to be found in practice. It 
arises from the magnetic jiroperties of many materials which, insignificant though 
they are under ordinary methods of observation, become of serious importance when 
