382 MR. W. HOPKINS ON THE CONSTRUCTION OP A NTT'S^ CALORBIETER 
does give with approximate accuracy the whole quantity of heat which emanates from 
a given surface under the conditions imposed by the instrument, for any values of 
t between limits which may be inferred from the experiments themselves. This is 
sufficient for my principal object — that of determining the absolute conductivities of 
substances of which, in a former memoir, I have given only the relative conductivities. 
It is certain that the whole quantity of emanating heat given by the empirical formula 
is approximately correct; the relative values of the two terms may possibly not be 
equally so. All that is proved respecting their relation appears to be, that it is inde- 
pendent of the difference of temperatures denoted by t. I pretend not to enter on the 
problem of determining the quantities of heat carried off by a surrounding gas by con- 
vection and conduction respectively, under any assigned conditions. 
Having the formula (1), we have next to determine the numerical values of the 
coefficients A and B. For this purpose, if effected independently, we should require 
two determinations of Q, for known values of 0, t, andy). In different series of experi- 
ments with radiating surfaces of the same natui’e (as glass, for example), the values of A 
are proportional to the areas of the radiating surfaces employed, the time during which 
the radiation takes place being always the same. These values also vary for smffaces of 
different kinds according to their radiating powers in a vacuum, of which it affords a 
relative measure. The values of B are considered the same for all surfaces, but are 
proportional to the areas of the radiating surfaces. Thus when an apparatus is used 
for the determination of Q, in which the area of the radiating suifface is the same, one 
determination alone of B is required for any number of surfaces ; and for the deter- 
mination of A one experiment at least is necessary -v^ith each kind of smfface. Duloxg 
and Petit determined these coefficients with great care for the surfaces of glass and 
silver, and the radiating surfaces (the bulbs of their thermometers) which they made use 
of ; and for either of those kinds of surface the values of A and B, in any other sets of 
experiments with glass or silver, will only vary from the above in the ratio of the areas 
of the radiating surfaces. In the following comparisons of the results of calculation and 
observation, I have adopted the values of A and B determmed by the French experi- 
menters increased in the proper ratio. Thus, taking A, and Bi to denote their coefficients 
for glass, we have 
A=?nAi, 
B=mB„ 
Q=m. A, «®(a'— l)-j-mBiy/i*, (2.) 
and one experiment only with glass is required theoretically for the determination of m. 
Also the coefficient mBj, when once determined, is determined for all surfaces of equal 
extent ; the coefficient mAj requires a separate determination for each kind of radiating 
surface. Practically the process has been to determine the mean value of m from a 
number of experiments, and then, adopting the corresponding values of the coefficients 
in (2.), to compare the calculated with the observed values. But before I enter into 
further details, I will describe the calorimeter which I have made use of. 
