August 27, 1885] 
NATURE 
395 
fact. For, n accordance with it, bodies of the same 
temperature continue to radiate heat to one another, and 
hence the thermometer will radiate heat to the concave 
reflectors, which we may suppose to be of the same 
temperature as itself. 
This heat will ultimately in great measure be reflected 
upon the ice or freezing mixture. Now, had this ice been 
of the same temperature as the other portions of the 
apparatus, it would have given back to the reflectors, and 
through them to the thermometer exactly as many heat 
rays as the latter had given to it. 
But the ice being of a lower temperature, does not 
radiate back as many rays to the thermometer as this 
instrument gives out to the ice, and the temperature of the 
thermometer fallsin consequence. It will be noticed that 
the same laws of reflexion and arrangement of mirrors that 
in the case where a hot body is placed in the one focus 
would have heated the thermometer in the other will, 
in the case of a cold body, cool the thermometer in the 
other ; so that, without resorting to the unlikely assump- 
tion that cold is a separate principle, we may explain the 
above experiment on the supposition that bodies of the 
same temperature radiate heat to one another, or, in 
other words, on the hypothesis of a movable equilibrium. 
Prevost’s first memoir was in 1791, and in 1804 Leslie 
published his inquiry into the nature and propagation of 
heat. He there demonstrated the fact that good reflectors 
of heat, such as metals, were bad radiators. Prevost, in 
a treatise on radiant heat, published in 1809, showed that 
Leslie’s conclusions followed from his theory, remarking 
that in a place of uniform temperature a reflector does 
not alter the distribution of heat, which it would do if 
it possessed at the same time the power of being a good 
reflector and a good radiator. Prevost seems to have 
entertained very correct views upon this subject, inasmuch 
as he conjectures that a good reflector is a bad radiator 
because, as it reflects the heat from without, so it also 
reflects the heat from within. Internal radiation, we shall] 
afterwards see, follows as a consequence from the theory 
of exchanges. 
Some time afterwards Dulong and Petit published their 
well-known memoir on radiation, which affords evidence 
of a peculiar kind in favour of the theory of exchanges. 
To illustrate the bearing of the experiments by Dulong 
and Petit on this theory, let us imagine that we have a 
hollow, blackened enclosure which is at the same time a 
vacuum, and that we have in its centre a large thermo- 
meter likewise blackened, the temperature of which is 
higher than that of the enclosure. We are supposed to 
be engaged in observing the rate of cooling of this ther- 
mometer, or, in other words, the excess of its radiation 
to the enclosure above that of the enclosure to it. Now 
let A denote the total radiation of the thermometer, which 
we may imagine to have the temperature a. Also let B 
denote that of the enclosure, which we may imagine to 
have the temperature 4. Then A—B will, by the theory 
of exchanges, represent the rate of cooling of the ther- 
mometer. Inthe next place let the thermometer have 
the temperature 4 and radiation B, while the enclosure 
has the temperature c and radiation c. Here B—C will, 
by the theory of exchanges, represent the rate of cooling 
of the thermometer. Finally, let @ be the temperature 
of the thermometer, and ¢ that of the enclosure. Then 
A—cC will, on the theory of exchanges, represent the 
radiation or rate of cooling of the thermometer. Now 
A—C=(A—B)+(B—C), that is to say, the rate of cooling 
in the third case will represent the sum of the two pre- 
ceding rates ¢f the theory of exchanges be true. 
It was found by Dulong and Petit that this was actually 
the case, for with a=140° and 6=80°, A—B was found to 
be 2°17. 
Again, with 6=80 and c=20, B—C was found to be 
1-40. 
Finally, with z=140 and c=20, A—C was found to be 
3°56. Now this is very nearly equal to 3°57, or the sum 
of the two preceding rates, so that the evidence deduced 
from these experiments is decidedly in favour of the 
theory of exchanges. 
In 1848 Provostaye and Desains made a definite ad- 
vance towards a clearer conception of this theory. It 
may be stated thus. If we place a thermometer in our 
hypothetical chamber of constant temperature it is well 
known that the instrument will give the same indication, 
in whatever manner we alter the substance of the walls, 
provided only that their temperature be left the same. 
It follows from this that the heat radiated, together 
with that reflected from any portion of the walls, forms a 
constant quantity independent of the nature of the sub- 
stance of which this portion is composed. We thus see 
that it is not correct to assert that the reflective power of 
a substance is inversely proportional to its radiative 
power, the true statement being that in the case of an 
enclosure of constant temperature such as that we are 
now considering, the sum of the heat radiated and re- 
flected from any portion is a constant quantity. 
It was likewise perceived by Provostaye and Desains 
that this constant sum, while equal to that of a lamp- 
black radiator, must be unpolarised, since heat from 
lampblack is unpolarised ; and hence that, since the re- 
flected heat is frequently polarised, the radiated heat 
must be polarised in an opposite manner, that is to say, 
in a perpendicular plane, in order that the sum of the two 
should be virtually unpolarised. Experimentally these 
observers found this to be the case. 
It will thus be seen that the inquiry had now reached a 
stage at which a perfectly clear conception had been 
formed of the character with respect to intensity and 
polarisation of the heat emanating from any portion of 
the surface of an enclosure of constant temperature. 
No attempt had however ,been made to split up the 
heterogeneous body of heat into its constituent wave- 
lengths, nor was it perceived that an extension of the 
argument must necessarily lead to a separate equilibrium 
for every individual description of heat. ; 
Internal radiation too, as a subject for experiment (if 
we except the remark made by Prevost), appears to have 
been overlooked, and its essential connexion with the 
theory of exchanges does not appear to have been per- 
ceived. ; 
In March, 1858, I communicated to the Royal Society 
of Edinburgh a memoir in which these desiderata were 
supplied. In this memoir it was shown by a simple 
process of reasoning that the heat-equilibrium must hold 
for every individual description of heat, and that as a 
consequence this would lead to various conclusions, all of 
which were experimentally verified. The following facts 
were thus established :-— ; 
(1) The radiating power of thin polished plates of 
different substances was found to vary as their absorbing 
power: so that the radiation of a plate of rock-salt was 
only 15 per cent. of the total lamp-black radiation for the 
same temperature. ‘ , 
(2) It was shown that the radiation from thick plates of 
diathermous substance is greater than that from thin 
plates, no such difference being manifested when the 
substances are athermanous. j 
(3) It was found that heat radiated by a thin dia- 
thermous plate is less transmissible through a screen of 
the same material than ordinary or lamp-black heat, the 
difference being very marked in the case of rock-salt. 
(4) Lastly, heat from a thick diathermous plate is more 
easily transmitted through a screen of the same material 
than that from a thin plate. ny 
All these facts can be explained by a legitimate 
extension of the theory of exchanges. : 
Let 1s recur to our hypothetical chamber, outside the 
walls of which we may suppose there is a boiling-water 
arrangement, in virtue of which these walls are kept at 
