384 M. MELLONI ON THE REFLECTION OF RADIANT HEAT. 
heat, as it issues from the source, be received on one of the two plates, 
the thinner, for instance, and as it emerges from this let it be trans- 
mitted through the other. The supposed absorption or purification will 
have taken place in the first plate; and allowance being made for the 
rays reflected at the two surfaces, none will reach the second plate but 
such as are completely transmissible by its substance, so that the less 
suffered by these rays in their passage through the second plate will be 
necessarily less than 0°077. But experiment shows that even in passing 
through the second plate the quantity of heat transmitted is exactly 
0923, and the quantity lost 0°077. It is clear therefore that no absorp- 
tion can have taken place in the passage through the first plate, and that 
0°077 is precisely the amount of loss produced by reflection at the first 
and the second surface of each plate. 
As the nature of the source of heat has no influence on the transmission 
of rock salt, the calorific rays must evidently suffer the same loss (0°077) 
inthe sum of the reflections which they undergo when entering and leay- 
ing the plate of rock salt. The same may be said of the different rays 
emitted by the same source, for the loss 0077 is constant with respect 
to heat emerging from all sorts of screens exposed to the action of any 
calorific radiation whatsoever. 
We may now, with the greatest facility, ascertain the proper value of 
each of the reflections. Let 1 represent the incident heat, and R the 
amount of reflection at the first surface, then 1 — R will be the quan- 
tity that penetrates the plate, and R (1 — R) the amount of reflection at 
the further surface ; for as the rock salt absorbs none, the whole quan- 
tity 1 —R arrives at the further surface, and is there reflected in the 
ratio of R:1. Now as the sum of the two reflections added to 0-923 
(the quantity transmitted) must reproduce the quantity of incident heat, 
which we represent by unity, we have the equation 
R+R(—R) +0923 =1*; 
* The heat reflected at the second is evidently returned to the first surface, 
where it undergoes in the interior of the plate a third reflection, by which it is 
again returned to the second surface, and a partial reciprocation of the heat be- 
tween the two surfaces is thus continued for some time. It is obvious that 
when the plate is perpendicular to the direction of the rays, there is always a 
portion of heat issuing from the surface, in combination with the transmitted 
rays, after having undergone three, five, seven, or more reflections. Although 
the portions thus added to the transmission are of very little value, yet, as their 
number is infinite, their sum may be supposed to constitute a sensible part of 
the calorific effect indicated by the thermomultiplier placed in the direction of 
the rays. Hence it might be reasonably objected that the equation R+ R 
(1 — R) + 0°923 = 1 is not perfectly true, as it rests on the assumption that 
0:923 is the exact value of the direct transmission. Fortunately, however, a 
very simple experiment, already described, furnishes a sufficient answer to the 
objection. Let the rock-salt lens be inclined at an angle of about 25° or 30° to 
the incident rays: the portions of heat which undergo the reflections repre- 
sented by the odd numbers 3, 5, 7, &c., will not, in issuing from the plate, 
