384 iM. 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 loss 

 suffered bj' these rays in their passage through the second plate Avill be 

 necessarily less than 0"077. But experiment shows that even in passing 

 through the second plate the quantity of heat transmitted is exactly 

 0"923, and the quantity lost 0'0T7. 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 sutfer the same loss (0*077) 

 in the sum of the reflections which thej' undergo when entering and leav- 

 ing the plate of rock salt. The same may be said of tlie different rays 

 emitted by the same source, for the loss 0'077 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 fii-st 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 fui'ther 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 -I- R (1 - R) -f- 0*923 = 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 wliich 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 pei-pendicular to tlie 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 tliermonmltiplier placed in the direction of 

 the ravs. Hence it might be reasonably objected that the equation R -|- R 

 (1 — R) + 0-923 = 1 is not periectl)' 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 inclinrd 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 lumibers 3, 5, 7, &c., will not, in issuing from the plate, 



