Eddy.] 'J36 [June 16, 



The paths of the projectiles relative to the screens can be readily found 

 by impressing upon the projectiles, in addition to their velocities v or «', a 

 velocity — u, numerically equal and opposed to that of the screens, while 

 the screens themselves are at rest. The composition of these velocities 

 will give the required relative velocity. 



In order to apply the mechanical analogy just considered to the case in 

 hand, let us replace the supposed projectiles by radiations which emanate 

 from warm bodies situated in the spaces A and B, and let the only radia- 

 tions at first considered be those in a direction perpendicular to the 

 ' screens. 



It is then evident that with such series of apertures as are represented in 

 the figure the screens a b c could be given such a velocity ti, as accompa- 

 nied by reflections from c would transfer radiations from the body A to B 

 unaccompanied by a compensating transfer from 5 to A, and thus the body 

 B would be heated at the expense of A. Even if radiations at the aper- 

 tures in a and b be not confined to rays perpendicular to the screens, but 

 take place instead in the manner usual at plane surfaces, it is still evident 

 that the usual interchange of radiations has been effectively interfered 

 with, and that the body B would be heated at the expense of A. In case 

 the radiations from the body B are reflected back through the same aper- 

 tures from which they started, it is quite unnecessary to have the series of 

 apertures in the screen a at equal distances. It is only necessary that the 

 series of apertures in b and c correspond to that in a. Indeed each aper- 

 ture in b can be conceived to be completely surrounded by a concave semi- 

 cylindrical reflector attached to c, of such a form as to return to b all radia- 

 tions from it when moving with the velocity u. This can certainly be 

 effected if the apertures in b are mere points and can be closely approxi- 

 mated to when they are small. Now, if there be in this cylinder a proper 

 aperture for the admission of the normal radiations from A through a, it 

 is evident that the radiations passing through this aperture from B, being 

 oblique, are, when the bodies are of equal temperature, less than those of 

 A passing through the same aperture, according to the Avell known law of 

 radiations, that the intensity is proportional to the cosine of the angle be- 

 tween the ray and the normal to the rsKliating surface. It is seen that with 

 sufficiently large value of ^^ it would be possible to overcome any ditl'er- 

 ence of temperature however great. 



In order to form an estimate of the amount by which the radia- 

 tion from AtoB exceeds that escaping from B through e, let us suppose 

 that the temperature of A and B are equal and that the velocity v of the 

 radiations, from both A and B is the same, and further, let the screen c be 

 midway between a and 6 at a distance p from each. Let the problem be 

 to compute the ratio between the radiations which pass through a given 

 aperture, as Cp from rt, and from b^ respectively, on tlie supposition that 

 the heat radiates from the equal apertures a^ and b^ as from plane surfaces 

 in the usual manner. 



