SCIENCE. 



[Vol. IV., No. 74. 



may be of use in arriving at correct conclusions re- 

 garding this matter. 



Let z and z' be taken as the foci of a semi-ellipse, 

 nyy'n', whose major axis is nn' ; and let the eccen- 

 tricity be so small that zy is greater than \nn'. Make 

 xz = nn' — 2xm. Let a concave reflecting surface 

 be supposed to be generated by revolving the semi- 

 ellipse through angles of + %tc and— ^rr about nn' ; 

 and let nn' represent a screen in which there are equal 

 small circular apertures at z and z' ; let there be also 

 equal apertures at x and x' ; and, in addition, let there 

 be apertures at y and y' no larger than will permit the 

 passage of cylindrical beams from the apertures at z 

 and z' respectively. 



At first let the apertures x and z' alone be open, and 

 remain so until the spherical front of the wave-sur- 

 face radiating from x has reached ra, and a second 

 wave-front of equal radius, z'r, has issued from z'. A 

 part of this latter wave has, at the conclusion of this 

 interval, been reflected from the concave mirror to- 

 wards the focus z. Let the apertures at x and z' be 

 then closed. 



Next let the aperture at y be opened at the instant 

 when the beams along xy and z'y reach y, and be 

 closed as soon as they have passed through y. They 

 will pass through simultaneously, since xy = z'y. 



Further, let the apertures z and x' be opened when 

 the beam along xy reaches z, and let them be closed 

 as soon as it has passed through z. The rays radiated 

 from z', which were reflected from the concave mirror, 

 will be brought to a focus at z, and pass through that 

 aperture simultaneously with the beam in the direc- 

 tion xy; for, by the properties of the ellipse, the total 

 distance traversed by any such ray is equal to nn' 

 = xz: hence the wave-fronts, starting from x and z' 

 at the same instant, will reach z simultaneously. 



We have now to consider what occurs at each of 

 the apertures y and z during the interval while they 

 are open. 



While y is open, abeam from x, of length xm, passes 

 through it toward B, and a beam from z', of equal 

 cross-section and length, passes through it away from 

 B. These beams are of equal cross-section, because 

 the tangent at y makes equal angles with the focal 

 radii zy and z'y. But these beams are not of equal 

 intensity in case A and B are of equal temperature, 

 because any plane aperture, such as that at z', does 

 not radiate equally in all directions. The intensity of 

 the radiation diminishes, according to the well-known 

 law, as the cosine of the angle between the direction 

 of the ray and the normal; i.e., the intensity is less 

 in the ratio of cos yz'y' to unity: hence less heat has 

 escaped at y than has passed through y toward B in 

 the ratio just mentioned. 



Now as to the quantities of heat passing through 



the aperture z. Let us for defmiteness take the body 

 B to be common air, enclosed in a capacious vessel 

 whose interior walls are perfectly black. Such being 

 the case, whatever be the intensity of the ray re- 

 ceived through z in any given direction, the intensity 

 of the ray simultaneously emitted through z will 

 depend only upon the previous temperature of B, or, 

 at most, only infinitesimally upon the intensity of the 

 ray received. Such being the fact, the beam emitted 

 from z in the direction of y' has the same intensity 

 as that previously emitted from z' towards y. But 

 the beam which is received at z by reflection from 

 y' has a very different intensity from this, for it is 

 the beam which was originally radiated from z' to- 

 wards y'. 



When, therefore, Mr. Fitzgerald says, that, " if heat 

 can go into B in the direction y'z, there would be an 

 escape of heat from B in the direction zy' as well as 

 in the direction zy, and so, to the two quantities of 

 heat coming into B, there would escape two equal 

 quantities," I feel that either he has made a mistake, 

 or he presumes upon the ignorance of the reader; 

 and, to use his own inimitable emphasis, I may say 

 that I am sure no American or other scientific man 

 agrees with him ; and I think I am justified in adding 

 that no Irishman will agree with him either, includ- 

 ing his own better self. To make this point still 

 more evident, we have only to consider what occurs 

 when the concave semi-ellipsoidal reflector without 

 apertures at y and y' is used to transmit radiations 

 alternately between z and z'. First let z be opened 

 during an interval such that rays of a length -£ nn' are 

 emitted ; then let both z and z' be closed for an equal 

 interval; next let z' be opened for an equal interval. 

 During this third interval, equal quantities of heat 

 pass through z', towards and away from B ; but is Mr. 

 Fitzgerald now ready to re-affirm his untenable propo- 

 sition that the quantities of heat received and lost in 

 any arbitrary direction are equal? Whether he is 

 willing to do so or not, these quantities are not in 

 general equal, his hasty affirmation of their equality 

 to the contrary notwithstanding. 



In close connection with this, it is pertinent to in- 

 quire once more what difference there is between the 

 equal quantities of energy which B has simultane- 

 ously emitted from and received through z'. The 

 kind of energy we call heat exists in two forms, — 

 radiant and non-radiant; the latter is often regarded 

 as identical with molecular agitation. Eadiant heat 

 may be totally reflected regularly, as light is by a per- 

 fect reflector ; it maybe totally reflected irregularly, 

 as light is at a white surface; it may be wholly ab- 

 sorbed, and the energy conducted or radiated away 

 with a different wave-length, as light is at a black 

 surface; it may be wholly transmitted, as light is by 

 a transparent substance; or there maybe any com- 

 bination of these. It is sufficient for our purpose to 

 suppose that the constitution of the body B is such 

 that regular reflection does not occur at its surface, 

 and that the absorption of the rays entering it takes 

 place in its interior, as in a partially or completely 

 transparent substance enclosed in a black vessel. 

 Now, when the rays have been absorbed, as they 

 must be under such circumstances before they can 

 be radiated away from B, their energy exists in the 

 non-radiant form. I have stated in my previous let- 

 ter, that, " after the energy reaches B, the path by 

 which it has arrived is of no consequence," and that 

 the direction which the rays may have had in coming 

 to B is immaterial to the question under discussion. 

 I stand ready to re-affirm this proposition, and now 

 do so. Mr. Fitzgerald evidently regards this state- 

 ment as so unscientific as to merit no reply what- 



