6 Prof. Kirchhoff on the Relation between the Radiating and 



From which it follows, either th'at fa is nothing for every value 

 of a, or that it is infinitely great when a vanishes. But when a 

 vanishes, X becomes infinite. Recollecting then the meaning of 

 /a, and recollecting also that p is a proper fraction, and that 

 neither e nor e 1 can become infinite when X increases without 

 limit, the second alternative cannot be admitted, and therefore 

 for every value of X we must have 



e^e 1 . 



§ 4. If the pencil which proceeds from the black body C 

 through the openings 1 and 2 consisted partly of rays polarized 

 in* a plane, the plane of polarization of the polarized portion must 

 rotate when the body itself rotates about the axis of the pencil. 

 Such a rotation must therefore affect the value of e. But since, 

 by the above equation, no such effect can be admitted, it follows 

 that no part of the pencil can be so polarized. It can also be 

 shown that no part of the pencil can be circularly polarized. "We 

 shall not give the proof of this here. Without this it will be 

 admitted that black bodies can be imagined so constituted that 

 there is no more reason why they should emit rays circularly 

 polarized in one direction more than the other. All the black 

 bodies hereafter mentioned are supposed to be of this kind, viz. 

 that they emit no polarized rays whatever. 



§ 5. The magnitude indicated by e depends, not only on the 

 temperature and length of the wave, but also on the form and 

 relative position of the openings ] and 2. Let w x and w; 2 be 

 the projections of these openings on the planes which cut the 

 pencil at right angles to its axis, and let s be the distance of the 

 openings apart ; then 



e—i , 



where I is a function of the length of the wave and the tempe- 

 rature only. 



§ 6. As the form of the body C is arbitrary, we may substi- 

 tute for it a surface which exactly fills the opening 1, and which 

 we shall call surface 1. The screen S, may then be imagined to 

 be removed. The screen S 2 may also be removed, if the pencil 

 to which e relates be defined as that which proceeds from sur- 

 face 1 and is incident on surface 2, which exactly fills the 

 opening 2. 



§ 7. A consequence that immediately follows from the equa- 



