( 6G9 ) 



It api)oavs from the al)o\e remarks lliat the ]iy|)oJliesis regarding 

 the liiiite "units of energy", Avhich has led to tlie ijitroduotion of the 

 constant //, is an essential part of tlie tiu'orv ; also that the qnestion 

 as to the mechanism by which the heat of a body produces electro- 

 magnetic vibratio]is in the aether is still left open. NcAei'theless, the 

 results of PiiANCK are most remarkable. His formula rei)resents very 

 exactly the energy of the radiations for all values of the wave-lengths, 

 whereas the following considerations are from the outset coufiued to 

 long waxes. We may at best expect to deduce from theui the 

 I'oi'in which the function in (1) takes foi' this exti'euie case. 



§ 3. Since, if we trust to KiU([iHOi'i''s law, the i-atio between the 

 emission and the absorjttion must l)e regarded as iudepeiideul of the 

 dimensions and the |)Osition of the body considered, we may simplify 

 the problem by an apjn'opriate choice of circumstajices. I shall 

 therefore consider a plate with parallel plane surfaces and 1 shall 

 suppose its thickness A to be so small that the absorption may hv 

 reckoned proportional to it and that the energy emitted by the jios- 

 terior layei-s may be supposed to pass through the i)late without any 

 sensible absorption. 1 shall also contine myself to the absorption of 

 [)erpendieularly incident rays and to the emission in directions making 

 infinitely small angles with the normal. 



Let a be the conductivity of the metal, i. e. the constant rati(> 

 between the electric current and the electric force, these latter ipian- 

 tities being expressed in the modified electrostatic units 1 have latelv 

 ijitroduced. ^j Then the absorbing powei- of the plate, the coefficient 

 by which we must multiply the energy of normal incident ravs, in 

 order to get the absorbed energy, is given by *1 



(7 . 



Here we shall substitute for a the value furnished by Drldk's 

 theory. Let the metal contain ditferent kinds of free electrons, which 

 we may distinguish as the i'^f, the 2''^^ the 3''^ kind, etc., and let 

 us su[)[)Ose that all electrons of one and the same kind have ecpial 

 charges, e(pial velocities of heat-nu)tion, or, as we may say, "molecular" 

 velocities, and travel over [>aths of equal mean length between two 

 successive encounters with particles of the metal. 



We shall write c^, e.^, .... for the chai-ges of the diffei-ent kinds 

 of electrons, if^, ii^, . . . tor the mean molecular velocitic^s, /j, /.^, . . . 



LoRENTZ, l^rncrcdings Acad, of Science, Amslcidain, Vol. 11, p. (lOS^ llKJIi. 

 -) See § 1:2 Iichnv. In (•le<(ioiiiaguelic units llic riinniila hccoiuci} 



