from an Electric Source. 173 



branches keeps close to the experimental black-body iso- 

 therm ; the following ones have nothing to do with 

 experience as far as it actually goes. Now, as I shall 

 show in detail at a later opportunity, the second branch of 

 the radiation curve, stretching from the first zero down to 

 the second zero of radiation, can be easily abolished as such. 

 In fact, if £ , the amplitude of the impressed force, instead 

 of being assumed constant, as hitherto, is taken to be inversely 

 proportional to 



9 9* 



10' — It' l *, 



the first two branches coalesce into one continuous branch 

 which fits with the experimental isotherms as well as the 

 first by itself did t, thus pushing the difficulty back to the 

 next, that is, originally the third branch. This possibility 

 is based upon the property of g{iu) of giving 



Lim ! r-^-i \ =M sinw i' • • V-i 



v:->w x ( (ttVll'i)"- 1 J 



so that J[iOi) becomes, apart from a constant factor, equal to 



W] 2 sin 2 // 1 



instead of vanishing at that critical frequency. Similarly, 

 by using the divisor io 2 —uy the second zero can be abolished, 

 and so on. In this way we might obtain the coalescence of 

 as many branches of the radiation curve as we like, pushing 

 the difficulty back, towards higher and higher frequencies 

 (or lower temperatures), until it ceases to be a practical 

 nuisance at all. And, pari passu with this procedure, the 

 specific-heat curve will be deprived of its caprices J. But in 

 thus abolishing branch after branch we must not go so far 

 as to forget that the several maxima of the emission curve 

 are not merely so many mathematical nuisances. For it 

 is only due to their existence that our source is capable of 

 emitting line-, and, generally, non-continuous spectra. And 

 it is certainly not undesirable to have essentially one and the 

 same conceptual radiator for all kinds of spectra. Notice 

 that the passage from continuous (via broad-lined) to the 

 sharpest line-spectra consists in (increasing K and) reducing 

 the dimensions of the source until it contains but a sinerle 



o 



* Where w, =4-49.34 is the first root of </(w) = 0, the following ones 

 being tc 2 = 7*7253, ios=10*9041, &c. 



t And even slightly closer. 



X In the case of silver, for example, we should not have to go very 

 far, for the time being, because the original formula, with e = const., 

 works quite well down to 4o or 43° absol., and the obseivations have 

 not, in that case, been pushed below 86°, 



