878 



Prof. H. L. Callendar on 



differences from Planck's formula (represented by the base 

 line), expressed as a percentage of the maximum, are plotted 

 in the curves. The differences are plotted on a wave-length 

 base for a temperature T=1000° Abs., for which the 

 maximum occurs at the point \ = 2'9 yu where all the formula? 

 are made to agree. It is well known that the formulae of 

 TVien and Ray lei gh (R) differ appreciably from experiment, 

 but it is remarkable how closely the sum of the two,. 

 represented by curve (0), agrees with Planck's expression 

 rj K dX = Ji\~'°(e bcAT — l) -1 . The maximum difference of 1 per 

 cent, which occurs on the short wave-length side of the 

 maximum, would be difficult to verify in the distribution 

 curve owing to its steepness on this side, and might be 

 compensated by a very slight shift of the maximum. There 

 are, however, several observations which indicate that 

 Planck 5 s formula gives results a little too low for short 

 wave-lengths. 



Fig. l. 



Wai/eleivcths in Microns ' 



Differences of DistributionTormulae from Planck's Formula at 1000° Abs. 

 on wave-length base, expressed in per cent, of maximum. 

 K, Eayleigb ; C, Callendar ; W, Wien ; dotted, Walker. 



On the short wave-length side, an interesting contrast is 

 presented by the ingenious empirical formula recently 

 proposed by G. W. Walker (Proc. R, S. A lxxxix. p. 393, 

 1914) on dynamical grounds, as representing the harmonic 

 analysis of an arbitrary series of disturbances with strictly 

 aperiodic damping. Walker's formula is a modification of 

 that of Kovesligetby, 1890, and is of the type, 



E x = *T 3 [\T/(\ 2 T 2 + a 2 )]*, (9) 



which evidently satisfies the conditions laid down by Wien, but 

 does not otherwise conform to the present theory. The curve 

 as shown by Walker is very similar in general appearance to 

 the distribution curves of Lummer and Pringsheim, especially 



