Measurements in the Extreme Infra-red Spectrum. 769 



that is, the weaker stripe being the longer waved, the maxima, 

 and minima are very markedly crowded together in that 

 portion of the interference curve where the interference is 

 most feeble ; on the contrary, if the weaker is of shorter 

 wave-length the distance between the maxima and minima is 

 here noticeably separated. To illustrate this two curves are 

 shown in fig. 7 (PL XIII.). They are obtained by the super- 

 position of two cosine curves whose periods are in the ratios of 

 7 : 6 and 7 : 8 respectively ; the curve a represents the instance 

 of the principal band accompanied by a long-waved radiation, 

 while curve /3 indicates the other case. To the latter type 

 belong all curves in figs. 3-5 with the exception of fig. 4, 

 which is an example of the a type. 



The interference curves furnish not only the necessary data 

 for the wave-length computation but also give a probable 

 idea of the homogeneity and energy distribution of such 

 rays *. Sufficient at least to give a good approximation, 

 is the following consideration : — We assume that the energy 

 distribution in each of the two spectral domains is expressible 

 by the equation 



*-**?£>? where -TT' ' • • « 



</>! and y l are constants, and c/>i7iAi are to be replaced by 

 cf) 2 7 2 ^2 f° r t° e second band calculations. 



This is the well known equation of the curve of resonance 

 which is obtained on allowing a slightly damped sine wave 

 of wave-length Xi and logarithmic decrement 7,, to impinge 

 on an infinite number of practically undamped resonators of 

 various wave-lengths, provided the intensities of vibration 

 of the various resonators are considered as function of" the 

 various characteristic wave-lengths. The wave-length of 

 the maximum of the energy curve (\j) should be identical 

 with the mean wave-length of the band whose energy distri- 

 bution is to be represented by equation (1). If it is possible, 

 then, to determine the constants y { and <p l which enter in 

 this equation, the energy curve can be drawn. 



To procure the magnitude 7 from the interference curve, 

 we assume the infinite number of undamped sine waves 

 which compose the band whose energy distribution is to be 

 investigated according to equation (1), replaced by a train 



* Our problem is one similar to that which Prof. A. A. Michelson had 

 to deal with, in drawing conclusions regarding- the energy distribution 

 of spectral lines from the visibility curves of the interference fringes 

 obtained bv great difference in optical path (Phil. Mag. [5] xxxiv. p. 280, 

 1892). 



Phil. Mag. S. 6. Vol. 19. No. 113. May 1910. 3 D 



