Interference-Bands. 199 



is nearly equal to unity, and the factors cos ft, cos ft r , cos a 

 vary but slowly with the order of the band and also with the 

 wave-length. Hence the width of the wth band is approxi- 

 mately proportional to the order, to the square of the wave- 

 length, and to the inverse square of the thickness. 



This series of bands, commencing at the limit of total 

 reflexion, and gradually increasing in width, are easily 

 observed with Herschel's apparatus by the aid of a soda- 

 flame. In order to increase the field of view, the flame may 

 be focussed upon the layer of air by a wide-angled lens. The 

 eye should be adjusted for distant objects, and the thickness of 

 the layer should be as uniform as possible. For the latter 

 purpose the glass surfaces may be pressed against two strips 

 of rather thin paper, interposed along two opposite edges. 



We have now to consider what happens when the source of 

 light is white. According to Airy's principle the centre of 

 the system is to be found where there is coincidence of bands 

 of order n, in spite of a variation of X. This is precisely the 

 question already dealt with in connexion with the other 

 system of bands., and the answer is embodied in (36). About 

 the achromatic centre thus determined will the visible bands 

 be grouped. 



And now the question arises, Are these bands achromatic ? 

 Certainly not. M. Mascart, to whom is due equation (37), 

 appears to me to misinterpret it when he concludes that the 

 bands are approximately achromatic*. At the central band 

 n is the same for the various colours. Consequently the 

 widths of the various systems at this place are approximately 

 proportional to X 2 . It will be seen that, so far from the 

 system being achromatic, it is much less so than the ordinary 

 system of interference-bands, or of Newton's rings, in which 

 the width is proportional to the first power of X. And this 

 theoretical conclusion appears to me to be in harmony with 

 observation. 



At first sight it may appear strange that an achromatic 

 centre should be possible with bands proportional to X 2 . The 

 explanation depends upon the fact that the limit of total 

 reflexion, where the bands commence, is itself a function of X. 

 The apparent width of the visible bands depends upon t, but 

 is not, as might erroneously be supposed, proportional to t~' 2 . 

 For this purpose n in (37) must be regarded as a function of t. 

 In fact, by (32), if u f be given, n varies as t/\ ; so that, in 

 estimating the influence of t, other circumstances remaining 



* Traite d'Optique, t. i. p. 451. u On s'explique ainsi que la largeur 

 apparente des franges voisines de la f range ackrornatique soit a peu pres 

 independante de la longueur d'onde dans une ouverture angulaire notable 

 et qu'on en distingue un grand nornbre." 



Q2 



