ON THE THEORY OF COMPOUND COLOURS. 423 



VI. Method of determining the Wave-length corresponding to any point 

 of the Spectrum on the Scale AB. 



Two plane surfaces of glass were kept apart by two parallel strips of gold- 

 beaters' leaf, so as to enclose a stratum of air of nearly uniform thickness. Light 

 reflected from this stratum of air was admitted at E, and the spectrun formed 

 by it was examined at AB by means of a lens. This spectrum consists of a 

 large number of bright bands, separated by dark spaces at nearly uniform intervals, 

 these intervals, however, being considerably larger, as we approach the violet end 

 of the spectrum. 



The reason of these alternations of brightness is easily explained. By the 

 theory of Newton's rings, the light reflected from a stratum of air consists of 

 two parts, one of which has traversed a path longer than that of the other, by 

 an interval depending on the thickness of the stratum and the angle of incidence. 

 Whenever the interval of retardation is an exact multiple of a wave-length, these 

 two portions of light destroy each other by interference ; and when the interval 

 is an odd number of half wave-lengths, the resultant light is a maximum. 



In the ordinary case of Newton's rings, these alternations depend upon the 

 varying thickness of the stratum ; while in this case a pencil of rays of different 

 wave-lengths, but all experiencing the same retardation, is analysed into a spectrum, 

 in which the rays are arranged in order of their respective wave-lengths. Every 

 ray whose wave-length is an exact submultiple of the retardation will be destroyed 

 by interference, and its place will appear dark in the spectrum ; and there will 

 be as many dark bands seen as there are rays whose wave-lengths fulfil this 

 condition. 



If, then, we observe the positions of the dark bands on the scale AB, 

 the wave-lengths corresponding to these positions will be a series of submultiples 

 of the retardation. 



Let us call the first dark band visible on the red side of the spectrum zero, 

 and let us number them in order 1, 2, 3, &c. towards the violet end. Let N 

 be the number of undulations corresponding to the band zero which are con- 

 tained in the retardation R; then if n be the number of any other band, N+n 

 will be the number of the corresponding wave-lengths in the retardation, or in 

 symbols, 



R = (N+n)\ (6). 



