THE THEOEY OF COMPOUND COLOUES. 
G7 
the instrument had been some time in use these positions were invariable, showing that 
the eye-hole, the prisms, and the scale might be considered as rigidly connected. 
§ VI. Method of determining the Wave-length corresponding to any point of the Spectrwni 
on the Scale AB. 
Two plane surfaces of glass were kept apart by two parallel strips of goldbeaters’ 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 spectrum formed by it was examined at AB 
by means of a lens. This spectrum consists of a large number of bright bands, sepa- 
rated by dark spaces at nearly uniform intervals, these intervals, however, being con- 
siderably larger as we approach the violet end of the spectrum. 
The reason of these alternations of brightness is easily explained. By the theory of 
Newtox’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 ordinaiy case of Newtox’s rings, these alternations depend upon the varying 
thickness of the stratum ; while in this case a pencil of rays of difierent 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 obseiwe the positions of the dark bands on the scale AB, the wave-lengths 
corresponding to these positions uflll be a series of submultiples of the retardation. 
Let us call the flrst dark band 'visible on the red side of the spectrum zero, and let us 
number them in order 1, 2, 3, &c. towards the \iolet end. Let N be the number of 
undulations con’esponding to the band zero which are contained in the retardation B ; 
then if n be the number of any other band, N -{-n "will be the number of the correspond- 
ing wave-lengths in the retardation, or in symbols, 
R=(N+w}> (6.) 
Now observe the position of two of Feauxhofee’s fixed lines with respect to the dark 
bands, and let Wj, n.^. be their positions expressed in the number of bands, whole or 
fractional, reckoning from zero. Let X,, be the wave-lengths of these fixed lines as 
determined by Feauxhofek, then 
R — (N+Wi)A, — 
^ 2^2 (^2 - 
N = 
/l2 Wj, 
whence 
( 7 .} 
( 8 .) 
