BANDS SEEN IN THE SPECTRUM. 
231 
or negative, gives the number of bands seen between F and G. For anything that 
appears from the imperfect theory of the bands given in tlie preceding article, it 
would seem that the sign of N was of no consequence. It will presently be seen, 
however, that the sign is of great importance : it will be found in fact that the sign 
indicates that the second arrangement mentioned in art. 2 must be employed ; 
that is to say, the plate must be made to intercept light from the thin end of the 
prism, v/hile the sign — indicates that the first arrangement is required. It is hardly 
necessary to remark that, if N should be fractional, we must, instead of the number 
of bands, speak of the number of band-intervals and the fraction of an interval. 
Although the number of bands depends on nothing but the values of N, the values 
of M are not without physical interest. For M expresses, as we have seen, the number 
of waves’ lengths whereby one of the interfering streams is before or behind the other. 
Mr. Airy speaks of the formation of rings with the light of a spirit-lamp when the 
retardation of one of the interfering streams is as much as fifty or sixty waves’ lengths. 
But in some of Professor Powell’s experiments, bands were seen which must have 
been produced by retardations of several hundred waves’ lengths. This exalts out- 
ideas of the regularity which must be attributed to the undulations. 
6. It appears then that the calculation of the number of bands is reduced to that 
of the retardation R. As the calculation of R is frequently required in physical 
optics, it will not be necessary to enter into much detail on this point. The mode of 
performing the calculation, according to the circumstances of the experiment, will 
best be explained by a few examples. 
Suppose the retarding plate to belong to an ordinary medium, and to be placed so 
as to intercept light from the thin end of the prism, and to have its plane equally 
inclined to the faces of the prism. Suppose the prism turned till one of the fixed 
lines, as F, is seen at a minimum deviation ; then the colours about F are incident 
perpendicularly on the plate ; and all the colours may without material error be sup- 
posed to be incident perpendicularly, since the directions of the different colours are 
only separated by the dispersion accompanying the first refraction into the fluid, and 
near the normal a small change in the angle of incidence produces only a very 
small change in the retardation. The dispersion accompanying the first refraction 
into the fluid has been spoken of as if the light were refracted from air directly into 
the fluid, which is allowable, since the glass sides of the hollow prism, being bounded 
by parallel surfaces, may be dispensed with in the explanation. Let T be the thick- 
ness of the plate, [/j the refractive index of the fluid, fjj' that of the plate ; then 
R=(^'-^)T (2.) 
If the plate had been placed so as to intercept light from the thick end of the 
prism, we should have had — R=(j«-'— / m;)T, which would have agreed with (2.) if we 
had supposed T negative. For the future T will be reckoned positive when the plate 
intercepts light from the thin end of the prism, and negative when it intercepts light 
