On the theory of certain bands seen in the spectrum / by G.G. Stokes.

  • Sir George Stokes, 1st Baronet
Date:
1848
Catalogue details

Licence: Public Domain Mark

Credit: On the theory of certain bands seen in the spectrum / by G.G. Stokes. Source: Wellcome Collection.

    12/18 (page 236)
    • • c , 1 proper multiplier of is -• This may be shown to be a necessary consequence of the principle mentioned in the preceding article, that light is never lost by inter- ference ; and this principle follows directly from the principle vis viva. In proving that is the proper multiplier, it is not in the least necessary to enter into the con- sideration of the law of the variation of intensity in a secondary wave, as the angular distance from the normal to the primary wave varies ; the result depends merely on the assumption that in the immediate neighbourhood of the normal the intensity may be regarded as sensibly constant. In the expression (a.) we have PM= 7)^} = V {f‘^-\-p^-\-q^—2px—2qy} if we write/' for s/f It will be sufficient to replace outside the cir- cular function by We may omit the constant/under the circular function, which comes to the same thing as changing the origin of t. We thus get for the disturb- ance at M due to the unretarded stream, or on performing the integrations and reducing, sin sinsin xf X/ X/ f 2f)- . . (b.) For the retarded stream, the only difference is that we must subtract R from vt, and that the limits of x are g and g-\-P. We thus get for the disturbance at M due to this stream, 2ckl X/ pk' (c.) If we put for shortness r for the quantity under the last circular function in {b.), the expressions (&.), (c.) may be put under the forms u sin r, u sin (r—a), respectively; and if I be the intensity, I will be measured by the sum of the squares of the coefficients of sin T and cos r in the expression so that u sin T-\-v sin (r — a), \—u^-\-v'^-{-2uv cos a. which becomes, on putting for u, v and a, their values, and putting I = y-^{(sin^)%(sin'^)%2sin^-sia^cos[f-^(4g+A+/f)]J. (U.) 12. Suppose now that instead of a point we have a line of homogeneous light, the