The Philosophical magazine; a journal of theoretical, experimental and applied physics . Mr. J. H. Pratt on the Supernumerary Bows in the Rainbow. 81 8. I will first find the intensities of these emergent rays, andcompare them. A cylindrical pencil of parallel rays falling on the diop ofrain will emerge through an element of the surface of the drop,of dimensions difierent to those of the element through which itpassed on entering; and the pencil will emerge, in the generalcase, not parallel, but diverging, both in the plane of the paperand at right angles to that plane. It will be necessary to
The Philosophical magazine; a journal of theoretical, experimental and applied physics . Mr. J. H. Pratt on the Supernumerary Bows in the Rainbow. 81 8. I will first find the intensities of these emergent rays, andcompare them. A cylindrical pencil of parallel rays falling on the diop ofrain will emerge through an element of the surface of the drop,of dimensions difierent to those of the element through which itpassed on entering; and the pencil will emerge, in the generalcase, not parallel, but diverging, both in the plane of the paperand at right angles to that plane. It will be necessary to cal-culate this in order to find the intensity of the emerging light. 9. And first, I will calculate the divergence at right angles tothe paper. Fig. Let SaicE (fig. 3) be the course of a ray through the drop. Draw Sc parallel to the incident rays through the centre of the diop. Let the figure revolve round Sc through a very small angle, so that the above ray may assume the position of a new ray SaiVE. Thus oa is the breadth of the incident pencil measured at right angles to the paper, = iv suppose. Then the wangle through which the plane revolves = —.—r ; and c& = rsin^ —;—r X r sm (0 + 6) =w ^——-. r sm 0 ^ sm <p This is the width of the pencil when it is emerging. The rayscE, cE make, each of them in its own plane, an angle 6 with 83 Mr. J. H. Pratt on the Supernumerary Bows in the Rainbow. the intersection SC of tlie planes. Hence these rays make witheach other the angle sin 6 x angle of incHnation of the planes = ,—-: and therefore at a distance D from the di-op, the r sm<prays are spread, at right angles to the paper, through the space sin (6+ 6) Dsin^ w :—j-^-^ +w ^—r. sm <p r sin 9 The first te
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