366 Cambridge Philosophical Society. 



axis of the ray. The sensation of light is due to the transverse vi- 

 brations. By assuming that the bifurcation of a ray takes place so 

 that the transverse velocity at each point is resolved into two velocities 

 at right angles to each other, and that these are respectively the 

 velocities at the corresponding points of the two parts into which the 

 ray is divided, Professor Challis finds, — 1, that if the original ray be 

 one of common light, the two parts are symmetrical about planes at 

 right angles to each other passing thi-ough the axis, and are each of 

 half the intensity of the original ray ; 2, that if the original ray has 

 been once polarized, the ratio of the two parts is equal to the square 

 of the tangent of the angle which the plane of the second polariza- 

 tion makes with that of the first ; 3, that whether the original ray 

 be one of common light or a polarized ray, the two parts, on pursuing 

 the same path, form a compound ray the intensity of which is in- 

 dependent of the difl^erence of phase. According to this theory, 

 elliptically or circularly polarized light is produced whenever a ray 

 of first polarization is divided into two parts which subsequently 

 pursue the same path in different phases. If the parts be made to 

 meet in the same phase, they constitute the original polarized ray. 

 Hence is explained the necessity of the analysing plate for the pro- 

 duction of colours by polarized rays transmitted through thin pieces 

 of uniaxal or biaxal crystals. The compound rays, if received directly 

 by the eye on leaving the crystal, would be of the same intensity 

 whatever be the difference of phase. But when they fall on the 

 plate, those incident in the same phase, being equivalent to rays of 

 first polarization, are incapable of reflexion, while the remainder, 

 which are incident in the form of elliptically or circularly polarized 

 light, are reflected in diff"erent degrees of intensity according to the 

 diflference of phase. The author states that he has extended this 

 theory to the phsenomena of double refraction. 



On a Change in the State of Vision of an Eye aff'ected with a 

 mal-formation. 



Twentyyears ago, the author communicated to the Society a state- 

 ment of the eff"ects of a mal-formation in his left eye. The rays of 

 light coming from a luminous point, and falling on the whole surface 

 of the pupil, do not converge to a point at any position within the 

 eye, but converge so as to pass through two lines at right angles to 

 each other, and, in the ordinary position of the head, inclined to the 

 vertical, as formerly described (Transactions of the Society, vol. ii.). 

 As the luminous i)oint is moved further from or nearer to the eye, 

 the image of the point becomes a straight line in one or other of the 

 positions above-mentioned. Since 1 825 the inclinations of the two 

 focal lines to the vertical, their lengthy and their sharpness do not 

 appear to have undergone any sensible change, but the distances at 

 which the luminous point must be placed to bring the focal lines re- 

 qiectively exactly upon the retina are increased, having been formerly 

 3*5 and 6 inches, and being now 4"7 and 8*9 inches. I'hus while 

 the shortsightedness of the eye is diminished the astigmatism remains 

 the same, 



" On the Geometrical Representation of the roots of Algebraic 



