VOL. LXXXVI.] PHILOSOPHICAL TRANSACTIONS. 727 



distance from that centre; and therefore, by Prop. 1 1 and 13 of the same book, 

 the ray moves in an ellipse by the inflecting, and an hyperbola by the deflecting 

 force, each having one focus in the centre of the body. The trutii of these 

 things mathematicians will easily determine. 



Prop. 6. If a ray fall on a specular surface, it will be bent before incidence 

 into a curve, having two points of contrary flexure, and then will be bent back 

 the contrary way into an equal and similar curve ; as in fig. ], pi. Q. 



Carol, to these propositions. If a pencil of rays fall converging on an inter- 

 posed body, the shadow will be less than the body by twice the sine of inflection. 

 And if a pencil fall diverging on the body, the shadow will be greater than the 

 body by twice the sine of inflection ; but less than it should be, if the rays had 

 passed without bending, by twice the sine of the difference between the angles 

 of inflection and incidence. — The sine or angle of incidence is greater than the 

 sine or angle of inflection, when the incident rays make an acute angle with the 

 body ; but when they make an obtuse or right angle, then the sine or angle of 

 inflection is less than that of incidence. The sine of incidence is greater than 

 that of deflection, if the angle made by the incident ray with the body be ob- 

 tuse, but less if that angle be acute or right. — If a globe or circle be held in 

 a beam of light, the rays may be made to converge to a focus. 



Hitherto it has been supposed, that the parts of which light consists have aJl 

 the same disposition to be acted on by bodies which inflect and deflect them ; 

 but we shall now see that this is by no means the case. 



Obs. 1. Into my darkened chamber I let a beam of the sun's light, through a 

 hole in a metal plate, fixed in the window-shut, of -yL- of an inch diameter ; and 

 all other light being absorbed by black cloth hung before the window, and in 

 the room, at the hole I placed a prism of glass, whose refracting angle was 45 

 degrees, and which was covered all over with black paper, except a small part on 

 each side, which was free from impurities, and through which the light was 

 refracted, so as to form a distinct and tolerably homogeneous spectrum on a 

 chart at 6 feet from the window. In the rays, at 2 feet from the prism, J placed 

 a black unpolished pin, whose diameter was every where -^ of an inch, parallel 

 to the chart, and in a vertical position. Its shadow was formed in the spectrum 

 on the chart, and had a considerable penumbra, especially in the brightest red, 

 for it was by no means of the same thickness in all parts ; that in violet was 

 broadest and most distinct ; that in the red narrowest and most confused, and 

 that in the intermediate colours was of an intermediate thickness and degree of 

 distinctness. It was not bounded by straight, but by curvilinear sides, convex 

 towards the axis to which they approached as to an asymptote, and that, nearest 

 in the last refrangible rays, as is represented in fig. 2 ; where ab is the axis, 

 IKLMNA and HGFEDA the two outlines. Nor could this be owing to any irregu- 

 larity in the pin, for the same thing happened in all sorts of bodies that were 



