298 PHILOSOPHICAL TRANSACTONS. [aNNO 1728. 



and at d, into the line dd ; so that the emergent ray will be dd, as it" the re- 

 fraction had been performed in the point n, and that point was in the surface 

 GG, without any curve at abed; and all the rest as we considered it before, with 

 this difference only, viz. That the ray is bent just as it comes out, or rather 

 when it is come out, of the dense medium ; whereas before we considered its 

 bending before it came into it. 



Of the Bending of Rays in Reflection. — But if the ray Ra, fig. 14, coming 

 out of glass into air, should come in such a direction, as to be wholly reflected, 

 as it will do when the angle Rap is of 45 degrees ; then the reflection will not 

 be made at the surface gg, nor above it in the glass; but under the said surface, 

 in the air, or even in a vacuum, or any medium less dense, or rather less rer 

 fractive than glass. 



MM represents the limits of the attraction of the glass, exerted in a direction 

 from MM to GG perpendicularly, as beforesaid. 



The ray na, moving in the direction Rr, at its emersion at a, is, for the rea- 

 sons before given, turned into the direction aa ; then at b, into the direction 

 bb ; at c, into the direction cc ; at d, into the direction dd ; at e, into the 

 direction ee ; and at f, into the direction ff parallel to gg ; then at g, the ray is 

 again turned towards the glass, by whose attraction changing successively into 

 all the directions gg, ii, kk, and 11 ; at last it re-enters the glass in the direction 

 mm, making the same angle with the perpendicular mp, that Ra made with ap. 

 Now as the lines perpendicular to gg, drawn from mm, are infinitely near, the 

 line abcdefghikhn must be a curve ; and as mm and gg are extremely near, the 

 vertex of the curve, whose tangent is ff parallel to gg, will be so near the point i, 

 as to be considered as coinciding with it, when we compare the angle of inci- 

 dence with that of reflection ; then also will the space between the parallels pm 

 and pa be so far diminished, that those two lines may be considered as coincid- 

 ing, the angles mmp and Rap being equal, whether the three points m, i, a, co- 

 incide or not. 



For these reasons, for common use, we may consider the reflection from the 

 under surface of the glass, as made at once in that surface at the point i. But 

 when things are strictly examined, experiments as well as the above reasoning, 

 show that there is such a curve as above mentioned. See experiment 6, fig. 10 

 and 1 1 ; and others are mentioned below. 



N. B. If any point of the curve abc, &c. between a and f, fall below, or be- 

 yond the line mm, the ray will then go on in a straight line, tangent to the 

 curve in that point where it leaves the line mm. 



Now let us suppose MedcbarM, in the same figure to be glass, or any other 

 dense medium, and mppR air, or any other rare medium, and Ra a ray of light 



