Re/lection and Refraction of Light. 1 99 



are different, the several points in ^ B, as A, X, &c. will become the 

 centres of new spherical waves, which in the same medium Y, will move 

 with the same velocity, so that when A Pa would have attained tlie posi- 

 tion D Bb, the new hemispherical wave excited at A, will have come 

 exactly to d, making the radius A d equal to A D ov P B ; and the wave 

 excited at A'', will at the same time have arrived at c, so that X c shall be 

 equal to X C, or Q B, the distance the original wave would have advanced 

 had there been no interruption : similarly will spherical waves be excited 

 at every point of the surface, and thus propagated by reflection into the 

 first medium. Let the circles be completed, and suppose the original wave 

 had arrived at tlie position DCBb, it is manifest that the spherical 

 surfaces, D C B, and Cc, will touch each other at C, the extremity of the 

 common radius S X C ; therefore the point c, will be in contact with a 

 similar and equal spherical surface G d c B \u the first medium : the same 

 will hold good for the waves excited at every point in the surface, as shewn 

 for that at X, hence the series of contacts will constitute the spherical 

 wave GdcB. Now to an eye at X, or C, the object or luminous point is 

 seen at S, and consequently to an eye at c, the reflected image is seen at 

 s, making the angle of reflection XsS equal to the angle of incidence 

 sSX, and in the same plane S A X. 



Refraction on this hypothesis is thus explained ; let Z be the denser 

 medium, then will the elasticity, and the velocity in it be less than in Y, 

 (post. 3, art. 6) therefore the radius of a spherical wave produced in its 

 surface at any point as £J, will be less than in the first medium ; let it be 

 JEn, while the former would have been U F, had the same elasticity and 

 consequently the same velocity continued : from i^dravv the tangent P G, 

 and from G, draw the tangent Gn to the new spherical surface j then S F 

 is perpendicular to the front of the original wave at F, and Gn is perpen- 

 dicular to that excited in the new medium at w,- now it is manifest, that 

 £GF is equal to the angle of incidence, and E Gn to the angle of refrac- 

 tion; and that E F and En are the sines of those angles to the radius GE, 

 but these lines are in a given ratio, viz. that of the velocities, which depend 

 on the elasticities of the two media ; hence the sines of incidence and 

 refraction are in a given ratio. These explanations satisfy the second, 

 third, fifth, and sixth of the facts stated art. 12, and the fourth partially, 

 but for the absorption of light, or indeed for the scattering of its rays at 

 the point of incidence, this theory assigns no complete and adequate cause. 



These explanations of reflection and refraction, it is admitted, are not 

 free from obscurities and defects ; arising from our total ignorance of the 

 kind of vibratory motion, supposed to be excited, and also from the 

 circumstance of the vibrations diverging in all directions. That the 

 quantity of reflected light should increase witli the angle of incidence, and 

 at different '.atcs in diflViont bodies is little in accordance with the prin- 

 ciples of the undulatory theory : the cas<' of total reflection seems also 



