On the MO f ION of LIGHT. 



refracting forces, according as they act in the fame or oppofite 

 directions *. 



I 



* It was about the beginning of 1784 that I inveftigated the foregoing demonftration, 

 which, as the reader will fee, is conducted after the method adopted by Sir Isaac New- 

 ton, in his demonftration of the 94th proposition of the firft book of the Principia. I 

 applied to my much efteemed colleague ' Mr Profeflbr Playfair, for his affiftance in a 

 cafe to which the foregoing demonftration may perhaps be thought not to extend, namely, 

 when the motion of the light, and that of the medium, are perpendicular to the refracling 

 furface. Before I had obtained a demonftration which pleafed me, he favoured me with 

 the following elegant analytical demonftration. 



Let v be the velocity of a particle of light when it has arrived at the diftance x with- 

 in the refracting medium (.v being counted from the point in which the particle began to 

 be afted on, and being lefs than the diftance from that point at which the motion of the 

 particle again becomes uniform.) Let y~ be the force acling on the particle at the" di- 

 ftance x. Let a be the velocity of the incident light, and c the velocity of the me- 

 dium in the oppofite direction. 



It is evident that the force f does not a£t on the particle during its paflage through 



v , 

 the whole fpace x, but only during its paflage through the part x. Therefore, 



1 i . C f v x j ' 2vfx • ifx _, 



v* — + 2 I ± , and 2v v = — t. — , or 2v = J That is, iv v + 2c v 



J V + c v ■+■ C V + c 



= zf'x, and, taking the fluent, v 1 + 2cv = 2jfx + C 1 . But when 2/fx = o, we 

 have v 1, +2cv = a* +2ac, and therefore v* + 2c v = a* +2ac+ 2/fx. Let 

 the fluent of 2/ 'x (aflumed, fo that x ftiall be the diftance at which the velocity of the 

 light again becomes uniform) be fuppofed = g 1 . Then v* + 2cv — a 1 + 2ac + g*. 

 Add c % to both fides of the equation. Then v 1 + 2vc + c* =: a % + 2a c + c* + g* 5 



and therefore v + c =: a + c +g*. But a + c is the relative velocity of the 

 incident light, and v + c is the relative velocity of the refrafted or accelerated light. 

 Therefore the fquare of the latter exceeds the fquare of the former by the conftant quan- 

 tity g *. Now, g 1 = 2jfx j and is therefore (by the celebrated 39th propofition of the 

 firft book of the Principia) the fquare of the velocity which a particle of light %vould 

 acquire if impelled from a flate of reft through the whole diftance at which the medium 

 ads on light. 



2 Since 



