On the MOTION of LIGHT. 103 



which entered the refradting flratum at A is at L. BL is the 

 velocity with which the light pafles through L, and Bb is its per- 

 pendicular velocity. This is evidently equal to d n, the perpen- 

 dicular velocity of the medium. Since, therefore, they have 

 the fame velocity in the diredlion LF, it is plain, that the light 

 will not pafs through the plane bL ; and becaufe it is fubjedled 

 to the adlion of the refradling forces, it will be defledled towards 

 AQ^ and will defcribe another arch LC of the parabola, and 

 will be met in C by the point c of the plane AQ^ which has 

 moved in the mean time through cC parallel to IL. The point 

 1 is the vertex of the relative path Ale, and the abfcifla Ig being 

 equal to BA, it is evident that f g, the relative perpendicular 

 velocity, is equal to twice BA, that is, to the fpecific velocity. 



If, as in fig. 4. the relative perpendicular velocity of the 

 light be lefs than the fpecific velocity, it will not pafs through 

 the whole refrad^ing ftratum : For draw I n parallel to AQ^ 

 cutting FL in n. It is plain than dn is the perpendicular ve- 

 locity of the medium, and dF the perpendicular velocity of 

 the light, and nF the relative perpendicular velocity. Becaufe 

 this is fuppofed lefs than twice AB, Ln is lefs than FL, and An 

 is not an ordinate to FL. Let oVh, parallel to An, touch the 

 parabola in V, and draw h k perpendicular to AB. Then oK, or 

 n d, is the perpendicular velocity of the light. Therefore, fince the 

 perpendicular velocities of the light in V, and of the medium, are 

 equal, the light is then the neareft pofTible to the plane BS, 

 which has now obtained the fituation b s. It is therefore in 

 the vertex of the relative parabola, or, drawing Vv parallel to 

 Ff, V will be the vertex of the relative path Avl ; therefore 

 the light, after pafTmg through V and L, will defcribe another 

 arch LC of its parabolic path, and it will be met in C by the 

 point c of the plane AQ^ which has in the mean time moved 

 along cC. Fig. 5. exhibits the fame particulars in the cafe 

 when the light within the medium is moving from the refradl- 

 ing ftratum, but is overtaken by it. 



Thus 



