102 On the MOTION of LIGHT. 



compounded of AE and Ee, which is equal and oppofite to AI, 

 is the relative velocity of the light in C, and Af, Ae, are the re- 

 lative velocities of the incident and refracted light. Now, Kc z 

 — AK X 4 Am and Ad 2 -cdX 4cr, rAKX 4cr. There- 

 fore, Ad a — Kc 2 = AK X ^TcT^^Am^ = AK X 4 AB. Now, 

 Ad 2 : Ae 2 - Ap 2 : Af 2 , - Kc 2 : Bl 2 , - AK : AB. Therefore, 

 Ae 2 — Af 2 rABX 4AB, = AO 2 . That is, when the light 

 has pafTed through, and emerges from the refracting flratum, 

 the difference between the fquares of the initial and final rela- 

 tive velocities is equal to the fquare of the fpecific velocity of 

 the medium. 



Also, (becaufe Qe 2 — QJ 2 — Ae 2 — Af 2 ) the difference 

 between the fquares of the initial and final relative perpendicu- 

 lar velocities, is equal to the fquare of the fpecific velocity. 



But it will not always happen that the light will emerge 

 from the refracting flratum after pafling over it, and it may fre- 

 quently happen that it will not pafs over the whole extent of it. 



Thus, fuppofe the light to be within the medium, moving 

 towards the refracting flratum, while the medium is moving 

 more flowly towards the fame quarter, or moving towards the 

 oppofite quarter ; and let the relative perpendicular velocity of 

 the light be equal to the fpecific velocity. Suppofe that the 

 light pafTes through the refracting flratum at A (fig. 3.) mo- 

 ving in the direction and with the velocity AF. It would de- 

 fcribe (by the action of the refracting forces) the parabola ALC, 

 of which AB', equal to AB, is the abfciffa from a diameter, and 

 B'L, equal and parallel to AF, is an ordinate. Draw In paral- 

 lel to AQ^ cutting FL in n. It is plain that d n is the perpen- 

 dicular velocity of the medium, dF the perpendicular velocity 

 of the incident light, and nF its relative perpendicular velo- 

 city. This is equal to twice AB by fuppofition. But FL is 

 equal to AB ; therefore Ln is alfo equal to AB, and An is an 

 ordinate to FL. Alfo, LB, drawn from L to B, is a tangent at 

 L, and bLs is the fituation of the plane BS, when the light 



which 



