' On the Velocity of Propagation of Light in Water. 337 



If, now, t] and z 2 are the angles of incidence, and r x and r 2 the 

 angles of refraction at the two surfaces (see fig. 8), then 



sin i x = n sin r xi sin2 2 =?isinr 2 , . . . . (1) 



r,+r 2 =«, (2) 



d=i l -H 2 — «, or i l = d— i 2 +a, .... (3) 



sin (d— « 2 + a)=?isin (a— r 2 ) (4) 



On inserting the minimum of the deflection, we find 



. _ . _ d+ot a, 



Suppose, now, a neighbouring ray with the same position of 

 the prism has the deviation d— 8, its index of refraction being v, 

 and its first angle of refraction being p { . It follows from the 

 invariability of the angle of incidence that 



sm— — =vsinp 1 (5) 



For the second angle of refraction we have 



8in(-i^-8j=vsiii(a--p 1 ). ... (6) 

 If,now,weputp 1 =- +/3 and develope (6), we find 



d + a — 8 8 d+u — 8 . 8. 



• u a u ■ a 



= vsin^cos p — v cos<j sin p. 



(7) 



Similarly, from (5) we find 



. d-\-u — 8 8 d+u—8 . 8 

 sm ^ — cos -+ cos sm- 



= v sm - cos p + v cos -~ sin p. 



(8) 



By the addition and subtraction of (7) and (8) we get the fol- 

 lowing : — 



. d+a—8 8 . a 



sin cos ^ = v sin -cos /3, ... (9) 



d+a — 8 .8 ex. . _ ,__. 



cos - — sm ^ = v cos rSlD|3. . . . (10) 



