192 THEORY OF MICROSCOPIC OBSERVATION. 



inclination of the rays coming from below, if the mirror and source 

 of light are of sufficient extent, is determined by the size of the 

 diaphragm. The angle under which the latter is seen from the 

 centre of the air-bubble is the same as that which is found by the 

 peripheral rays of the incident cone of light. If this angle = 30, 

 then also the angle of deviation, which the emergent rays form 

 with the corresponding incident ones, is determined for marginal 

 rays, such as T S, which before and after the refraction lie on 

 the surface of the cones of light. 



If we draw through the point of intersection 0, of the incident 

 and emergent rays, the perpendicular X Q, and if the angles of 

 aperture taken at 60 and 30 are denoted by &> and 8, we get 



LSO T = 180 - L TOR-, 



c\ 



or, since LTOR = LQOR-LQOT = ^ , 



6 



LSO T = 180 - ^^; 



Zi 



therefore, in the given case, 



L S T = 180 - 15 = 165. 



Now, since a radius drawn through bisects this angle of 

 deviation and crosses the direction of the ray in the air-bubble at 

 right angles, if the angle of incidence is denoted by a, the angle 

 of refraction by a', and half the angle of deviation by />, we 

 obtain the further relation 



a - a = 90 - p = 7i. 



If we assume the mean refractive index of water to be T3356, this 

 equation will be satisfied if a 20 45', while a will therefore 

 = 28 15'. 



The position of the point P is thus determined : the triangle 

 C P J gives the relation 



CP: r = sin a: sin f~180 - (90 - ?' 

 consequently, 



OP-r. sina = sin 20 45 ' . r = -64838 . r 



sm ' sin6 C 



in (90 + | 



interpret them correctly in detail. "We can at any rate affirm that Harting's 

 statement does not explain the microscopic image of the air- bubble, hollow 

 cylinder, &c. The reader wishing to follow out these points should not shrink 

 from mathematical explanations. 



