196 Mr. A. Mallock. Growth of Trees, with a Note on 



between the surfaces makes a small angle with the surfaces themselves, can 

 be easily observed. 



When the angle of emergence (i) from the face of the prism is nearly 

 7r/2, and the angle (r) at which the ray strikes the face internally is 

 therefore, nearly r?i~^//x, a small change in r causes a large change in i. 



If i = 90 — ly, so that 7 is the angle which the emergent ray makes with 

 the face of the prism, and if e is the difference between r and the angle of 

 total internal reflection (?'o), then dyjde = (B + e)/ N/(2Be), where B stands 

 for ^l cos ro. 



Thus, when e = 0, dy\de=-<:c. This has an important effect on the 

 positions and appearance of the interference bands. 



Below the face of the prism (fig. 5) let there be a flat glass plate touching 

 the face at 0, and inclined to it at a very small angle «. Take as the 

 origin, and the face of the prism as containing the axis of x\ then the 

 distance y between the two surfaces at x is ax. 



E 



Fig. 5. 



If a ray within the prism strikes the surface at A, making an angle r 

 with the axis of y, the transmitted part makes an angle 7 with the face, and, 

 being reflected from the lower plate, again enters the prism in a du'ection 

 hardly differing from r (on account of the smallness of a). It is then in a 

 condition to interfere with the ray reflected from the prism surface at its 

 point of entry. The optical lengths of the paths of the interfering rays are 



