The President's Address. By E. M. Nelson. 169 



Example (2 ante).—p' = 4-050,2- = - 1-683, q' = 0-6898, 

 h = 0-3, K = 0-1247, 



tanS = 0-03, 9 = l°-43' ; tan <£ = 0-0741, <£ = 4°-14; 



tan/3 = 0-1807,/? = 10°- 15'; 



8 = 5°- 57', S' = 6°-l'. 



EXPLANATION OF FIGURES. 



Fig. 40 is an enlarged picture of an aplanatic homogeneous-immersion front of 

 N A 1 • 3, the refractive index of the glass being 1 • 5, and of N A 1 • 3. O is the object, 

 and V its virtual image. AO=1'0; AV=T5; radius AC = 0-6; COH = C*HV 

 = = 60° -4'; CVH = CHO = <f> = 35° - 18'; sin 6 = /* sin <p ; AV = u AO: 



_. fiAO 



radius = • 



M + 1 



Fig. 41 shows the barrel-distortion of the image represented by the small arrow 

 in fig. 44. 



Fig. 42 illustrates a pincushion-distorted virtual image, which woidd be formed 

 by the eye-lens if the image at the small arrow in fig. 44 were rectilinear. 



Fig. 43. B and C represent the positions of the lenses, ami B the distance 

 between them, = d. A B = p, B E = p', C E = q, and CD = q'. 



Fig. 44 represents a 10 power eye-piece for the short tube. The large arrow is 

 the objective image, the curvature of which is exaggerated ; the small arrow illus- 

 trates the objective image reduced in size and rendered more curved by the influence 

 of the field-lens. Note : — The curvature of this smaller arrow is in the same direction 

 as that of the large arrow, and not in the opposite direction as often represented. The 

 principal points of each lens are represented by dots, and those of the entire eye-piece 

 by the lines H and H', while the lines F and F' indicate the focal points ; the focal 

 lengths being of course H F and H' F'. The positions of the principal points of each 

 lens, as well as those of the cardinal points of the eye-piece, are drawn to a scale of 

 2 : 1, and are correctly placed. The diaphragm of the eye-piece is close to H'. 



April 18th, 1900 N 



