176 TESTING THE MICROSCOPE. 



the distance is proportionally great), we obtain the angle of 

 aperture co according to the formula 

 * co d 



tan 2 =21' 



Its determination may also be obtained by construction with 

 sufficient accuracy. 



(4.) Abbe's Method. Under the object-stage, at a known dis- 

 tance from the plane of adjustment, a horizontal scale is applied, 

 whose zero point is approximately in the centre of the field 

 of view. Pointers are moved along the scale to the right and 

 left until they touch the margin of the bright circular aperture- 

 image in the upper focal plane of the objective. The positions of 

 the pointers are now read off, and the arithmetical mean taken, by 

 which the possibly somewhat excentric position of the zero point 

 is corrected. We thus obtain the linear distance of the extreme 





Jt 



FIG. 102. 



marginal points shown in the focal plane of the objective; and 

 since this distance is proportional to the sine of the angle of 

 aperture, the latter can at once be determined by reference to a 

 table, in which the angular values corresponding to the different 

 distances are once for all computed. 



In order to obtain a favourable illumination for greater distances, 

 Abbe's scale is applied to the side a b (Fig. 102 A and B) and to the 

 two adjacent sides a m and b n (Fig. 102 B) of a rectangular plate 

 of glass, 1 and is viewed from above by the reflexion at the sur- 

 face m n, which is inclined at an angle of 45. By continuing the 

 graduations of the scale upon the two sides at right angles to a b, 



1 This apparatus is now well known as Abbe's Apertometer, and is made 

 semicircular in shape. Vide " Journ. Royal Micr. Soc." i. (1878), p. 19, art. 

 by Mr. C. Zeiss ; and iii. (1880), p. 20, art. by Dr. E. Abbe. [ED.] 



