ZOOLOGY AND BOTANY, MICROSCOPY, ETC. 



831 



relative size of the two kinds of globules varied from 2 • 00 to 2 • 43, 

 while with the other observers they were approximately the same, the 

 forms and different dimensions of the two corpuscles being without 

 practical influence. If we take the mean of the relative sizes of 

 the images of the two kinds of corpuscles for each observer, and 

 divide by each of the means, and so find the length of distinct vision, 

 the quotient ought to be approximately equal to unity for all four 

 observers, if the apparent size of the images were exactly proportional 

 to the distances of distinct vision. The following comparison shows 

 however that it is not so : — 



Whilst, therefore, the apparent size of a microscopical image is 

 principally affected by the length of distinct vision, yet there is an 

 additional influence, similar to the personal equation (e7-reu7- person- 

 nelle) of astronomers, which produces more or less modification. 



Conditions of Aplanatism for Wide-angled Pencils. — It is a very 

 common supposition that the necessity for constructing microscopical 

 objectives of several lenses, instead of one only, is entirely a question 

 of correcting spherical and chromatic aberrations, — that the practical 

 method for correcting spherical aberration with a wide-angled pencil 

 in fact consists in the distribution of the refraction over several lenses. 



The dioptrical researches of Professor Abbe — from which the law 

 of aplanatic convergence * was one particular result — show that the 

 successive refraction of the rays by several lenses one above the other 

 is the essential condition on which depends the formation of an image 

 hy wide-angled pencils, quite independently of the question of spherical 

 and chromatic correction. 



If an objective of say 140° angular aperture were constructed 

 which should collect the rays in a similar mode to that of a single 

 lens (where the semi-diameter of the emergent pencil 

 p = /tan u and not/ sin u), and this objective was perfectly 

 corrected for spherical aberration, a plane object would 

 nevertheless be delineated like Fig. 193 — a conical 

 surface with a point, instead of a plane or moderately 

 curved field. 



A single lens can never fulfil the condition of aplanat- 

 ism — that is of correct formation of the image — except 

 for small angles for which the tangent and sine are nearly identical.! 



Penetrating Power of Objectives. — We have added to the 

 Numerical Aperture Table on the wrapper of the Journal a further 



* See this Journal, ante, p. 322. 



t See further on this subject, this Journal, iii. (1880) p. 509. 



3 I 2 



Fig. 193. 



A 



