ZOOLOGY AND BOTANY, MICROSCOPY, ETC. 
71 
(5) Microscopical Optics and Manipulation. 
Microscopic Vision.* — Dr. G. J. Stoney considers that in the recent 
paper by Lord Bayleigh, an abstract of which apj>eared in this J ournal 
(1896, p. 681), the generality of Abbe’s method of studying the images 
formed by Microscopes is not sufficiently appreciated. In the present 
memoir, therefore, his object is to offer a fuller account of this generality 
than he has given elsewhere.f 
The author begins by contrasting two of the many possible methods 
of resolving the disturbance of the tether in front of and close to the 
object. The most obvious resolution into spherical waves is the foun- 
dation of Airy’s method of studying the images formed by telescopes, 
while the mode of resolution into plane waves is the foundation of 
Abbe’s method of studying the images formed by Microscopes (the 
Diffraction Theory). 
As fundamental principles, seven propositions are then discussed, 
with the help of which, and the more familiar laws of optics, it is 
claimed that nearly everything in microscopic vision may be explained. 
Proposition 1. 
However complex the contents of the objective field , and whether it or 
parts of it be self luminous or illuminated in any way , however special , the 
light which emanates from it may be resolved into undulations , each of ivhich 
consists of uniform plane waves. 
This is practically an extension of Fourier’s theorem. By the 
objective field is to be understood the whole of the object and its sur- 
roundings, of which an image is formed by an instrument, or in the eye 
of the observer. To prove this proposition the author conceives a plane 
through the object, perpendicular to the line of sight (the Objective 
Plane), to be divided up into squares, one containing the projection of 
the objective field, and the others replicas. The proof then follows from 
the fact that a point in the objective field with the corresponding points 
in the replicas forms a system which by the theory of diffraction gratings 
will produce a disturbance of the aether resolvable into plane waves. 
Proposition 2. 
The standard image may be regarded as resulting from the superposition 
and mutual interference of uniform luminous rulings of equidistant parallel 
bright lines , extending over the whole field of view ; each ruling being pro- 
duced by the convergence upon it, after the reversal, of two or more of 
the undulations of uniform plane waves, into which the light emitted by 
the object may be resolved. 
By the standard image is meant the image formed by imagining 
the undulations to travel backwards to the positions that had been 
occupied by the original object. The image thus formed will therefore 
be the most perfect which the light from the object is capable of 
forming, and may be used as a standard of perfection which cannot be 
exceeded by the images formed by any optical contrivance. In the 
microscopic image, owing to the fact that the angular aperture of the 
objective is less than 180°, the amount of detail falls short of that in 
the standard image. With the best immersion lenses with aperture 120° 
* Phil. Mag., xlii. (1896) pp. 332-49, 423-42, 499-528. 
f See ‘On the Foundation of the Diffraction Theory,’ English Mech., December 
13, 1895, p. 380. 
