362 
SUMMARY OF CURRENT RESEARCHES RELATING TO 
(8) Special attention is called to the fact that the Abbe theory deals 
with complex objects ; for only such objects are subject to resolution. 
Single particles and uniform areas are outside its domain. These latter, 
however, are microscopic objects, and all objects are essentially different 
shaped aggregations of points. An isolated point-like particle, no 
matter what its minuteness, may be seen if it present sufficient contrast 
with the surrounding microscopic field. The size of the disc image is 
no less than a limit determined finally by aperture. That limit in size, 
varying inversely with aperture, determines the limit of resolving power. 
This is the gist of the theory of microscopic vision which harmonises 
with our experimental study of aperture. 
Microscopic Vision.* — A paper read by Mr. E. M. Nelson under the 
above title gives an interesting historical sketch of the theory of micro- 
scopic vision and its present position. 
After glancing at Dr. Goring’s experiments on angular aperture in 
1837, Mr. Nelson goes rather fully into the history of the controversy 
initiated by Dr. Pigott in the M. M. J. (July 1870). Amid much error 
and much high-sounding Greek verbiage, Dr. Pigott had the merit of 
stating several important truths, viz. : — 
(1) That a water-immersion lens can have a greater aperture than any 
dry lens, and similarly a homogeneous than a water-immersion. 
(2) That illuminating power is increased by the use of higher re- 
fractive media. 
(3) The suggestion of homogeneous immersion. 
Possibly Dr. Pigott’s lucubrations suggested to Mr. P. B. Tolies the 
improvements connected with his name ; for in 1874 he actually con- 
structed a balsam immersion objective, and in 1873 an apertometer on 
much the same principle as that now known as Abbe’s ; moreover, the 
word “ homogeneous ” as applied to immersion objectives is probably due 
to Mr. Tolies. 
Mr. Nelson now traces the history of diffraction from Fraunhofer, 
through Herschel and Nobert, to Dr. Barnard in 1869. Fraunhofer, in 
studying the well-known equation sin 0 = -r , had thought that the limit 
o 
of microscopic vision was reached when 8 = A. and 6 consequently 
equalled 90°. If Fraunhofer’s theory were correct, not even the 9th 
band of Nobert’s 19th band test-plate (56,300 lines per inch) could 
be resolved in monochromatic yellow light ; but Dr. Barnard and 
Colonel Woodward had resolved up to the 19th (112,600 lines per 
inch) with a P. and L. water immersion 1/16. 
We are now brought to the era when the opinions of Abbe and 
Helmholtz were made known to this country by Dr. Fripp. Abbe’s 
great idea of using Snell’s equation (law of sines) as a standard to which 
all kinds of aperture might be referred, simplified matters, and put fresh 
meanings into and enlarged the ideas connected with aperture. Both 
Pigott and Tolies used Snell’s law, ^ sin <£ = /j! sin </>' ; but Abbe went 
further, and said, p, sin <f> = fi sin </>' = numerical aperture. 
Among the enlarged ideas put into the word “ aperture ” by Prof. 
Abbe, its photometric value stands first. The radiation of light from 
* Proc. Bristol Naturalists’ Soc., viii. pt. ii. (1896-7) pp. 141-66 (6 figs.) 
