ZOOLOGY AND BOTANY, MICROSCOPY, ETC. 
815 
in what way upon these, the resolving power of the Microscope depends. 
The deduction, thus made, that the resolving power does depend upon 
certain factors, leads at once to the consideration of a limiting value for 
it. Naturally, inquiries of this kind, as to how far we can hope to 
advance, have only a relative value, and can necessarily be only con- 
sidered from the point of view of our present resources. 
The fundamental formula for the capacity of the Microscope given 
by both the theory of Abbe and that of Helmholtz for central illumi- 
nation is 
a 
where 8 denotes the smallest distance of the elements of a regular 
structure which can be distinguished by an optically perfect objective, 
A. the wave-length of the effective light (in vacuo), and a the aperture of 
the system. This equation shows that 8, the smallness of which is a 
measure of the capacity of the Microscope, can be diminished in two, and 
in only two, ways. We can either (1) increase a, or (2) diminish X. 
Since the work of Abbe and Helmholtz, increase in the magnitude of 
a, i. e. of the aperture, has been the great aim of all opticians who have 
attempted jthe improvement of the Microscope. Now a = n sin u where 
n denotes the refractive index of the medium in front of the first lens of 
the system, and u the angle made with the axis by the extreme ray from 
a central point of the object which can traverse the system. On purely 
geometrical grounds this angle u cannot exceed 65°, in order that a 
certain, even though very small, space may intervene between object and 
system (for the cover-glass and room for adjustment). Thus the value 
of sin u can scarcely exceed 0 * 95. When, as is generally the case, this 
geometrical limit has been reached, the aperture can only be increased 
by raising the value of n the refractive index of the medium in front of 
the objective. We are thus led to the principle of immersion systems. 
With respect to these it must be borne in mind that it is not sufficient 
simply to interpose between object and objective an “ immersion liquid ” 
of high refractive index : it is also essential that no medium shall be 
present between object and immersion liquid, even in the microscopically 
thinnest layer, whose refractive index is less than that of the immersion 
liquid. Otherwise, however high may be the refractive index of the latter, 
the aperture of the system will be reduced by total reflection to the 
magnitude a' = n\ if n' is the lowest refractive index of any layer 
occurring between object and immersion liquid * Now for most prepara- 
tions we are compelled to use cover-glasses. Those usually employed, 
which can be easily made and are consequently moderate in price, have 
refractive indices of 1 • 52 to 1 * 53. The limit of aperture to be attained 
by the use of such glasses is therefore only about 1*44 to 1-45. To 
obtain higher apertures, cover-glasses of high refractive indices must be 
used, and here many difficulties are met with. 
The firm of Schott and Genossen have prepared glasses having 
refractive indices as high as 2*0. But cover-glasses made of such glass 
are very costly owing to the loss of material involved in their construc- 
tion, since they have to be ground down to the required thickness of 
* See this Journal, 1890, p. 11. 
