^Z^MSS^ I^oyal Microscopical Society. 297 
beads le^s than 80,000 to the inch : whilst a visual angle of 6" would 
represent an object whose diameter in the field of a microscope 
magnifying 1000 linear must be ^4 6-Foooth, or less than the 
3,000,000th part of an inch. From this we can form some idea 
of the exceedingly minute character of objective aberration; even 
for a good Jth object-glass it does not exceed the 50,000th of 
an inch.* 
The extreme difficulty of defining a minute row of beads arises 
from the uncorrected aberrations confusing their images, by which 
several images overlap and obliterate the form of individual beads ; 
stiU more is it increased if one set of beads be confused with the 
images of an underlying stratum of intersecting rows, forming a 
complicated beaded lattice-work, as in many interesting scales. 
The Society will permit me to observe that I have found in the 
difficult enterprise of resolving the Podura scale into its component 
beads, the definition may be refined, partly by selecting such pencils 
of rays as pass through the lenses of the object-glass, so as to form 
an image with the most perfect aplanatism, or freedom from spherical 
aberration; all other rays causing haze and nebulous definition, 
and therefore with the least possible use of excentrical pencils of 
light such as emanate from ordinary condensers. In these high- 
power researches the integrity or perfection of the illuminating 
pencil of rays is as important as that of the refractions of the ob- 
jective. In my experience I have found an oblique centrical pencil 
of aplanatic and achromatic cones of light of small aperture (15° 
to 20°) of the greatest practical utility, the obliquity being varied 
according to the object in view. 
Another circumstance is worthy of note, viz. the position of 
the stigmatic image, or of the distance from the back lens of the 
object-glass where there is a real focus. If a precious stone of 
refractive index //^ = 1*6861 can be found, such as is free from a 
double image, the equation for aplanatism 
2^^ - - 4 = 0 
will be satisfied if the gem be a plano-convex lens with the plane 
turned towards the object; the image would be formed without 
aberration. But till this can be found and worked, a search for the 
real focus or best image should not be neglected along the axis of 
the instrument. 
By elaborate calculation it appears that the variation of the 
distance between the front lenses of an object-glass produces a 
* The aberration of lenses depends upon their general shape, and for illumi- 
nation, crossed lenses should be formed into bull's-eyes. 
Convexo- Crossed lens 
Lenses. Piano'convex. plane. Equi-convex. Crossed lens. reversed. 
erra ion ^qq^qq » loooOO ' 100000 ' 100000 ' 100000 * 
