2 
It will be necessary to allude to several points in this 
paper of paramount interest in microscopical observations at 
the present moment, and I venture here to rapidly glance at 
the issues which must now be undertaken (it is hoped) by 
physicists better qualified in every way for the difficult task, 
where, in the cause of science, ‘‘to rest and be thankful” 
amounts to disloyalty to nature and her bountiful revela- 
tions. 
These researches, more or less significant according as 
they may affect future microscopical interpretation, have 
been patiently followed out during a considerable period, as 
against the general belief in the perfection of modern instru- 
ments, which have commanded the award of the highest 
honours in international exhibitions ; and but for the con- 
currence of some able observers, formerly opponents, the 
writer could, perhaps, hardly have dared to traverse esta- 
blished views almost fundamental. 
I propose, therefore, to establish the following points by 
careful experiments and calculation. 
That whilst the microscope far exceeds the telescope in 
amplifying power, its various appliances introduce unsus- 
pected sources of error ; that many of its showings are the 
result of a toilsome complicated system of illumination, de- 
pendent upon the degree of individual experience in hitting, 
as it were by hazard, upon the best defining pencil of trans- 
mitted rays suitable to produce the desired features and conceal 
the lenticular imperfections of special glasses ; that residuary 
aberration (hitherto ignored) plays an important part in pro- 
ducing delusive appearances, either within, without, or at 
the best or aristokratic focus; that it may be readily detected 
by the aberrameter ; that aperture produces very remarkable 
results upon the visibility of eidolic appearances; that the 
residuary aberration is capable of ready detection and mea- 
With an eye-piece of th focal length (inches being understood through- 
out this paper as the unit) and a focal length jth, corresponding to the 
increased effect of the most celebrated objectives now constructed by Messrs. 
Powell and Lealand, capable of resolving Nobert’s 19th band of lines ruled 
on glass, 112,668 lines per inch, it will be seen 
100 
ia ale 
The powers of the glasses calculated by this formula precisely correspond to 
the list of powers of the different combinations with a C or third eye-piece 
of one inch focal length. 
_ Objective . 2in. lin. Zin. Zin. thin. Athin, Athin, JAthin. 
Power. . — 100 200 400 800 1600 2500 5000 
and four times these powers for a deep eye-piece of 3 focal length. 
= 20,000 linear. 
