180 Transactions of the Eoyal Mierosco^pical Society, 
excited much attention.* So many persons in recent years have 
seen Nobert's bands at least twice as close with half the power, that 
the conclusion can hardly be avoided that the glasses must have 
been of late greatly improved in quality. The opticians, by the 
continual study of these lines and of the natural lines of the dia- 
toms (formerly so much admired, before a more perfect resolution 
had been attained), at length drew forth the practical result that 
the widest possible aperture was absolutely required for the highest 
efforts of resolution in these interesting objects. This practical 
result anticipated by many years the theory lately popularized by 
Helmholtz. 
According to the results of the undulatory theory of light, the 
size of the fringes of diffraction of a bright disk or line of light 
which are capable of totally obscuring an object of less diameter 
than these fringes, varies as the sine of the half aperture for the 
same wave of light. Accordingly the resolving power for brilliant 
disks or lines of light varies proportionally to the natural sines of 
these apertures for one kind of light. For t 
2 sin. a 
If A be constant, e varies inversely, as sin. o or sin. semi-aperture. 
Professor Helmholtz having given some prominence to this 
formula, deduced from those of La Grange, it may be well to re- 
peat that — 
€ represents the smallest interspace recognizable between two 
bright lines or disks : on the condition that the diffraction fringe of 
one does not overlap that of its neighbour. 
\ represents the length of the wave of light under considera- 
tion, which for mean rays is generally taken thus : 
A = 0-00055 mm. 
= 0-00055 X -0393708, 
the metre being 39 • 37078984 Enghsh inches, so that I find 
^ = 46T82 iiich. 
And half the wave-length for an extreme aperture of nearly 180° is 
therefore s^ko^ of an inch. This very curiously closely approximates 
to the recent elaborate measures of diatoms, such as the Amj^hijpleura 
joellucida. 
Argument : e vabies as . ^ . ^ being a Constant Factor. 
sm. a 2 
* I am indebted to Mr. Broun's paper for this statement. 
t Dr. Fripp has done great service to the readers of the * Monthly Microscopical 
Journal ' by his able translation of the paper by Herr Helmholtz, one of the most 
brilliant of Continental mathematicians. 
