238 Transactions of the Royal Microscopical Society, 
Still further reduced by a J, placed before the prism, would be : 
1 _i_ _ i_ 
14 2 > 144» 146' 
Supposing, now, the prism to be 100 inches from the i condenser, 
the miniature would be again reduced 800 times, and the size of the 
miniatures in January, April, and July should be, in fractions of 
an inch : 
11300 0? 115000? TTTooo* 
But if the actual disk be measured with a delicate eye-piece, 
screw-micrometer and spider lines, the disk in May measured 
Tirio^ of an inch; and the black ring nearly the s-^iwo, as nearly 
as the extreme brightness permitted of such estimation. 
Eoughly, then, it may be stated that generally the solar disk 
formed by a lens should be one-hundredth part of the focal length ; 
for a 1-inch lens gives an average of tI^ inch in the mean value. 
Doubtless the moon can be examined microscopically in a 
similar way, and its diameter by a 1-inch lens would also nearly 
equal 
yig^ inch. 
And some persons have actually turned the microscope into a weak 
telescope. 
3. The Practical Application of the Wave Theory to the Cal- 
culation of the BlacJc and White Diffraction Rings and the 
Central Dishs consequent upon the Vibration of the Particles 
of Ether and the Interference of Undulating Waves. 
The expression for the disturbance of an ethereal particle at a 
given point and instant of time is composed of two factors ; the 
first expressing the intensity of the brightness, or showing dark- 
ness ; and the second factor involves the distance of the origin of 
light, the aperture, the velocity of the wave, its length, and the 
epoch.t 
* A most remarkable effect of diffraction is observed here. If you enlarge 
the disk by reducing it less at a certain point, no diffraction rings are developed ; 
but however much you reduce the disk, the spurious disk remains of the same 
size, but the rings become fainter and fainter. The disk is really shaded off 
towards the perimeter, and hence as the light fades more and more the disk also 
begins to diminish, for it is really brightest at its central part. 
t Sir Gr. B. Airy, in his ' Treatise on the Undulatory Theory of Optics,' 
obtains the following expression for the disturbance : 
„ri„.{^(.^ + !^)_B}. 
Professor Helmholtz gives a similar formula : 
(2 IT 1 « 
A sin. < — (^ac + db — at) + constant > • . 
