DR, G. W. ROYSTON-PIGOTT ON A SEARCHER FOR APLANATIC IMAGES. 593 
In consequence of this unexpected discovery, regarding the quality of a “very fine” 
one-eighth, it was returned to the opticians to their surprise for better compensation. 
It was then, after more accurate compensation by them, again submitted to precisely 
the same testing conditions. 
New results . — Appearance of a slight nebulous yellow cloud through which could be 
distinctly seen the ivory scale finely graduated, the bulb sparkle, and even minute sepa- 
rated mercurial particles scattered within the glass stem (fig. 7). 
The definition had been therefore decidedly reformed. Previously, however, to the 
alteration, experiments had been tried for the purpose of ascertaining whether a defective 
glass would still form a fine miniature. It might be reasonably expected that such slight 
errors as had escaped the notice of eminent opticians would not materially injure a minia- 
ture image in which the aberration would probably be reduced in the miniature itself. 
The image of the thermometer now formed with the imperfect eighth was viewed with 
a fine sixteenth (at about 800 diameters), when it was gratifying to observe a very beau- 
tiful display of the picture well defined in all respects (fig. 4). 
These and other experiments appeared to warrant an important conclusion — that an 
image-test miniature formed by an objective of fair quality enjoyed sufficient accuracy 
of definition in miniature (even when the object was placed at varying distances from 
the stage or focal point of vision) to form a trustworthy test of microscopical definition, 
provided the aperture of the miniature-forming objective was equal to that of the 
objective to be tested. 
To estimate the size of a miniature («) of a given object (4) placed at a considerable 
distance ( d ) from the miniature (fig. 1 «), it is necessary to consider that the conventional 
focal length F of an objective may be defined to be 10 inches divided by the micrometric 
ratio of amplification (to) when the image is thrown on a screen 10 inches from the object, 
so that 
F= — , when d= 10 
m 
or 
( 1 ) 
When very deep objectives are used (fig. 1) the position of the plane of focal vision 
varies very slightly for a considerable increase of the length of the microscope, so that if 
the draw tube be graduated, the increase of power is nearly proportionate to the in- 
creased length or reading, because the focal plane being nearly fixed, the image will 
appear upon a screen enlarged proportionally as its distance (d) increases. On reversing 
the rays, the miniature diminishes in proportion as a given object is removed further from 
it : from which it follows that approximately, and sufficiently near for the purpose in hand, 
to co d when F is constant 
4 m 2 
