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PROFESSOR MARTIN DUNCAN’S ADDRESS. 339 

minuteness may be microscopically displayed as well as minute 
miniature images.” To this part of Dr. Pigott’s observations it 
may be pointed out that it has never been supposed, so far as I am 
aware, that there is any limit of w7s¢bz/zty in the Microscope other 
than that imposed by the sensibility of the observer’s retina, the 
correction of the objective, and the illumination. The question of 
a limit of visibility is quite distinct from that of a limit of separation, 
just as in telescopic vision a single star is always visible, however 
small its visual angle, provided it is sufficiently dvzgh7, but a double- 
star requires a certain minimum aperture of the objective, dependent 
on the angular distance of both stars. 
Discussing the variability of the blackness and thickness of the 
marginal annulus of refracting molecules, as exemplified in a glass 
spherule ‘1 inch diameter, and in the featherlets of the death’s-head 
moth and plumelets of Aipparchus Janira with objectives of 
20° Ang. Ap. power 200, and 140° Ang. Ap. power 800, he 
writes :—“ If then the minute fibrillee of the plume can be clearly 
distinguished as closely packed black lines at a visual angle of 20 
seconds with a low aperture of 20°, this result is fatally opposed 
to the popular idea that very close lines, or very minute lines or 
bodies, can only be distinguished with large angular aperture. 
These lines were most sharply seen though less than zy$59 inch 
thick.” After denoting the disappearance of distinctive shadows 
and consequent obliteration of structural molecules with excessive 
angular aperture, illustrating his meaning by the structure of 
Podura scales, with different stops and under very varying condi- 
tions, Dr. Pigott states that he has come to the conclusion that 
residuary abberration was not the only cause of the obstinate 
obscuration of minute crowded molecules in translucent organic 
forms, but that 
“ Excessive angular aperture, he found, attenuated mar- 
gin. . . . There is, it may be said, something unnatural in 
the mode of vision intrinsic to very high angled glasses, It 
is undoubtedly true that such a glass presents an a//-round 
vision. It really conveys visual rays from a given brilliant 
particle, at every inclination in azimuth and altitude, and 
this too at one and the same instant. To illustrate this 
position a minute die may be imagined the zg¢gq0 inch 
broad. The highest angled objective really enables the 
observer to collect rays emanating from four sides and the 
top at the same instant. The human eye could at most 
view three sides at once. Doubtless the effect of this 
angular vision all round the corners, causes particles to look 
spherical, when sufficiently minute, even if cubical.” 
Now it is not necessary to say plainly that this view is founded 
upon a fundamental error, “belonging,” to use Professor Abbe’s 

