The Present Limits of Vision, By Dr. Royston-Pigott. 183 
spaces quite as wide as the thickness of the lines (indeed, Mr. 
Broun's examination of photographs of these lines, as well as my 
own, confirm this estimate) ; and therefore the absolute diameter of 
the lines themselves would be about the 224,000th of an inch. Such 
a line, or rather, if conceivable, such a black line as this would, if 
placed at ten inches distance, subtend an angle of 
i" very nearly (one-ninth of a second). 
Viewed with a power of 18, its angle would be 
2 seconds. 
With a power of 540 the visual angle would be raised to 
60" or 1' 
(more accurately ^^-r second, which would give 21*75 instead of 
18, and then the power would be 650 instead of 540). 
If therefore the lines on Nobert's plate 112,000 to the inch 
were really simple black lines, they ought, with ordinary sight, to 
be easily distinguishable with a magnifying power of about 600 
diameters, and this would make a visual angle thirty times greater 
than Mr. Broun's result above stated. 
But these lines in general are grooves ploughed in glass of a 
prismatic, round or irregular section ; and since they can only be 
seen with extremely obHque illumination (looking as it were 
sideways) by means of the very wide -angled objective generally 
found necessary, it is probable that the available shadow may be 
much less than the supposed breadth of the line, and quite inde- 
terminable. 
In cutting lines on glass with a diamond, I have been occa- 
sionally much surprised with the beautiful little curls or ringlets 
cut cleanly out of the glass surface ; but this only happened when 
the diamond holder was rotated into one particular position, and 
inclined at one particular angle. When, therefore, we are looking 
at such fine " Nobert " grooves in glass, we are somewhat in the 
dark as to what kind of object or shadow we are really observing. 
For if different grooves be cut in glass, forming differently shaped 
channels in section, whether oval, circular, square, or triangular, a 
remarkable difference in appearance will be observed when viewed 
and illuminated obliquely with transmitted light. Nobert' s grooves 
are, as it were, unknown fobjects, for we know not and never shall 
know the sectional shape of the hollow rulings that compose them. 
The detection of these lines is essentially fitted for high-angled 
glasses; but for real useful physiological work they give but an 
indifferent test of depth of focus, so requisite for everything but 
mere surface markings. When we descry Nobert's XIX. band of 
lines, do we see the breadth of a line, the shadow of the side of a 
