____
/ 4D squared 2D
The semi-conjugate axis = \/ ----- = -----
3 ___
\/ 3

[TEX: \text{The semi-conjugate axis} = \sqrt{\frac{4D^2}{3}}
= \frac{2D}{\sqrt{3}}]

Since the distance from the center of the curve to either focus is
equal to the square root of the sum of the squares of the semi-axes,
the distance from o' to either focus

____________
/4D squared 4D squared 4D
= /\ /----- + ----- = ----
\/ 9 3 3

[TEX: \sqrt{\frac{4D^2}{9} + \frac{4D^2}{3}} = \frac{4D}{3}]

We can therefore make the following construction (Fig. II.) Draw a d
the chord of the arc a c d. Trisect a d at o' and k. Produce
d a to l, making a l = a o' = o' k = k d. With a k as a
transverse axis, and l and d as foci, construct the branch of the
hyperbola k c c' c", which will intersect all arcs having the common
chord a d at c, c', c", etc., making the arcs c d, c' d, c"
d, etc., respectively, equal to one-third of the arcs a c d, a c' d,
a c" d, etc.

* * * * *

TEST CARD HINTS.

By Dr. F. OGDEN STOUT.

I know it is the custom with a great many if not the majority of
opticians to fit a customer without knowing whether he has presbyopia,
hypermetropia, or any of the other errors of refraction. Their method
is first to try a convex, and if this does not improve, a concave,
etc., until the proper one is found. This, of course, amounts to the
same thing if the right glass is found. But in practice it will be
found both time saving and more satisfactory to first decide with what
error you have to deal. It is very simple, and, where you have no
other means of diagnosing (such as the ophthalmoscope), it does away
with the necessity of trying so many lenses before the proper one is
found. You should have a distance test card placed at a distance of
twenty feet from the person you are examining, and in a good light.

A distance test card consists of letters of various sizes which it has
been found can be seen at certain distances by people with good
vision. Thus the largest letter is marked with a cc, meaning that this
should be seen at two hundred feet, and another line, XX, at twenty
feet, which is the proper distance for testing vision for distance,
for the reason that a normal eye