RL. W. Wood—Demonstration of Caustics. 301 
Art. XXXII.— Demonstration of Caustics; by RoBert 
WILLIAMS Woop. 
THE caustic surfaces by reflection from concave mirrors can 
be shown geometrically to be the paths to which all the reflected 
rays are tangent. A simple way of demonstrating this experi- 
mentally is the following: A strip of thin steel about 16 
inches long, by 1 in width, is polished on one side until it has 
a good mirror surface. An accurate optical surface is of course 
unnecessary. The curve, for example a semi-circle, whose 
caustic is to be shown is drawn on a piece of photographic 
_ printing paper, and pinned down onto a board with a dozen or 
more pins, stuck vertically through the line. The steel strip 
is bent into this are, and pressed firmly against the row of pins, 
the ends being held in place by a couple of small nails. In 
front of the steel are across the diameter is set up a strip of 
Bristol board with a number of vertical slits, about = of an 
inch wide, and half an inch apart. On setting up the board 
in strong sun-light, in a plane pointing a little below the sun, 
the parallel rays passing through the slits trace their course on 
the paper, are reflected and trace their reflected paths also, 
which in the case of a semi-circular mirror will all be found to 
be tangent to an epicycloid. The complete curve can be 
traced by raising the grating for a moment or two. During 
the exposure it is best to bridge over the steel arc with a piece 
of card-board to exclude diffused daylight. 
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Epicycloidal Caustic showing tangential rays. 
The accompanying drawings (figs. 1 and 2) are copied 
directly from the photographic tracings, and are of course nega- 
tives, the black lines representing the paths traced by the 
luminous rays. It is not easy to get a parabolic surface that 
shall bring all the rays to a focus, each side of the curve being 
apt to have afocus of its own; buta little careful manipulation 
and changing the position of the pins a trifle, will usually 
