Take four flat sticks--size or material does not matter, but for an
example let them be of deal--eighteen inches long, half an inch wide,
and a quarter of an inch thick, and plane them up true and smooth. At an
inch from the end of each stick make a dot, and divide the sixteen
inches between the dots into inches, half inches, etc., as if the sticks
were measuring rules. Using the dots as centres, bore in each stick a
round hole just large enough to hold a piece of brass or other tubing
whose internal diameter is that of a pocket pencil. Into one end of each
stick fit a section of the tube, opening the edge as in eyeleting to
prevent the quarter-inch ring so made from slipping out. Take a pair of
the sticks, and hinge them together at the ends which have not been so
treated with a piece of the tube--it will be about half an inch
deep--eyeleting as before. Hinge the other pair together in the same
way.
Now take a half-inch block of wood of any shape you please, but not more
than two inches across; bevel it round its upper edge, and through its
centre from the back drive an inch screw whose threaded part will just
fit into the holes in the sticks. Screw it in till the head is flush
with the bottom of the block. You now want a tracer or stile, for which
take a similar screw, and cut off its head by filing the smooth part
down to a gently tapering point. Slip the screw into the hinge of one of
the couples, and keep it in its place by a leather washer above and
below, making the distance between the under side of the wood and the
point exactly that of the thickness of the block.
[Illustration]
Now get half a dozen half-inch round-headed dresser-hooks, and put the
apparatus together in the way shown in the diagram, where B and C are
the points at which your sticks are hinged. Slip one of the legs over
the block F, and screw it down so that it will move freely but firmly
with a leather washer. Place the leg (C D) under F B, and screw it into
position from the upper surface with one of the dresser-hooks. Place the
leg (C E) over A B, and screw that into place with another hook, also
from above. The third hook is beneath the apparatus just close to B, the
fourth beneath just close to A, and the fifth and sixth are used to
screw the block on to the drawing-board, and are put in on the bevel, so
that their heads will not project above the surface of the block. The
tracer is screwed point downwards at C, the pencil is at A; and
pencil-tracer, block, and hooks at A and B are all of equal length, so
that the machine moves smoothly and evenly over the flat surface of your
drawing-board.
Now place a map beneath the tracer, and a plain sheet of paper beneath
the pencil. Hold the tracer with the right hand, the pencil with the
left, and carefully guide the tracer over the outline of your map. Let
the pencil move about as it pleases, and you will find that whatever the
tracer does the pencil will mimic. The pencil will gradually draw a copy
of the map, but it will move twice as fast as the tracer, and make its
copy twice the size of the original. This is the result of the way we
have at present arranged our pantagraph. The principle is that the copy
compared with the original is always in the same proportion as the
distance from the block to the pencil bears to that from the block to
the tracer. Here the distance in a straight line from F to A is double
that from F to C, hence the copy is double the size. The position of the
tracer between the pencil and the block depends on the points in the
sticks at which they are screwed together, and these you can vary to
suit any scale you desire, remembering always that your figure (C G B H)
must have its opposite sides equal--that is to say, C H must always
equal G B, and C G must always equal B H.
To enlarge your map, the distance from F to C must be less than from F
to A; to reduce your map the distance must somehow be greater. Hence you
have only to transpose your pencil and tracer, putting the pencil at C
and the tracer at A. To reverse the map, and keep it of the same size,
put the block at C and the tracer at F. In short, by shifting about the
pencil, block, and tracer in the different holes you will soon
understand the curious properties of your new copying-machine. One thing
do not forget, and that is that when you shift your pencil the hook
which is put close by to steady its pressure on the paper should be
moved with it.
The pantagraph, or pantograph, was invented by Christopher Scheiner two
hundred and eighty years ago; and, carefully made of brass, is in many
forms now used in architects’ and other offices where much drawing and
copying are done. If not made quite truly its lines may be shaky, but it
will be found invaluable for the accurate placing of points, to which
lines can be afterwards filled in.
The pattern we have given is easy to make. The instrument may be of
different dimensions and of different materials. It may be fitted
together in a different manner, but it must have its central figure with
the opposite sides equal.
Our mathematical friends will soon be able to demonstrate the reason of
its action, and it may be no little satisfaction to the bulk of our
readers to find that there is some practical use in old Euclid after
all!