t to zero and the shaft be turned, with the first disk clamped,
till a desired number appears on the zero line; let then the first disk be
released and the second clamped and so on; then the fixed disk will add up
all the turnings and thus give the product of the numbers shown on the
several disks. If the division on the disks is drawn to different scales,
more or less complicated calculations may be rapidly performed. Thus if for
some purpose the value of say ab cubed [root]c is required for many different
values of a, b, c, three movable disks would be needed with divisions drawn
to scales of lengths in the proportion 1: 3: 1/2. The instrument now on sale
contains six movable disks.

_Continuous Calculating Machines or Integrators._--In order to measure the
length of a curve, such as the road on a map, a [Sidenote: Curvometers.]
wheel is rolled along it. For one revolution of the wheel the path
described by its point of contact is equal to the circumference of the
wheel. Thus, if a cyclist counts the number of revolutions of his front
wheel he can calculate the distance ridden by multiplying that number by
the circumference of the wheel. An ordinary cyclometer is nothing but an
arrangement for counting these revolutions, but it is graduated in such a
manner that it gives at once the distance in miles. On the same principle
depend a number of instruments which, under various fancy names, serve to
measure the length of any curve; they are in the shape of a small meter
chiefly for the use of cyclists. They all have a small wheel which is
rolled along the curve to be measured, and this sets a hand in motion which
gives the reading on a dial. Their accuracy is not very great, because it
is difficult to place the wheel so on the paper that the point of contact
lies exactly over a given point; the beginning and end of the readings are
therefore badly defined. Besides, it is not easy to guide the wheel along
the curve to which it should always lie tangentially. To obviate this
defect more complicated curvometers or kartometers have been devised. The
handiest seems to be that of G. Coradi. He uses two wheels; the
tracing-point, halfway between them, is guided along the curve, the line
joining the wheels being kept normal to the curve. This is pretty easily
done by eye; a constant deviation of 8 deg. from this direction produces an
error of only 1%. The sum of the two readings gives the length. E.
Fleischhauer uses three, five or