Problems, and one which is most generally used.

For example, supposing we wish to find out the variation from a straight line on a curve of 400 feet radius with a locomotive whose extreme centre of wheels are 20 feet. We wish to know this to find the width of tire to be put on the forward driving wheels to prevent falling off the rails. We are supposing now an 8-wheel engine, 4 drivers, and 4 wheels in a truck.

Now we have the radius, a b, 400 feet, and the chord, a c, 20 feet, which is the distance the wheel centres are apart; from b, as a centre, we describe the arc, a d c, with b a, as radius. Bisect the chord, a c, at f; then af will equal 10 feet, and f c equal

10 feet. Now to find the distance, f d, which is the versed sine:

RULE. Find the square of a b, and from it subtract the square of a f; the remainder find the square root of, then the product; subtract from a b, and the remainder will give the distance, df.

A TABLE of the Fractional Parts of an Inch, when divided into thirty-two parts; likewise a foot of twelve inches, reduced to

The great utility of the above table is to facilitate the multiplication and division of parts of an inch; also in calculations. For example, suppose a sheet of iron to be 20ğ inches long, 12 and inches broad, and and of an inch in thickness, what number of cubic inches does it contain?

32

32

1. A LEVER is an inflexible bar, either straight or bent, supposed capable of turning round a fixed point, called the fulcrum.

According to the relative positions of the weight, power, and fulcrum, on the lever, it is said to be of three kinds, viz. when the fulcrum is somewhere betwixt the weight and power, it is of the first kind; when the weight is between the power and the fulcrum, it is of the second kind; and when the power is between the weight and the fulcrum, it is of the third kind, thus: