that
the pace of neither man nor horse is constant in length during all rates
of walking; consequently, where precision is sought, it is better to use
this Table on a method of approximation. That is to say, the traveller
should find his approximate rate by using the number of seconds
appropriate to his estimated speed. Then, knowing the length of pace due
to that approximate rate, he will proceed afresh by adopting a revised
number of seconds, and will obtain a result much nearer to the truth than
the first. Table I. could of course be employed for finding the rate of a
carriage, when the circumference of one of its wheels was known; but it
is troublesome to make such a measurement. I therefore have calculated
Table II., in terms of the radius of the wheel. The formulae by which
the two Tables have been calculated are, m=l x 0.5682 for Table I., and
m=r x 3.570 for Table II., where m is the appropriate number of seconds;
l is the length of the pace, or circumference of the wheel; and r is the
radius of the wheel.

The Tables will be found on the next page.

[Tables I and II appear on p 34].

b. When the length of Pace is unknown till after observation.--In this
case, the following plan gives the rate of travel per hour, with the
smallest amount of arithmetic.

For statute miles per hour--Observe the number of paces (n) taken in 5.7
seconds: let i be the number of inches (to be subsequently determined at
leisure) in a single pace; then ni/100 is the rate per hour.

For geographical miles per hour--The number of seconds to be employed is
5. This formula is therefore very simple, and it is a useful one. (A
statute mile is 1760 yards, and a geographical mile is 2025 yards.)

For finding the rate in statute miles per hour in a carriage--Observe
the number of revolutions (n) made by the wheel in 18 seconds: let d be
the number of inches in the diameter of the wheel; then n d/200 is the
rate per hour.

The above method is convenient for measuring the rate at which an animal
gallops. After counting its paces it may be through a telescope, during
the prescribed number of seconds, you walk to the track, and measure the
length of its pace. If you have no measuring tape, stride in yards
alongside its track, to find the number of yards that are covered by 36
of its paces. This is, of course, identical with the number of inches in
one of its paces.

Convenient Equivalents.--The rate of 1 mile per hour, is the equivalent
to