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