evolutions of a wheel.

=1887. Length of pace.= The length of a man's pace at a natural walk
is about 30 inches, varying somewhat in different men. Each man must
determine his own length of pace by walking several times over a known
distance. In doing this be sure to take a natural pace. When you know
your length of pace you merely count your paces in going over a
distance and a simple multiplication of paces by length of pace gives
your distance in inches.

In going up and down slopes one's pace varies. On level ground careful
pacing will give you distances correct to within 3% or less.

The following tables give length of pace on slopes of 5 degrees to 30
degrees, corresponding to a normal pace on a level of 30.4 inches:

+-------------------------+-----+-----+-----+-----+-----+-----+-----+
|Slopes | 0 deg.| 5 deg.| 10 deg.| 15 deg.| 20 deg.| 25 deg.| 30 deg.|
+-------------------------+-----+-----+-----+-----+-----+-----+-----+
|Length of step ascending | 30.4| 27.6| 24.4| 22.1| 19.7| 17.8| 15.0|
|Length of step descending| 30.4| 29.2| 28.3| 27.6| 26.4| 23.6| 19.7|
+-------------------------+-----+-----+-----+-----+-----+-----+-----+

For the same person, the length of step decreases as he becomes tired.
To overcome this, ascertain the length of pace when fresh and when
tired and use the first scale in the morning and the latter in the
afternoon.

The result of the shortening of the pace due to fatigue or going over
a slope, is to make the map larger than it should be for a given
scale. This is apparent when we consider that we take more paces in
covering a given distance than we would were it on a horizontal plane
and we were taking our normal pace.

In going up or down a slope of 3 or 4 we actually walk 5 units, but
cover only 4 in a horizontal direction. Therefore, we must make
allowance when pacing slopes.

In counting paces count each foot as it strikes. In counting strides
count only 1 foot as it strikes. A stride is two paces.

In practice it has been found that the scale of strides is far more
satisfactory than a scale of paces.

=1888. How to make a scale of paces.= Having determined the length of
our pace, any one of the following three methods may be used in making
a working scale:

_1st method._ The so-called "One thousand unit rule" method is as
follows:

Multiply the R. F. (representative fraction) by the number of inches
in the unit of m