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 each of the rates in the following list:--
Yards. Feet. Inches. 29.333, or 88.000, or 1056.000, in one minute or 0.488, or 1.466, or 17.600, in one second
Measurement of Length.--Actual measurement with the rudest makeshift, is far preferable to an unassisted guess, especially to an unpractised eye.
Natural Units of Length.--A man should ascertain his height; height of his eye above ground; ditto, when kneeling: his fathom; his cubit; his average pace; the span, from ball of thumb to tip of one of his fingers; the length of the foot; the width of two, three, or four fingers; and the distance between his eyes. In all probability, some one of these is an even and a useful number of feet or inches, which he will always be able to recollect, and refer to as a unit of measurement. The distance between the eyes is instantly determined, and, I believe, never varies, while measurements of stature, and certainly those of girth of limb, become very different when a man is exhausted by long travel and bad diet. It is therefore particularly useful for measuring small objects. To find it, hold a stick at arm's-length, at right angles to the line of sight; then, looking past its end to a distant object, shut first one eye and then the other, until you have satisfied yourself of the exact point on the stick that covers the distant object as seen by the one eye, when the end of the stick exactly covers the same object, as seen by the other eye. A stone's throw is a good standard of reference for greater distances. Cricketers estimate distance by the length between wickets. Pacing yards should be practised. It is well to dot or burn with the lens of your opera-glass a scale of inches on the gun-stock and pocket-knife.
Velocity of Sound.--Sound flies at 380 yards or about 1000 feet in a second, speaking in round numbers: it is easy to measure rough distances by the flash of a gun and its report; for even a storm of wind only makes 4 per cent. difference, one way or the other, in the velocity of sound.
Measurement of Angles.--Rude Measurements.--I find that a capital substitute for a very rude sextant is afforded by the outstretched hand and arm. The span between the middle finger and the thumb subtends an angle of about 15 degrees, and that between the forefinger and the thumb an angle of 11 1/4 degrees, or one point of the compass. Just as a person may learn to walk yards accurately, so may he learn to span out these angular distances accurately; and the horizon, however broken it may be, is always before his eyes to check him. Thus, if he begins from a tree, or even from a book on his shelves and spans all round until he comes to the tree or book again, he should make twenty-four of the larger spans and thirty-two of the lesser ones. These two angles of 15 degrees and 11 1/4 degrees are particularly important. The sun travels through 15 degrees in each hour; and therefore, by "spanning" along its course, as estimated, from the place where it would stand at noon (aided in this by the compass), the hour before or after noon, and, similarly after sunrise or before sunset, can be instantly reckoned. Again, the angles 30 degrees, 45 degrees, 60 degrees, and 90 degrees, all of them simple multiples of 15 degrees, are by far the most useful ones in taking rough measurements of heights and distances, because of the simple relations between the sides of right-angled triangles, one of whose other angles are 30 degrees, 45 degrees, or 60 degrees; and also because 60 degrees is the value of an angle of an equilateral triangle. As regards 11 1/4 degrees, or one point of the compass, it is perfectly out of the question to trust to bearings taken by the unaided eye, or to steer a steady course by simply watching a star or landmark, when this happens to be much to the right or the left of it. Now, nothing is easier than to span out the bearing from time to time.