things being premised, it will be readily understood that outline forms sufficient for an entire series of lunars will extend over many pages--they will, in fact, require eighteen pages. There are four sets of observations for time:--one E. and one W., both at beginning and close of the whole; one for latitudes N. and S.; six for six sets of lunars, as described above; six for the corresponding altitudes of the stars, which have to be computed; and, finally, one page for taking means, and recording the observations for adjustment, etc. Each double observation for latitude would take one page; each single time observation one page; and each single compass variation one page. An occulation would require three pages in all; one of which would be for time. At this rate, and taking the observations mentioned above, a book of 500 pages would last half a year. Of course where the means of transport is limited, travellers must content themselves with less. Thus Captain Speke, who started on his great journey amply equipped with log-books and calculation-books, such as I have described, found them too great an incumbrance, and was compelled to abandon them. The result was, that though he brought back a very large number of laborious observations, there was a want of method in them, which made a considerable part of his work of little or no use, while the rest required very careful treatment, in order to give results commensurate with their high intrinsic value.
MEASUREMENTS.
Distance.--To measure the Length of a Journey by Time.--The pace of a caravan across average country is 2½ statute, or 2 geographical, miles per hour, as measured with compasses from point to point, and not following the sinuosities of each day's course; but in making this estimate, every minute lost in stoppages by the way is supposed to be subtracted from the whole time spent on the road. A careful traveller will be surprised at the accuracy of the geographical results, obtainable by noting the time he has employed in actual travel. Experience shows that 10 English miles per day, measured along the road--or, what is much the same thing, 7 geographical miles, measured with a pair of compasses from point to point--is, taking one day with another, and including all stoppages of every kind, whatever be their cause,--very fast travelling for a caravan. In estimating the probable duration of a journey in an unknown country, or in arranging an outfit for an exploring expedition, not more than half that speed should be reckoned upon. Indeed, it would be creditable to an explorer to have conducted the same caravan for a distance of 1000 geographical miles, across a rude country, in six months. These data have, of course, no reference to a journey which may be accomplished by a single great effort, nor to one where the watering-places and pasturages are well known; but apply to an exploration of considerable length, in which a traveller must feel his way, and where he must use great caution not to exhaust his cattle, lest some unexpected call for exertion should arise, which they might prove unequal to meet. Persons who have never travelled--and very many of those who have, from neglecting to analyse their own performances--entertain very erroneous views on these matters.
Rate of Movement to measure.--a. When the length of pace etc., is known before beginning, to observe.--A man or a horse walking at the rate of one mile per hour, takes 10 paces in some ascertainable number of seconds, dependent upon the length of his step. If the length of his step be 30 inches, he will occupy 17 seconds in making 10 paces. Conversely, if the same person counts his paces for 17 seconds, and finds that he has taken 10 in that time, he will know that he is walking at the rate of exactly 1 mile per hour. If he had taken 40 paces in the same period, he would know that his rate had been 4 miles per hour; if 35 paces, that it had been 3.5, or 3½ miles per hour. Thus it will be easily intelligible, that if a man knows the number of seconds appropriate to the length of his pace, he can learn the rate at which he is walking, by counting his paces during that number of seconds and by dividing the number of his paces so obtained, by 10. In short the number of his paces during the period in question, gives his rate per hour, in miles and decimals of a mile, to one place of decimals. I am indebted to Mr. Archibald Smith for this very ingenious notion, which I have worked into the following Tables. In Table I., I give the appropriate number of seconds corresponding to paces of various lengths. I find, however, 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.
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 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