Number of Observations requiring record.--A traveller does excellently, who takes latitudes by meridian altitudes, once in the twenty-four hours; a careful series of lunars once a fortnight, on an average; compass variations as often; and an occulation now and then. He will want, occasionally, a time observation by which to set his watch (I am supposing he uses no chronometer). He ought therefore to provide himself with outline forms for calculating these observations, even if he finds himself obliged to have them printed or lithographed on purpose; and in preparing them, he should bear the following well-known maxims in mind:--
Let all careful observations be in doubles. If they be for latitudes, observe a star N. and a star S.; the errors of your instruments will then affect the results in opposite directions, and the mean of the results will destroy the error. So, if for time, observe in doubles, viz., a star E. and a star W. Also, if for lunars, let your sets be in doubles--one set of distances to a star E. of moon, and one to a star W. of moon. Whenever you begin on lunars, give three hours at least to them, and bring away a reliable series; you will be thus possessed of a certainty to work upon, instead of the miserably unsatisfactory results obtained from a single set of lunars taken here and another set there, scattered all over the country, and impossible to correlate. A series should consist of six sets, each set including three simple distances. Three of these sets should be to a star or stars E. of moon, and three to a star or stars W. of moon. Lunars not taken on the E. and W. plan are almost worthless, no matter how numerous they may be, for the sextant, etc., might be inaccurate to any amount, and yet no error be manifest in their results. But the E. and W. plan exposes errors mercilessly, and also eliminates them. One of the best authorities on the requirements of sextant observations in rude land travel, the Astronomer Royal of Cape Town, says to this effect:--"Do not observe the altitude of the star in taking lunars, but compute it. The labour requisite for that observation is better bestowed in taking a large number of distances." So much delicacy of hand and of eyesight is requisite in taking lunars that shall give results reliable to seven or eight miles, and so small an exertion or flurry spoils that delicacy, that economy of labour and fidget is a matter to be carefully studied.
These 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 2 1/2 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 3 1/2 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.