The Pyrenees

by Hilaire Belloc

The rule for heights is, divide by 3, shift the decimal point one place to the right, and you have the height in English feet, within a certain limit of error, which I shall presently detail.

The rule of thumb as applied to measures of distance is to take the number of kilometres (a kilometre is 1000 metres, and is, as one may say, the French mile), divide by 8, and multiply by 5, and you have the corresponding number of English miles within a certain limit of error, which I shall describe presently.

For all ordinary purposes these two rules are sufficient, though in both cases they somewhat exaggerate. They make a French distance measured in English miles a little too far, and a French height, measured in English feet, a trifle too high.

The exact constant of error is, in the case of the heights, 1.6 feet in every 100. Thus if your rough calculation gave you a height of 10,160 feet, the exact height ought to be just 10,000; you see upon the map in the blue figures referring to metres, “3048” (which happens by the way to be within two steps of the height of the Bac Lactous). You divide by 3, add a 0, and get 10,160, and you know by the constant of error that the true height is just exactly 10,000 feet.

The knowledge of this constant gives us a rough-and-ready method of getting a height within a very small degree of accuracy, and for any purposes where such accuracy is required, I recommend it. It consists in cutting off the last three figures, multiplying what is left by 4, and then again by 4, and subtracting that from your first rough calculation. It sounds complicated, but it does not take half a minute, and you will be well within two feet of any height; for most heights you are likely to calculate, you will be right within a few inches.

For instance, you see 2403, in blue figures upon the map dividing by 3 and shifting your decimal point, you at once get 8010; there is your rough calculation, which you know to be a trifle in excess of the truth. Cut off the last three figures and you have left 8, multiply 8 by 4, and then again by 4, and you have 128 as the amount of your error. The peak is by this calculation 7882 feet high, and rough as the rule is you are within 20 inches of the truth: the exact height of such a peak in English feet is 7883.7624....

However, if you want absolute accuracy, multiply the French measure by 3.2808992, and you will be sufficiently near the truth to save your soul.

As to distances, the exact proportion of error, when you turn miles into kilometres by dividing by eight and multiplying by 5, is 2 inches or so short of 50 feet too much in every mile; when, therefore, you are dealing with a hundred miles, you are very nearly, but not quite a mile out in this form of calculation. The error is, within a very small fraction, 1%.

If therefore you want an easy rule for turning your rough calculation into an accurate one, you cut off the last two figures and subtract from your total the figures thus left. For instance, 244 kilometres divided by 8 gives 30½, and that multiplied by 5 is 152.5; cut off the 52, leaving “1” on the left, subtract that 1 (making 151.5), and you are within a few yards of accuracy. As questions of distance count nothing in mountains compared with questions of height, I will make no mention of decimals, but proceed to a very different matter, which is the way of counting that the mountaineers have, and this you will do well to heed blindly.

When you are tired and distracted and wondering perhaps whether you can push on, if you have the good luck to find a shepherd, he will tell you your distance to such and such a place in hours. The Spanish, the Gascon, the Béarnais, and the Catalan dialects all use the same words, so far as sound goes, for this kind of measure, and the Basque will never speak to you in Basque: it is part of the Basque tenacity never to do this. So if you find yourself in any part of the high hills where a man can talk to you of distances, you always hear the same sounds “Dos Oras,” “Quart’ Ora,” “Mi’ Ora,” and the rest. This habit, as every reader knows, is universal throughout the world wherever true peasants exist; but in mountains, whether they be Welsh or African, it is not only universal, but it withstands all the invasion of the modern world.