Before the introduction of railways we scarcely possessed any standard by which an idea could be formed of the distances and movements of the planets by comparison with those which exist on the terrestrial globe. Thus, the mean distance of the moon from the earth is about 237,000 miles. A steam-carriage on a railway, proceeding uninterruptedly, at the rate of 25 miles an hour, would run 237,000 miles in 1 year, 4 weeks, and 2 days. This falls within the limits of our conception. We may imagine something analogous to this, supposing a carriage, or rather a succession of carriages, to be kept constantly at work for rather more than two years, and working 12 hours per day. But our powers of imagination fail us in estimating a distance equal to that of the earth from the sun, namely, ninety-five millions of miles.[12] Our steam-carriage illustration is here no longer available, since it falls far beyond the boundaries of probability. Proceeding uninterruptedly at twenty-five miles an hour, it would require 433 years to move over a space equal to ninety-five millions of miles.—Dr. Lardner.
Precocious Mental Calculation.
A rare exceptional instance of this faculty being cultivated and matured for a highly-useful purpose, is presented in the case of Mr. Bidder, the eminent civil engineer, known in his childhood as “the Calculating Boy.” (See a portrait in the Boy’s Own Book.)
George Parkes Bidder, when six years old, used to amuse himself by counting up to 100, then to 1000, then to 1,000,000: by degrees, he accustomed himself to contemplate the relations of high numbers, and used to build up peas, marbles, and shot, into squares, cubes, and other regular figures. He invented processes of his own, distinct from those given in books of arithmetic, and could solve all the usual questions mentally more rapidly than other boys with the aid of pen and paper. When he became eminent as a civil engineer, he was wont to embarrass and baffle the parliamentary counsel on contested railway bills, by confuting their statements of figures almost before the words were out of their mouths. In 1856, he gave to the Institution of Civil Engineers an interesting account of this singular arithmetical faculty—so far, at least, as to show that memory has less to do with it than is generally supposed: the processes are actually worked out seriatim, but with a rapidity almost inconceivable. They are accomplished mentally by occupying the mind simultaneously with the double task of computing and registering. The first—computing—is executive, or reasoning, and is that portion of the process, which, whilst it is the most active, is not that which causes the greatest strain upon the mind. The result is recorded by the second faculty, registering, which is the real strain upon the mind, and that by which alone the power of Mental Calculation is limited.
Experience has shown that, up to a certain point, the power of registering is as rapid as thought; but the difficulty increases, in a very high ratio, in reference to the number and extent of impressions to be registered, until a point is reached, the registering of which, in the mind and by writing, are exactly balanced. Below that point, mental registration is preferable; above it, that by writing will be as quick, and more certain.
All the rules employed by Mr. Bidder were invented by him, and are only methods of so arranging calculation as to facilitate the power of registration: in fact, he thus arrives at a sort of natural algebra, using actual numbers in the place of symbols. When he first began to deal with numbers (in his 6th year), he had not learned to read, and certainly long after that time he was taught the symbolical numbers from the face of a watch.
A brief outline of Mr. Bidder’s method is given in the Year-Book of Facts, 1857, pp. 149-152. The paper, in extenso, has been edited and published by Mr. Charles Manby, F.R.S., Honorary Secretary to the Institution of Civil Engineers.
The Roman Foot.
The late celebrated architect and antiquary, Luigi Canina, made a great number of inquiries as to the length of the ancient Roman foot. He measured very carefully the Antonine and Trajan columns, and found them (exclusive of their pedestals and some pieces let in to repair them) exactly alike. This height, which was known to have been 100 Roman feet, was measured with extreme care by means of rods of wood carefully dried, and found to be exactly 29·635 French mètres. Measuring chains were then constructed of this length, and the Roman miles (mille passuum) carefully measured down the Appian Way as far as the twelfth mile, and were found to correspond with the traditional sites of the milestones. The great length of these measurements being such an extensive check, their accuracy was at once accepted by the Roman archæologists as the best authority known. This would make the ancient Roman foot 11·66753 English inches; and the mile 4861·41 English feet; being about one-eleventh less than our English mile of 5280 feet. For rough reckoning the antiquary may deduct one-eleventh from Roman miles to bring them into English; or may add one-tenth to English miles to bring them into Roman; the ratio being 10:11, but inversely. There is a common error in supposing the Roman mile, or mille passuum, was 1000 paces, or single steps. This is not the case: the military passus consisted of two steps (gressus), or about 5 feet Roman.—Notes and Queries.