Tools of Measurement.
In many of the arts, more especially those which belong to engineering and carpentering as a part of architecture, it is absolutely necessary to make sure of a perpendicular line, i.e. a line which, if continued, would reach from any point of the earth’s surface to its exact centre below and its zenith above. Were it not for the power of producing this line, none of the great engineering works of modern or ancient days could have been undertaken.
Take, for example, the wonderful tunnels which have been driven through the earth, of which the Mont Cenis Tunnel is one of the greatest triumphs of modern engineering. Beginning, as the workmen did, at opposite ends of a tunnel many miles in length, and labouring only by the lines laid down by the engineers, the men worked steadily on until they met in the centre.
A few blows, and the then narrow dividing wall was shattered, the men shook hands through the aperture, and then, after enlarging it, leaped wildly from one side to the other, having successfully solved the great problem. With such marvellous precision had the lines been laid, that only a few inches had to be smoothed down on either side, and the sides or walls of the tunnel showed no traces of the junction.
So rapid has been the progress of engineering that a tunnel of a mile in length would, within the memory of man, have been thought as daring a project as was the Mont Cenis Tunnel, which has just been given as an example. Indeed, I know of a railway tunnel, not quite a mile in length, where the engineers had committed some error, so that the two halves, instead of meeting exactly, overlapped each other so much that the mistake was only discovered by the workmen, who heard the strokes of their companions’ picks on their sides, and not in front. Consequently, a great waste of time took place, and the centre of the tunnel had to be made with a double curve, like the letter S, and trains are obliged to slacken speed until they have passed it.
Those who have lived long enough to remember the current literature of the past generation will call to mind the ridicule that was cast upon the idea of a tunnel that should pass under the Thames. That it would be useful if it could be completed, no one ventured to doubt, but that such an idea could be conceived by any one out of a lunatic asylum was rather too much for the journalists of the day. However, the tunnel was made, and so proved the theorists wrong on the one side. And, when made, it was of very little use, which proved them wrong on the other side. Now the proposal to carry a submarine tunnel from England to France excites not half the opposition that was elicited by the comparative child’s-play of a tunnel under the Thames.
The only mode of laying down the lines on which the men worked is by suspending very heavy balls to very fine wires, and then, by means of delicate optical instruments, ascertaining whether the wires are in line with each other.
Familiar instances of the use of this principle may be seen in the plumb-rule and level of the builder or carpenter. The latter, with a base of ten feet in length, is often used by the gardener when he wishes to lay the absolutely level lawns that are required for our modern game of croquet, where the hoops are scarcely wider than the balls, and the lawn has in consequence to be nearly as level as a billiard table.
I may here remark that the name plumb-rule is derived from the Latin word plumbum, or lead, in allusion to the leaden weight at the end of the string. The word “plumber” is due to the same source, and signifies a worker in lead.
These invaluable aids to the development of civilisation are due to one principle, namely, that which we call Gravitation, but which ought more properly to be termed Attraction, and which attracts all parts of the earth towards its centre. We are all familiar with the anecdote of Newton and the falling apple, which may be true or not, but which at all events bears on the present subject. No matter on what portion of the spherical earth a tree may be, every fruit becoming disengaged from it is attracted to the earth, the line which it takes, unless disturbed by external forces (such as wind, &c.), being that which passes from the zenith to the centre of the earth.
This imaginary line is a perfect perpendicular, and the visible line which is formed by the delicate wire of the tunnel-boring engineering instrument, or the comparatively coarse string of the plumb-rule and level, are approximations sufficiently close for practical purposes. So it is in a mathematical proposition. As mathematical lines have no breadth, they are simply indicated or represented by the lines of the figure, the bodily eye being incapable of seeing what is perfectly visible to the mental eye, namely, length without width. So the wire and string perform in practical work exactly the same office which is fulfilled by the lines of a mathematical proposition drawn on paper.
We have already, when treating of the Fall-trap, seen how this principle is brought into operation by those who are utterly incapable of discerning the physical principle, though they can apply it materially with wonderful effect.
It is, perhaps, needless to mention the value of the Measure to any handicraftsman.
I well remember that when, some twenty-four years ago, I was taking lessons from a carpenter in the art of making ladders, gates, fences, hurdles, and other rough-and-ready work, my quaint old tutor related an anecdote of and against himself. He very ingeniously set me to work at boring the auger-holes in the gate-posts which were to be united by the mortise chisel and mallet, and to sweeten the rather severe, because unaccustomed, labour, told me that, when he was a boy, he was doing just the same thing.
Being rather tired of twisting the auger handle (and no wonder either), he withdrew the instrument, and put his finger into the hole by way of ascertaining its depth. Immediately he found himself on his back, having received a tremendous box on the ear from his father, whose parental wrath was excited by the idea of his son condescending to use his finger by way of measure, when he had a two-foot rule in its own special pocket.
There are, however, many cases where even a two-foot rule would be insufficient for the work, and where a measure of thirty or forty feet is needed.
Now, there is no doubt that by means of a two-foot, or even a six-inch, rule any number of feet might be measured accurately; but, considering the number of junctions that have to be made, it is not likely that any pretence to accuracy could be insured.
Then, a rod of forty, or even of twenty, feet in length would be awkward and unmanageable, and the only plan left is to take a string or cord of the requisite length.
Even here, however, is a difficulty. The string would not allow of short measurements, such as inches, being written upon it. Let, however, a broad tape of inelastic material be substituted for the string, and all is easy enough.
The next plan is to provide for the portability of the tape in question, to insure its reduction into the smallest possible compass, and to be sure that it is not twisted so as to damage its accuracy. These objects are all attained by the ordinary Tape Measure of the present day, which, whether it be a yard measure in a lady’s workbox, or a surveyor’s measuring tape, is a ribbon of comparatively inelastic material, coiled up when not wanted, and capable of being drawn out to its fullest extreme when needed.
Putting aside the breadth of the line, and consequently disregarding the liability to twist, we have in the Fishing-reel of the modern angler an exact case in point. So we have in the lady’s yard measure, and in the gardener’s or builder’s tape, all these being modifications of the same idea.
Suppose now that we pass to Nature, so as to ascertain whether any such provisions were in existence before it was imitated, however unconsciously, by man. This certainly was the case with one of the commonest and most insignificant of our insects, the little Gall-fly, belonging to the genus Cynips. It could not lay its eggs without the aid of a very long ovipositor, and, owing to structural details, it cannot carry that ovipositor in a straight line, as is done by many insects, some of which have already been mentioned. Accordingly, it is coiled up exactly like our measuring tapes, and can be unrolled when needed. The long, protrusible tongues of the Wryneck, Creeper, and Woodpecker are examples of a similar structure, the tendinous portions being coiled round the head when not needed.