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. [Illustration: FALLING FRUIT.] [Illustration: PLUMB-RULE.] [Illustration: LEVEL.] 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.