compound. If this force were absent, there would be no such thing as a compound substance, and we should be limited in our range to some fifty or sixty substances, most of which are metals. Thus we see that the force of gravitation binds the larger masses of the universe together, and prevents the earth from leaving the sun. The force of cohesion binds together the various particles or molecules of the bodies which we see around us, while in virtue of chemical affinity we obtain a much greater variety of substances than we should otherwise have. Force does not, however, always produce motion. Thus a stone, lodged on the top of a precipice, is not in motion, although in virtue of the force of gravitation of the earth, it presses or weighs upon the ground of the cliff. But this same force which causes the pressure of the stone against its support, will cause it to fall downwards over the side of the cliff, with a continually increasing velocity, when once the support is removed, and it is free to obey the attraction of the earth. While the stone lay on the top of the cliff, the force with which the earth attracted it was counteracted by an opposite force-namely, the resistance of the support on which the stone was placed; and when this resistance was removed, the stone began to fall, and continued to do so with increasing velocity until it reached the bottom of the cliff. We thus see that the simplest effect of a force is the production of motion, and it is only when the force is resisted by another that we have equilibrium or repose. In the following pages, therefore, we shall commence with the case where a single force produces motion, and end with that where two or more counteracting forces produce equilibrium or repose. CHAPTER I. LAWS OF MOTION. LESSON I.--DETERMINATION OF UNITS. BEFORE proceeding further, let us fix upon our units of measurement. 7. Unit of Duration.-In the first place, with respect to duration or time, the second will be the most convenient unit, and being in general use nothing further need be said about it. But as regards the units of length and mass, those in use in this country are by no means well adapted for the purposes of science, in which respect the metrical system of France has decided advantages over all others. Being a decimal system, all calculations are by it rendered extremely simple, besides which it is in general use amongst the scientific men of all countries. 8. Unit of Length.-The metre is the foundation of the metrical system of linear measure, one metre being equal to 39°37079 English inches. In the following table the metre and its decimal derivatives on the one hand are compared with British inches on the other : One kilometre (one thousand metres) 39370 79000 In the margin is a scale, representing a decimetre or tenth part of a metre, which is subdivided into centimetres and millimetres. 9. Unit of Superficial Extent or Surface.-The measures of surface and capacity follow easily from those of length. Of the former we have squares, of which the sides are millimetres, centimetres, decimetres, and metres; a square metre being likewise called a centiare. We have also the square whose side is ten metres, called the are, and the square whose side is 100 metres, called the hectare. 10. Unit of Capacity or Volume.-Again, with regard to measures of capacity or volume, we have the cubic millimetre, the cubic centimetre, called the millilitre, the cubic decimetre, called the litre, and the cubic metre, called the kilolitre. The relation between the measures of length, surface, and capacity is seen from the following table : 8 LENGTH. SURFACE. square decimetre (A) Millimetre square millimetre square metre or centiare CAPACITY. cubic millimetre. cubic centimetre. cubic decimetre or litre. cubic metre or kilolitre. If we take the first column, or that of length, we find that (B) is ten times as great as (A), (C) ten times as great as (B), and so on, each letter denoting a length ten times as great as the preceding one. Again, if we take the second column, or that of surface, we find that (B) is 100 times as great as (A), (C) 100 times as great as (B), and so on. And, finally, if we take the third column, or that of capacity, we find that (B) is 1,000 times as great as (A), (C) 1,000 times as great as (B), and so on. FIG. 1. Thus ten is the multiplier in the first column; the square of ten, or 100, the multiplier in the second; and the cube of ten, or 1,000, the multiplier in the third. Keeping the table in view, the following examples will render evident the excellences of the metrical system, as compared with that in use in England. Question I.-How many square feet are there in 150 square inches? Answer.-Since one foot is equal to twelve inches, one square foot is equal to 12 X 12 or 144 square inches. Hence there are 15010416 square feet in 150 square inches. = Question II.- How many square centimetres are there in 150 square millimetres? Answer.-1'50. Question III.-How many cubic yards are there in 93 cubic feet? Answer.-Since there are three feet in a linear yard there are 3 × 3 X 3, or 27 cubic feet in one cubic yard, and hence there are 3 or 34 cubic yards in 93 cubic feet. Question IV.-How many litres are there in 1,789 millilitres? Answer.-1789. These examples are quite sufficient to show the superiority of the metrical system of measures. 11. Unit of Mass.-In the next place, according to this system the relation between the unit of volume and that of mass is of a very simple kind. The unit of mass is that of one cubic centimetre of pure water at the temperature of 4° centigrade, which is the point of maximum density of water. The mass of this bulk of water is called a gramme, and the gramme has decimal derivatives similar to those of the metre. The following table shows the relation between the French and English system of estimating masses : 12. Unit of Velocity.-Velocity, or rate of motion, is easily understood, for we have constantly before us bodies in motion as one of the most familiar experiences of life. A railway train passes, and we estimate that it is moving at the rate of forty miles an hour. We have a perfectly distinct conception of this velocity, even although the train should not travel the whole hour, or the whole forty miles. We mean that were it to go on moving at the same rate at which it was moving when we saw it, it would in the course of an hour pass over forty miles. Perhaps it begins to slacken its pace shortly after, so that its velocity is soon reduced to thirty miles an hour, then to twenty miles, then to ten miles, until it finally stops. Thus its velocity during the operation of stopping has been continually changing from the high speed of forty miles an hour downwards, and during no two seconds has it continued to move at the same rate, and yet we can say with propriety that at such an instant the train was moving at the rate of thirty miles an hour. We mean, of course, that if the train were to keep the same velocity or rate of motion it had at the given instant, it would in one hour move over thirty miles. We thus see that we mean the same velocity when we say a body is moving at the rate of thirty miles an hour, or sixty miles in two hours, or fifteen miles in half an hour, or 7 miles in a quarter of an hour. In fact, velocity means the whole space moved over divided by the time taken, or calling s the space, S t the time, and ʊ the velocity, then v =—. t Having already fixed upon the metre as our unit of length and the second as our unit of duration, the most convenient unit of velocity will be the velocity of one metre in one second. The velocity of two metres in one second will be denoted on the scale by 2, that of three metres in one second by 3, and so on. 13. Remarks on Unit of Mass.-By its mass we mean the quantity of matter contained in a body. While we confine ourselves to bodies of the same kind, it is very easy to estimate the relative mass, for this will vary as their volume. If, for instance, we have a number of similar cubes of iron, we know at once that the united mass of two such cubes will |