the other end, let us suppose, is closed for the present by the thumb. Referring to Fig. 38 we see that if the vertical height of D A above the liquid surface is not more than the barometric height for the liquid, the liquid will remain within the tube. Now by the laws of pressure in any continuous body of fluid at rest, the pressure is the same at all points in the same horizontal layer, and the pressure increases with the depth below the free surface. Hence the pressure at E is that of the atmosphere, and if the end B be lower than E, the pressure at B is greater than that of the atmosphere. Thus, when the end B is opened, the portion B E of the liquid will flow out, and the vacuum thereby created will draw down other portions of the liquid to occupy successively the same position and then flow out. The action will clearly cease as soon as the surface of the liquid in the vessel has sunk to the level of either end of the tube. 96. Diffusion of Gas.-This short sketch of the properties of gas would be incomplete without reference to diffusiona law which was first put in a clear shape by the late Mr. Graham. His experiment consists in having a tube (Fig. 39) filled with a gas-let us say, with hydrogen-the lower extremity being immersed in a liquid, while the upper extremity is closed with a porous partition that will allow the particles of gas to move through it. Under these circumstances he found that in the course of time the liquid rose in the tube, showing that there was a diminution in the volume of gas. He also found that the quality had become changed, so that, while hydrogen had escaped through the pores of the partition, air had entered. If this process be carried on sufficiently long, all the hydrogen will escape, and the tube will be full of atmospheric air; but the volume of air will not be equal to the original volume of hydrogen, and in general, if the gas within the tube be lighter, bulk for bulk, than that outside, a greater volume will go out than will enter, so that the interior volume will diminish; but if the gas in the tube have a greater specific gravity than that outside, the reverse will take place. FIG. 39. 97. Absorption of Gas by Solids and Liquids.-In conclusion, we shall very briefly allude to the absorption of gases by solids and liquids. Thus charcoal has the power of absorbing or retaining in its pores a considerable quantity of various kinds of gas. Many liquids likewise have the power of absorbing or retaining gas, sometimes to a very great extent thus water absorbs carbonic acid gas, and when strongly impregnated with this gas forms the beverage known as soda-water. It also absorbs ammoniacal gas, as well as hydrochloric acid gas, and becomes, in the one case, liquid ammonia, and in the other, liquid hydrochloric acid. CHAPTER III. ENERGY. LESSON XIII.-DEFINITION OF ENERGY. 98. It is only of late years that the laws of motion have been fully comprehended. It has, no doubt, been known since the time of Newton that there can be no action without reaction; or if we define momentum to mean the product of the mass of a moving body into its velocity of motion, then whenever this is generated in one direction an equal amount is simultaneously generated in the opposite direction, and whenever it is destroyed in one direction an equal amount is simultaneously destroyed in the opposite direction. Thus the recoil of a gun is the appropriate reaction to the forward motion of the bullet, and the ascent of a rocket to the downrush of heated gas from its orifice; and in other cases where the action of the principle is not so apparent, its truth has notwithstanding been universally admitted. It has, for instance, been perfectly well understood for the last 200 years that if a rock be detached from the top of a precipice 144 feet high it will reach the earth with the velocity of 96 feet in a second, while the earth will in return move up to meet it, if not with the same velocity, yet with the same momentum. But, inasmuch as the mass of the earth is very great compared with that of the rock, so the velocity of the former must be very small compared with that of the latter, H in order that the momentum or product of mass into velocity may be the same for both. In fact, in this case, the velocity of the earth is quite insensible, and may be disregarded. The old conception of the laws of motion was thus sufficient to represent what takes place when the rock is in the act of traversing the air to meet the earth; but, on the other hand, the true physical concomitants of the crash which takes place when the two bodies have come together were entirely ignored. They met, their momentum was cancelled, and that was enough for the old hypothesis. So, when a hammer descends upon an anvil, it was considered enough to believe that the blow was stopped by the anvil; or when a break was applied to a carriage-wheel, it was enough to imagine that the momentum of the carriage was stopped by friction. Let us now consider some of those influences which helped to prepare men's minds for the reception of a truer hypothesis. 99. Work. We live in a world of work, of work from which we cannot possibly escape; and those of us who do not require to work in order to eat, must yet in some sense perform work in order to live. Gradually, and by very slow steps, the true nature of work came to be understood. It was seen, for instance, that it involved a much less expenditure of energy for a man to carry a pound weight along a level road than to carry it an equal distance up to the top of a mountain. 1 It is not improbable that considerations of this kind may have led the way to a numerical estimate of work. Thus if a kilogramme be raised one metre high against the force of gravity, we may call it one unit of work, in which case two kilogrammes raised one metre high, or one kilogramme raised two metres high, will represent two units, and so on. We have, therefore, only to multiply the number of kilogrammes by the vertical height in metres to which they are raised, and the product will represent the work done against gravity. The force of gravity being very nearly constant, and always 1 Energy means simply the power of doing work. in action, is a very convenient force to measure work by, and it is generally made use of for this purpose; we shall therefore take as the unit of work the kilogrammetre, or the work represented by one kilogramme raised one metre high, against the force of gravity at the earth's surface. 100. Relation between Energy and Momentum.--Having thus defined work, the next point is to connect it with momentum. Now, we have already seen (Art. 45) that a body shot upwards with the velocity of 98 metres per second will rise 49 metres in height before it stops, so that if a kilogramme be shot upwards with this velocity, it will ascend this height against the force of gravity. Hence a man who projects a kilogramme vertically upwards with the velocity of 98 metres per second will thereby have imparted to the moving kilogramme an amount of energy which will enable it to raise itself 49 metres in height, and thus to perform 4'9 units of work. Again, it has been shown (Art. 45) that if the kilogramme be projected upwards with twice this velocity, or that of 196 metres per second, it will now rise four times as high; for it will rise 196 metres in height before it stops, instead of only 4'9 metres as before. We thus see that the work which can be accomplished by a moving body is increased four times by doubling the velocity; in other words, it is proportional to the square of the velocity. Again, if the body projected upwards have the mass of two kilogrammes, it will do double the work of a single kilogramme projected upwards with the same velocity, so that the work which a moving body is capable of doing is proportional to its mass. A little reflection will convince us that the work capable of being done by a body whose mass (in kilogrammes or thousands of grammes) is m, and whose velocity is v, will be represented by the expression mv2 (A). Thus if m = 1, that is to say if the mass be one kilogramme, and if v = 9·8, that is to say, if it be projected upwards with the velocity of 98 metres a second, we shall have by the above expression |