or lake maintains itself at rest, and takes a level surface, practically plane if the confined space is small, but otherwise curved into a nearly spherical form. On the other hand if there be an outlet for the water, as the particles have little cohesion they yield to the force of gravity and descend. Thus rain falling on the tops of mountains, if the soil is not soft and easily penetrable, collects in rills which unite and form larger streams. These descend along the sides of mountains and mix with others so as to produce rivers. The course is determined by the nature of the ground, and the general tendency of the water to descend. It is found that if the descent be about a foot in four miles the stream in a straight channel would flow at the rate of about four miles in an hour: the average slope of the large rivers of the world is greater than this. It belongs to Physical Geography to describe the various peculiarities which rivers present in their courses from the mountains in which they rise to the seas into which they fall, such as the cataracts which they form when they change their level suddenly and violently, and their occasional disappearance and reappearance after flowing for some time underground.

389. A canal is an artificial channel of water made to connect two places. If the two ends are not in the same level surface the entire course cannot be in one level surface; and even if the two ends are in the same level surface it may be difficult or impossible to construct the canal entirely on one level owing to the presence of mountains. Of course if the canal were one unbroken channel the water would descend from the higher parts leaving them dry, and would overflow the banks at the lower parts. To obviate this the canal in part of its course consists of separate portions called locks which stand at different levels, and which are separated from each other by flood-gates. When a boat is taken through this part of the canal a communication is opened between the compartment in which the boat is and that into which it is to pass the water in the two compartments is thus brought to the same level, the gates between them are opened and the boat is drawn onwards. Thus every time a boat passes up or down through the locks some water

T. P.

11

is lost from the highest part of the canal; and the supply must therefore be perpetually renewed by natural or artificial means.

390. The mode in which water is conveyed through our large towns offers an interesting exemplification of the principle that liquids stand at a level. A reservoir is formed at as high an elevation as the water is desired to reach; this is kept full by means of water falling into it or being pumped up into it from lower levels. Pipes proceed from the reservoir through the town which is to be supplied, and in any of these the water will rise to the height which it has in the reservoir; so that it can be brought to the upper rooms of tall houses. The ancient Romans were in the habit of bringing water to their towns from a distance, by means of aqueducts, that is by artificial channels constructed on a level surface, or on a gentle descent. Hence it has been supposed that they were not acquainted with the principle that liquids stand at a level; but it seems to be now made out that it was not ignorance of this principle but a want of the necessary pipes which kept them from using the modern system. Even in recent times the ancient system has been adopted as possessing some special advantages; an example is furnished by an aqueduct for supplying water to New York.

XXXI. VOLUMES OF SOLIDS IMMERSED IN
LIQUIDS.

391. If we wish to determine the volume of a solid body of known regular form, as a cube or a sphere, we have only to use the rules for the process which are given in books on Mensuration. Thus, for instance, the solid body may be in the form of a brick 9 inches long, 3 inches broad, and 2 inches deep; and then we know that the volume is expressed in cubic inches by the product of the numbers 9, 3, and 2; that is the volume is 54 cubic inches. But rules cannot be given for finding the volume of any irregular body, as a stone or a coal. It is a natural consequence that we usually estimate the quantity of solids by weight rather than by volume, that is by pounds and ounces rather

than by cubic feet and inches. On the other hand liquids, by their property of yielding and filling all the corners of a vessel in which they may be placed, allow us to determine their volumes easily; and accordingly we usually estimate the quantity of liquids by volume.

392. But we may also use the fundamental property of liquids, namely their extreme mobility, to determine the volume of a solid. We suppose that the solid will sink in a certain liquid if left to itself; then if the solid be put into a vessel of the liquid it will displace liquid equal in bulk to its own. There are various forms in which this fact may be presented. Thus suppose a vessel of sufficient size just full of water; let a solid be carefully dropped in and the water which runs out accurately collected: then this water is obviously just equal in bulk to the solid. The volume of the water collected may be ascertained by pouring it into a vessel which has already been measured and has lines marked on its surface indicating how much it holds when filled up to an assigned level. Or again, take a vessel containing some water, though not full, and observe the level at which the water stands; then put in the solid, which we suppose to go to the bottom and to be perfectly covered by the water. The water now rises to a higher level than before, and the bulk of the solid is exactly equal to that of the water which would be comprised between the two levels. This quantity can be easily calculated if the vessel be of suitable shape; for instance, if the vessel have a rectangular base and its four sides vertical, the volume is found by the rule which we have already exemplified in Art. 391.

393. We have supposed the solid to sink in the water, but we know that many substances, as wood for example, will not sink in water. In this case we must press the solid into the water by a slender wire, or by other means. Or we may attach the solid to another of such a nature that both together will sink in water, and thus we can find the volume of both together; then we can find separately the volume of the sinker, and finally, by subtraction, the volume of the solid with which we are concerned.

394. In the same manner as we propose to find the whole volume of a solid we may also find the volume of any

part of it we please, provided the part is such as could be cut off by a plane. We have only to keep that part with which we are concerned just below the surface of the water, and observe how much of the water runs over if the vessel were originally full, or through what space the level rises if the vessel were originally only partly filled.

395. There are however practical difficulties which may obstruct the process in the case of some bodies. Thus the solid may be soluble in water; then perhaps some other liquid may be found in which the solid is not soluble. Or the water may make its way into the pores of the substance, as it would within a sponge; then perhaps a thin coat of varnish can be applied sufficiently durable to keep out the wet during the short time occupied by the process.

XXXII. WEIGHTS OF SOLIDS IMMERSED
IN LIQUIDS.

396. In the preceding Chapter we have treated of the immersion of solids in liquids as affording a method of determining the volumes of solids. In that Chapter there is no mechanical principle involved; the whole is a matter of mensuration, that is of elementary Geometry: but we are now about to introduce the reader to some very important mechanical facts. Let us suppose that a person takes a stone weighing about 5 pounds, fastens a string to it, and holds the other end of the string; then he supports the stone, that is he exerts a force sufficient to balance the weight of 5 pounds. Let him now hold the string so that the stone may be immersed in a bucket of water; if the stone rests on the bottom of the bucket it is supported without the exertion of any force by the person. But let us suppose the stone not to touch the bottom of the bucket; in this case the weight is apparently much less than before the stone was immersed, and will seem to the person holding the string to be about 3 pounds. The fact is one which can be easily verified to any extent, and it is universally found that when a heavy body is thus suspended in a liquid in which it would sink if left alone its weight seems diminished; the heavy body is as it were to some degree supported by the liquid. It is customary to say that the solid loses a portion of its weight.

397. The next point to settle is the amount of this diminution of weight. The following is found to be the law: when a solid is suspended in a liquid the weight is diminished by the weight of an equal bulk of the liquid. Or instead of saying by the weight of an equal bulk of the liquid we may say by the weight of the liquid displaced. This law can be easily verified. In the case of the stone which we considered in the preceding Article the weight can be accurately determined before immersion. Again, when the stone is immersed let the end of the string instead of being held by the hand be fastened to the end of the arm of a balance, or to a spring which serves as a weighing machine; thus the apparent weight can be accurately determined. Therefore, by subtraction, the diminution of weight becomes known. And, as in the preceding Chapter, we can find the bulk of the liquid which is equal to the bulk of the solid; and consequently the weight of so much liquid becomes known. From these results we can make the requisite comparison, and thus the truth of the law which we have stated is established.

398. Besides the direct comparison of weights by which, as we have shewn in Art. 397, the truth of the law is established, there are indirect methods by which we obtain the same result. Before the stone is immersed its whole weight is supported by the hand. Suppose the sides of the vessel are vertical. When the stone is immersed the weight of which the hand is relieved must be thrown on the vessel in some way, and we may naturally infer that in consequence there must be an increase of pressure on the base just equal to this, and therefore the same increase in the pressure of the vessel on the ground or on any supports on which it rests. Take a vessel full of water and attach it to some weighing machine; suspend the stone in the vessel; then water runs out equal in bulk to the stone, but the spring weighing-machine does not alter its reading. The relief afforded to the weight of the stone immersed is thus inferred to be exactly equal to the weight of an equal bulk of the water.

399. Or we may establish the truth of the law by reasoning. Suppose a solid immersed in a liquid. The