tinguished 'philosopher conceived the idea of having a long thin rod with small balls at each end accurately balanced in a horizontal position, by a fine thread attached to its middle point. This lever is a species of pendulum, which may oscillate backwards and forwards in a horizontal plane by the horizontal attraction of two masses, brought near its ends on opposite sides; just as the common pendulum makes oscillations in a vertical plane, from the attraction of the mass of the earth in a vertical direction. Two large masses of lead were brought near the small balls at the end of this lever when perfectly at rest, but on opposite sides, so that the effect of each would be to move the lever in the same direction; the lever will begin to move, and continue to make oscillations as long as the large masses are near the balls. This is the most unexceptionable proof of the attraction of matter on matter which can possibly be conceived; the motion of the lever is most certainly due to the attraction of the masses of lead, and the force is evidently the same in kind as that by which a body falls to the earth; the only difference in these two forces arises from the difference of the attracting This fundamental fact of the attraction of the balls being established, we have only to observe the time of the oscillations, and the length of the lever, the centre of the great masses being considered as the centres of attraction. From these observations, incomparably more accurate than any which can be made on the attractions of a mountain, Cavendish determined the mean density of the earth to be about 5 times the density of water. The density thus assigned by Cavendish is not at all greater than might be conjectured from pendulum observations. Newton had long before advanced it as a probable supposition that the density of the earth might be about five or six times that of water; and the perfect agreement of the result of many modern experiments with this conjecture, is one proof, among many others, of the wonderful accuracy and penetration of that philosopher.

masses.

65. Concluding Remarks.-We cannot leave this subject

without taking a brief review of the peculiar method of reasoning which is employed in the establishment of the laws at which we have arrived, and briefly stating the illus. tration which may be derived from the pendulum of the establishment of physical laws and theories.

The theory of the pendulum is essentially a mathematical theory; the simple pendulum is a mere hypothesis, and the laws of its motion must consequently be ascertained by analysis. Hence is obtained a relation betwixt the length of the imaginary string which sustains the oscillating imaginary particle, the time of its vibrations, and the intensity of the force to which it owes its motion, or gravity. Next, the theory of the motion of a solid mass points out certain cases in which the motions of a pendulum, such as we can make, are identical with the preceding imaginary pendulum. Thus, then, we obtain an instrument with which observations can be made, and the laws of whose motions are exactly defined by theory. The next step is to apply this pendulum in observations; here practical considerations and theory together determine what is to be observed. In the equation which theory gives, and by which it connects together the time of a pendulum's vibration, its length, and the intensity of gravity, it may at first sight appear indifferent which two of these three quantities are observed, since the third can then be calculated; but if all could practically be observed, there would be no necessity for the assistance of the mathematical theory. In this case, however, the time and length may be observed, but the force of gravity cannot: it must be calculated from the other two. Thus, we see how, in the case of the pendulum, theory and experiment are combined to obtain an accurate result. Had the intensity of gravity been determined by Atwood's machine, or in any other manner, then the length of the pendulum would be calculated from this, and the time of its vibra→ tion. But the pendulum presents far greater facilities for the determination of the intensity of gravity than

any other instrument; and it is employed for this purpose in preference to all others.

Again, the pendulum furnishes us with distinct evidence of the complete truth of the laws of motion. It does not supply a separate proof for each law, but a complete verification of all three. For instance, the first law of motion asserts, that a body in motion will go on moving for ever, unless acted on by some external force; now we are convinced that a pendulum would go on swinging for ever, if the resistance of the air and friction could be entirely removed. The motion of the pendulum is in no case rectilinear, but its curvilinear motion is in exact conformity with the second law of motion, and thus the motions of a pendulum may be considered as establishing these two laws. The real conviction, however, which we have of the truth of the laws of motion results, as has been already stated, on the extraordinary agreement of long-calculated results, obtained on the supposition of their truth, with the actual observed fact. Were the laws of motion not true for the celestial bodies, the whole planetary theory and its predictions would rest on untrue hypotheses; but we have the most perfect confidence in the results, and a thorough conviction of their truth; the hypotheses, therefore, or the laws of motion on which they rest, cannot be untrue.

The pendulum, as we have already seen, furnishes us with a most sure method of ascertaining whether the predictions of Newton, and the laws of gravity at the surface of the earth, are true or false; it also furnishes us with an example of what was termed (Art. 3.) the determination of constants. We may determine any one of the three quantities, the time, the length, the force, by assuming the laws for two of them. For instance, suppose the length of the pendulum to be the constant to be determined; we know now that the time of an oscillation depends on the intensity of gravity; we know also that the force of gravity varies with the latitude; the laws of these two variable quantities

being assumed, or supposed known, we may proceed to determine by calculation the constant length of the pendulum. If, on the calculations being made for the assumed time of oscillation and force of gravity at London, Paris, and the Cape, the length comes out the same, we have very high evidence of the truth of the principles which lead to such an invariable result.

In conclusion, we must call the attention of the student to the general illustration which the pendulum affords of all oscillatory movements. We shall hereafter have several instances in which the particles of bodies are said to perform oscillations that is, move backwards and forwards about some mean position, which was their position of rest. The language and laws of the oscillations of a pendulum are at once transferred to these. The motions of the particles are said to be isochronous, that is, each takes the same time to pass and repass from one extreme position to another. A most important illustration of the preceding remarks will be furnished in treating of Acoustics. The particles of any sounding body, as a bell, execute regular oscillations, or go through a periodic series of isochronous movements; when these oscillations cease, the bell ceases to sound.

K

CHAP. VI.

ON FLUIDS.

SECTION I.

GENERAL PROPERTIES OF FLUIDS-TRANSMISSION OF PRESSURECONDITIONS OF EQUILIBRIUM.

66. THE existence of matter in its three different states depends on the relative adaptation of the forces to which the particles are subject; in solid matter the force of cohesion is very great, but the particles of fluid matter can be moved amongst each other without any sensible resistance. Fluids are generally divided into liquids and gases; in the former, the forces of attraction and repulsion seem to be very nearly balanced; but in the latter, the force of repulsion is such that the particles will recede from each other unless prevented by some extraneous force, as the resistance of the sides of the containing vessel. The attraction of cohesion does exist in some small degree amongst the particles of a liquid; for a drop of water generally assumes a form which is nearly spherical. This form is, however, considerably modified by the action of gravity, and by the attraction of the mass with which it is in contact. The particles of a liquid adhere also with different degrees of force to different solids;

some cases they do not adhere at all, or the solid cannot be wetted by the liquid. These forces of cohesion and of adhesion may be measured by direct experiment; if a flat plate be brought into contact with the surface of a liquid, a greater force will be required to raise it again than is re