comparing this space with the space through which the earth draws the moon, or the sun draws a planet, in one hour, only making the proper allowance for difference of distances.

For the masses of the other planets, I explained that there is no method but by the disturbances which they produce in the Solar System; and that these are made available by computing with an assumed mass what the perturbations would be, and altering the mass till these agree with the observed perturbations. Those of Jupiter's satellites, as I explained, are found in an analogous way.

For our moon, I indicated several different methods. One of these was, to infer (by theoretical considerations) from the observed amount of lunar nutation, what is the amount of lunar precession; to subtract this from the whole observed precession, which leaves solar precession; and thus to obtain the proportion of lunar precession to solar precession, which is the same as the proportion of the force with which the moon tends to pull the earth's surface from its centre to the similar force of the sun. A second method was from the proportion of lunar and solar tides, which is referred to the same proportion of forces as in the first method. A third method was, from the circumstance that it is not the earth, but the centre of gravity of the earth and moon, which moves very nearly in an ellipse round the sun. A fourth method

was, that knowing the earth's attraction at its surface, and computing from this its attraction at the moon, we could infer from that the distance of the moon from the centre of gravity of the earth and moon. In the two latter methods we are led to an immediate comparison of the weight of the earth with that of the moon.

I shall now repeat what I said in commencing this course of lectures that I fully believe that there is no part whatever of these subjects of which the principle cannot be well understood by persons of fair intelligence, giving reasonable attention to them; but more especially by persons whose usual occupations lead them to consider measures and forces; not without the exercise of thought, but by the application only of so much thought as is necessary for the understanding of practical problems of measures and forces.

APPENDIX.

I.

FOUCAULT'S PENDULUM EXPERIMENT.

In the year 1851, a method of rendering the earth's rotation visible to the eye was made known by M. Foucault, who had been led to discover it by considering the effect of the rotation of the earth on the apparent motion of a pendulum vibrating freely at the earth's surface.

If a heavy body, as for example, a sphere of metal be suspended by a string from a point A, Figure 66, vertically above N, the North Pole of the earth, and allowed to hang freely, the motion of the earth about its axis ANS will twist the string, and so cause the sphere to rotate about its vertical diameter. If, now, the sphere be drawn aside to a point B and allowed to drop gently, it will begin to vibrate in the plane NAB, and as the rotation communicated to the sphere does not tend to withdraw it from that plane, it will continue constantly to move in it. A spectator near N, partaking of the earth's motion, changes his position with reference to this fixed plane: but being unconscious that he is moving himself, he attributes to the fixed plane a motion exactly similar

to his own, but in the opposite direction. To him it will therefore appear to revolve from east to west

E

N

B

S

FIG. 66.

about the line NA, making a complete revolution in the course of a day. At the South Pole a similar appearance would be observed.

At places situated elsewhere on the earth's surface, it is less easy to anticipate the result; but some idea of the effect produced on the plane of vibration may perhaps be conveyed by the following explanation.

It has been remarked above, (page 108,) that a single force, acting in a given direction, may be resolved into two forces acting in given directions: and that these two forces acting together may be

regarded as producing the same effect as the single force acting alone. In like manner a single motion of rotation about a given axis may be resolved into two motions of rotation about two given axes: and if these two motions take place simultaneously, they may be regarded as together producing the same effect as the single motion. Thus, if a body (which for the sake of simplicity we may suppose to be

A

B

0

FIG. 67.

spherical) be made to rotate about the line OA, Figure 67, any point in it will describe a circle in a plane perpendicular to OA, with its centre on that line. Suppose that in a given time the point P is thus brought from one position P to another R; then it is possible to produce the same change in position by giving the body two successive rotations about two lines, OB, OC. For by virtue of a rotation about the line OB, P may be made to describe the