determining the earth s density. Bouguer had the merit of pointing out the form in which the experiment might be made, and of making the trial, though in a rude and insufficient manner, in the Peruvian Andes in 1738. Maskelyne proposed to the Royal Society in 1772 to repeat the observation on some British mountain. Skiddaw and the Yorkshire Hills were first thought of, but finally Schihallion in Perthshire was preferred. The distance between the two stations, obtained with Ramsden s 9-inch theodolite, was 4364 4 feet, which in the latitude of Schihalliou corresponds to 42" 94 of latitude. The observed difference of latitude by 337 observations with Sisson s 10-feet zenith sector was 54" 6. The excess, or 11" 6, is the double attraction of the hill drawing the plumb-line towards itself at the two stations. The sine of this angle, or I7 ao4, represents the actual ratio between the double attraction of the hill and the attraction of the earth. But by the computation of the attraction which the hill ought to exert, from its figure, as determined by Maskelyne s gauges, were its density the same as that of the globe generally, this ratio should amount to $^$3, which can only be accounted for by assuming the earth to be denser on the average than the hill of Schihallion in the proportion of 17,804 to 9933. A careful lithological survey of the hill enabled Professor Playfair to deduce the probable mean
specific gravity of the globe to be between 4 - 56 and 4 87.
A second method was devised by the Rev. Mr Michell, but fi rs t p u t in practice by Mr Cavendish in 1797-8. It consisted in measuring the force of gravitation between two spheres of such small size that they could be moved by the hand nearer to or farther from one another. To provide a balance so delicate as to measure the almost inappreci able attraction of such small bodies, Michell imagined the balance of torsion. His apparatus came into the hands, first of "WoUaston, then of Cavendish, who made the experiment. He used a very light rod of deal, six feet long, suspended by a fine silver or copper wire, forty inches long, within a wooden case to defend it from currents of air. At each end of the lever was hung a ball of lead, two inches in diameter, and by a simple contrivance a pair of leaden spheres, weighing together 348 pounds, could be brought simultaneously into the neighbourhood of the balls (but outside the case), on opposite sides, so that their attractions might concur to swing the suspended lever out of the posi tion of repose which it had previously taken up, under the action of the slight twisting force of the silver wire. A new position of rest was thus established, the small balls being pulled as much one way by the attraction of the spheres as they were urged in the opposite direction by the torsion of the wire. The position of repose being observed from a distance by a telescope (to avoid disturbance from the heat of the observer s body), the great spheres were then changed in position so as to act upon the opposite sides of the small balls, from what they formerly did. The deflection and new stable position would be as much on the other side of the zero, and the arc described would be an accurate measure of the double deflection. The force of torsion for one degree of deflection is known by the time of oscillation of the lever and balls when free, and as the forces are exactly as the angles, the force corresponding to any displacement becomes known. Cavendish found the joint attraction of the small balls and large spheres to be about 4 .^ of a grain, their centres being 8 "85 inches apart, and he thence computed the density of the earth to be 5 48 times that of water. The experiment has been repeated since by Reich of Freiberg and Baily of London. The former obtained 5 44, the latter 5 GO for the earth s specific gravity, this last result being worthy of much confidence, from the extraordinary care taken to avoid errors and to obtain independent values of the quantities sought.
A third method of determining the earth s density depends on the fact that a pendulum suspended at a cousiderable height above the earth would swing more slowly than at the surface, while if it be at the summit of a mountain, though it will still swing more slowly, the attraction of the mountain will slightly accelerate the rate of swing. Carliui and Plana, by observations made on this plan, have deduced 4 950 for the mean density of the earth. The objection to this method, as well as to the Schihallion experiment, resides in our uncertainty as to the actual mean density of any given mountain mass. If the experi ment could be carried out by pendulum observations made at the base and on the summit of a conical or conoidal mass, of some known material and of great height, the true density of the earth could thence be very accurately determined.
A similar objection applies to the converse of the third method described above. If a pendulum be suspended at the bottom of a deep mine, of known figure, and existing in a region whose geological structure is well known, the change of rate gives a means of calculating the density of the earth, since it obviously depends on the calculable difference of attraction due to increased proximity to the earth s centre (reducing the attraction), and to the absence of counter-attracting matter where the mine is dug out (which in effect increases the attraction). In the Harton colliery, experiments were carried out by Mr Dunkin on this plan in accordance with arrangements devised by the astro nomer royal. It was found that gravity was increased by ia ^ 90 th part at the lower station, 1260 feet below the mouth of the mine, where the upper station was placed. Hence Airy found that, on taking into account the con figuration of the mine and the structure of the surround ing region, a density of 6 5 65 resulted. Very little reliance can be placed, however, on results obtained by this method.
It may be fairly assumed that the earth s mean density amounts to about 5 6 times the density of water, combin ing which with the known dimensions of the earth, we find that the earth s weight in tons may be roundly ex pressed by the number 6,000,000,000,000,000,000,000.
or, seeing that the earth circles around the sun, we regarded the axis as moving always parallel to itself, while the earth traversed her path in the plane of the ecliptic. But we must now take into account variations in its position with reference to the ecliptic. In this inquiry we should naturally take the ecliptic as our plane of reference, if we were assured that the position of the plane of the ecliptic is constant, in other words, that the sun s path in the heavens undergoes no change. This is, in fact, so nearly the case that the ecliptic forms a suitable reference circle for the fixed stars far more suitable for example than the equator itself. The star s latitude, that is, its distance from the ecliptic measured on the arc of a great circle through the poles of the ecliptic, is very nearly constant ; while the longitude, or the distance between the point T and the point where the great circle through the star cuts the ecliptic, undergoes, as will presently appear, a varia tion nearly uniform, and nearly the same for every star ; whereas the declination and right ascension of stars are undergoing variations which are neither alike for different stars nor uniform for any star. Yet the place of the ecliptic on the heavens is not absolutely constant. The ecliptic, in fact, is inclined about l to the invariable plane mentioned at the end of Chapter VI., and this inclination is undergoing a slow process of change, while
the nodes of the ecliptic on it are slowly shifting. A