nets are known, the mean densities are all that are required for the solution of the problem. Now, in homogeneous, unequal, spherical bodies, the gravities on their surfaces are as their diameters, when the densities are equal; or the gravities are as the densities, when the bulks are equal: therefore, in spheres of unequal magnitude and density, the gracity is in the compound ratio of the diameters and densities; or the densities are as the gracities divided by the diameters. But the diameters are known, and the gravities at the surface are nearly found, either by means of the revolutions of the satellites, or by calculations deduced from the effects the plan. ts are found to produce upon each other; consequently the relation of the densities becomes known. The inean density of the earth was calculated by Dr. fiution, from observations made by Dr. Maskelun at the mountain Schchatlien; he made it to that of water as 9 to 2, and to common stone, as 9 to 5, on the supposition that the hill is only of the density of common stone. He also states the mean densities of the sun and planets to that of water, thus: sun, 1; mercury, 9; venus, 51; earth, 4; mars, 37; jupiter, 1; saturn, ol; and georgium sidus, o These densities are such as the bodies would have if they were omogeneal; and may be admitted as a fair estimate of the whole, although the density of each planet may vary considerably at different distances from the surface. From the densities, as thus estimated, and the known diameters, we may readily find the proportions of the quantities of matter; they are as under: the sun, 333928; mercury, 1654; venus, 8899; the earth, 1; mars, 0875; jupiter, 3121; saturn, 97.76; georgium sidus, 16.84.

placed in the focus of a telescope, one fixed and the other moveable, or both moveable, they may be made to approach or recede one from the other till they appear to touch exactly two opposite points in the disc of the planet, and then the index shews the apparent diameter in minutes and seconds. The apparent diameters of the planets when at about their respective mean distances from the earth, are as follow: mercury, 11"; venus, 58′′; mars, 27′′; jupiter, 39"; saturn, 18"; georgium sidus, 3" 54"". And from these apparent diameters, and the respective distances from the earth, the diameters of the sun and planets have been determined in English miles as here stated: mercury, 3224; venus, 787; mars, 4189; jupiter, 89170; saturn, 79042; georgium sidus, 35112; the sun, 883246. Observations upon the planets herschel, saturn, jupiter, and mars, prove that there is a sensible difference between their equatoreal and polar diameters; and it is probable that there is a like difference between the diameters. of the other planets, but this has not yet been determined by observation

358. Since the apparent diameters of distant bodies vary inversely as their distances, we may, having the distances from the earth at which the respective planets subtended the above angles, and knowing their mean distances from the sun, find the mean apparent diameters of all the planets, as seen from the sun; they have been thus given: mercury. 20"; venus, 30"; earth, 17; mars, 10"; jupiter, 37" ; Saturn, 16"; georgium sidus, 4".

39. To measure the quantity of matter in distant bodies appears a problem of insuperable diffi culty but this has been effected to a consid rable degree, by the principles of the Newtonian philosophy. Since the quantity of matter in a globe is proportional to the mean density multiplied into the cube of the diameter, and the diameters of the pla

nets are known, the mean densities are all that are required for the solution of the problem. Now, in homogeneous, unequal, spherical bodies, the gravities on their surfaces are as their diameters, when the densities are equal; or the gravities are as the densities, when the bulks are equal: therefore, in spheres of unequal magnitude and density, the gravity is in the compound ratio of the diameters and densities; or the densities are as the gracities divided by the diameters. But the diameters are known, and the gravities at the surface are nearly found, either by means of the revolutions of the satellites, or by calculations deduced from the effects the plants are found to produce upon each other; consequently the relation of the densities becomes known. The mean density of the earth was calculated by Dr. Hution, from observations made by Dr. Maskelyn: at the mountain Schchullien; he made it to that of water as 9 to 2, and to common stone, as 9 to 5, on the supposition that the hill is only of the density of common stone. He also states the mean densities of the sun and planets to that of water, thus: sun, 1; mercury, 9%; venus, 5; earth, 4; mars, 37; jupiter, 1; saturn, oŢi; and georgium sidus, o These densities are such as the bodies would have if they were omogeneal; and may be admitted as a fair estimate of the whole, although the density of each planet may vary considerably at different distances from the surface. From the densities, as thus estimated, and the known diameters, we may readily find the proportions of the quantities of matter; they are as under: the sun, 333928; mercury, 1654; venus, 8899; the earth, 1; mars, 0875; jupiter, 3121; saturn, 97.76; georgium sidus, 15.84.

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I I

CHAPTER XIV.

On the Rotations of the Sun and Planets, and the Inclinations of their axes.

ART. 390. BESIDES that motion of the planets by which they move round the sun in elliptical orbits, most of them, and from analogy we conclude all of them, have another motion, which causes them to turn round on their axes: this motion is called their rotation. After attentive observations on the planets, and indeed on the sun also, it will be found that there are dark spots on their discs, of different shapes and sizes; it will be seen likewise, that these spots change their apparent places, and pass from one side of the body to the other; that, after disappearing for a rather longer time than they were visible, they again become visible on the side where they were first seen, and again pass over the disc, as before; that their apparent velocities continue to increase till they arrive at the middle of the disc, after which they gradually decrease, and are slowest just before they are hidden from view; that these spots appear to widen as they advance from the margin towards the middle of the disc, where they appear most round and broad, and as they approach the edge they become oblong and slender: from these observations it is concluded, that the spots adhere in some manner to the sun and planets, and that their apparent motion and change of magnitude are occa

sioned by the real motion of the bodies on which they are.

391. The physical nature and cause of these motions, or, as they are called, diurnal rotations, will be in some degree evinced from the following considerations: If a sphere of homogeneous matter, placed in an unresisting medium, receive at the same time one or several impulses in the plane of the same great circle, and in directions oblique to its surface; these impulses will give that sphere two motions, the one a uniform rotation about the axis of that great circle, which preserves a constant situation; the other, an equally uniform translation in the plane of that great circle. For, let EBN (fig. 4, Pl. V.) be the plane of a great circle of a sphere (which call the plane of its equator), and let A B represent the direction and action of a power in that plane it is manifest, that if AB had been in the direction of one of the axes of the globe, and consequently perpendicular to the surface, the action of that power would have caused the globe to move uniformly in that direction; but A B being oblique to its surface, it follows, from the composition and resolution of forces, that its effort must be divided into two, the one B O perpendicular to its surface, the other BH a tangent thereto; so that the two right lines BO, BH, become sides of a parallelogram HO, the diagonal of which is BIAB. Now BO expresses that part of the effort AB which impels the globe uniformly in the direction B L, which is in the plane of the equator (Art. 267.); and BH expresses the part of the effort AB that imparts to the point B of the globe's surface a tendency to recede from the centre C along the tangent BH. This effort BH, then, is like a uniform projectile force impelling B towards H. But, because of the connection and reaction of all the parts of the globe, the point B returns as much towards the centre C,