Spherical

“ His proposition that the universe is spherical is, however, not based on observation, but on considerations of the perfection of the spherical form, the general tendency of bodies—a drop of water, for example—to assume this form, and the sphericity of the sun and moon. ”

“ However, somehow or other the conception of a spherical earth was gradually grasped, and the heavenly bodies were perceived all to revolve round it: some moving regularly, as the stars, all fixed together into one spherical shell or firmament ”

“ Thus the most perfect idea we can possibly acquire of a sphere, is by conceiving an infinite number of straight rays of equal lengths, issuing from the center, as from the eye, spreading every way alike; and circumscribed or wound about at their other extremities with close connected circular threads, or lines, forming a true spherical shell. ”

“ Given two spherical bodies of similar material but of unequal magnitude and originally possessing the same degree of heat, the smaller body will cool more rapidly than the larger, by reason of the greater proportion which the surface of the smaller sphere bears to its volume than that of the larger sphere to its volume—this proportion depending upon the geometrical ratio which the surfaces of spheres bear to their volumes, the contents of spheres being as the cubes and the surfaces as the squares of their diameters. ”

“ But the spherical shape, necessitated by this argument, follows also from the fact that the motions of heavy bodies always make equal angles, and are not parallel. This would be the natural form of movement towards what is naturally spherical. Either then the earth is spherical or it is at least naturally spherical. And it is right to call anything that which nature intends it to be, and which belongs to it, rather than that which it is by constraint and contrary to nature. ”

“ The method assumes that gravity is measured on the earth’s surface at a sufficient number of points, and that it is conformably reduced. In order to secure the convergence of the expansions in spherical harmonics, it is necessary to assume all masses outside a surface parallel to the surface of the sea at a depth of 21 km. ”

“ If we say that the specific gravity of a body is 6, we mean, that its weight is six times as great as that of a portion of water, exactly equal to it in bulk.
Spectrum. That appearance of differently coloured rays, which is produced by the refraction of the solar ray, by means of a prism, is called the prismatic spectrum; it exhibits most distinctly, and beautifully, all the colours seen in the rainbow.
Sphere. A globe, or ball.
Spheroid. Spherical; a body approaching nearly to a sphere in its figure. The earth, is denominated an oblate spheroid ”

“ Many hollow cylinders and spherical figures, we know do exist on the surface of the earth; and notwithstanding their own gravity, which the different parts exert on each other, as well as the gravity of the earth, they retain their shape and position; and had the matter in the earth originally been thrown by a centrifugal force into the form of a hollow sphere, or had the first creating power originally given it that shape,—I can discover no good reason for a change; neither should I entertain any apprehensions of the particles of matter coalescing at the centre. ”

“ Now we are going to see how vastly important in its effects is the fact that the earth is spherical in form. Sir Isaac Newton, who first worked out mathematically the law of gravitation, proved that a spherical body attracts, and is attracted, as if its entire mass were concentrated in a point at its centre. ”

“ Therefore, if the heaven moves in a circle and moves more swiftly than anything else, it must necessarily be spherical.
Corroborative evidence may be drawn from the bodies whose position is about the centre. If earth is enclosed by water, water by air, air by fire, and these similarly by the upper bodies-which while not continuous are yet contiguous with them-and if the surface of water is spherical, and that which is continuous with or embraces the spherical must itself be spherical, then on these grounds also it is clear that the heavens are spherical. ”

“ If all the parts of a spherical fluid, homogeneous at equal distances from the centre, lying on a spherical concentric bottom, gravitate towards the centre of the whole, the bottom will sustain the weight of a cylinder, whose base is equal to the superficies of the bottom, and whose altitude is the same with that of the incumbent fluid. ”

“ ABERRATION IN REFLEXION AT SPHERICAL SURFACES.
15.We found in the beginning of the last Chapter, that a cone of rays incident on a spherical surface were not so reflected as to meet in a point, but that the point which we called the focus of the reflected rays was, in fact, the mathematical limit of the intersections with the axis of rays chosen more and more nearly coincident with it. Let us now examine how much the intersection of the axis with a ray at a small but sensible distance from it, differs from this.
Taking the centre of the surface as the point to measure from, (Fig. 12.) ”

“ But as the bodies of the solar system are nearly spherical, they will all act upon one another and upon bodies placed on their surface, as if they were so many centres of attraction; and therefore we obtain the law of gravity, that one sphere will act upon another sphere with a force directly proportional to the quantity of matter, and inversely as the square of the distance between the centres of the spheres. ”

“ If the earth is a perfect sphere, then its attraction on any other body is exactly the same as if its mass were all concentrated at its centre (§ 182) , and so also the attraction on it of any other body such as the sun or moon is equivalent to a single force passing through the centre o of the earth; but this is no longer true if the earth is not spherical. ”

“ If by any distribution of imaginary sources within the spherical surface we can effect this, the value of the corresponding potential outside the sphere is the true and only one. The potential inside the sphere must really be constant and equal to that at the surface. ”

“ Just as beings which are confined within a narrow region surrounding a point on a spherical surface, may fall into the error that a sphere is a geometric figure in which one diameter is particularly distinguished from the rest. ”

“ The deviation from a perfectly spherical shape is so inconsiderable that in an artificial globe of eighteen inches diameter it would hardly amount to the thickness of a sheet of paper; still, small as this is represented on a miniature scale, it has, doubtless, great importance on the great scale of a world like this, both in affecting somewhat the perturbation of other heavenly bodies which depend on the earth, as well as the perturbations in the earth’s own motion. ”

“ Unless the spheroid be in certain positions, the sphere possesses still higher beauty, as presenting the same circular and highly beautiful outline in every position; although a variety of positions is not essential to the perception of its peculiar beauty, whenever the observer has learned by different methods, and especially by different degrees of convergence of the two optic axes, to estimate the relative distances of the different points of the visible hemisphere, and thus to recognise the spherical form. ”

“ Let us consider a hot spherical body, whose energy we wish to communicate to another equal sphere, absolutely cold, and suppose for a moment that they have a thin outside crust absolutely impermeable to heat, and that the mass of each sphere is concentrated in a single little ball, to whose motion the heat is due, the ball in the cold sphere will of course lie still at the bottom, while the other is flying about at an inconceivable rate ”

“ That every visible figure will be represented by that part of the surface of the sphere, on which it might be projected, the eye being in the centre. And every such visible figure will bear the same ratio to the whole of visible space, as the part of the spherical surface which represents it, bears to the whole spherical surface. ”

“ Spherical space is not very easy to imagine. We have to think of the properties of the surface of a sphere—the two-dimensional case—and try to conceive something similar applied to three-dimensional space. Stationing ourselves at a point let us draw a series of spheres of successively greater radii. The surface of a sphere of radius should be proportional to ; but in spherical space the areas of the more distant spheres begin to fall below the proper proportion. There is not so much room out there as we expected to find. ”

“ The centre of gravity of the hemispherical base is, of course, in its axis; and therefore tends to approach the horizontal plane as much as possible, and this can never be accomplished, until the axis becomes perpendicular to the horizon. Whenever the curved surface is in any other position, the centre of gravity is not in the lowest place to which it can descend, as may be seen by the diagram which I have just sketched. ”

“ A second reason for the spherical form of the earth is that when we move north and south the stars change their positions with respect to the horizon, while some even disappear and fresh ones take their place. This shows that the direction of the stars has changed as compared with the observer’s horizon; hence, the actual direction of the stars being imperceptibly affected by any motion of the observer on the earth, the horizons at two places, north and south of one another, are in different directions, and the earth is therefore curved. ”

“ A sphere of such a radius would contain as many spheres of ten trillions of miles radius as one could put cubic inches in 850 cubic miles, or 216,000 trillions. This sphere could hold as many suns of one million miles diameter as there might be grass seeds that would cover a million of earth’s for one mile in depth, each earth containing on its surface 200 millions of square miles, and every cubic inch thereof representing 27 millions of grass seeds. When we think that each seed represents two millions of earths can we comprehend the greatness of the universe? ”

“ and I prepared a tube, at first of lead, in the ends of which I fitted two glass lenses, both plane on one side, but on the other side one spherically convex, and the other concave. ”

“ B. A sphere you mean, my dear: a circle is a round line, every part of which is equally distant from the centre; a sphere or globe is a round body, the surface of which is every where equally distant from the centre.
Emily. If, then, the earth is not a perfect sphere, but prominent at the equator, and depressed at the poles, would not a body weigh heavier at the equator than at the poles? For the earth being thicker at the equator, the attraction of gravity perpendicularly downwards must be stronger. ”

“ When we come to the study of the earth as a body, we find it composed of four particles: the atmosphere, the hydrosphere, the lithosphere, and the centrosphere. When we consider it as a body we consider form and structure; when we consider the spheres as particles their relations are those of space, one above another; thus in the body there is form, in the particles there is position, and that which is position in the particle constitutes structure in the body. ”

“ If the globe be solid, on what principle could a large portion of its surface, which is said to be lighter than the parts beneath, sink into a dense medium? How could a heavy mass, lying a thousand fathoms deep at the bottom of the ocean, rise, and be suddenly elevated above the surface of the water, when all below is so compact, and governed by an opposite and immutable tendency? ”

“ Let A be the weight of the globe in vacuo, B its weight in the resisting medium, D the diameter of the globe, F a space which is to 4/3D as the density of the globe to the density of the medium, that is, as A to A - B, G the time in which the globe falling with' the weight B without resistance describes the space F, and H the velocity which the body acquires by that fall. ”

“ You know full well that the condition of the outer sphere is, as I have described it, a bleak, turbulent surface, the roof of the earth on which man exists, as a creeping parasite does on a rind of fruit, exposed to the fury of the ever-present earth storms.
"The central circle, or medial sphere, the shell, or layer of gravitation, lies conformably to the outer configuration of the globe, about seven hundred miles towards its center. It stretches beneath the outer circle (sphere) as a transparent sheet, a shell of energy, the center of gravitation. ”

“ He maintains, as I do, that if the elasticity of our atmosphere is unlimited, its extension must be commensurate with the universe, that every orb in space will, by gravitation, gather around itself an atmosphere proportionate to its gravitating power, and that, by taking the known quantity of the earth’s atmosphere as our unit, we may calculate the amount of atmosphere possessed by any heavenly body of which the mass is known. ”

“ The material crust of the earth rests on this placid sphere of vigor, excepting in a few places, where, as in the crevice we have entered, gaps, or crevices, in matter exist, beginning from near the outer surface and extending diagonally through the medial and inner spheres into the intra-earth space beyond. This medial sphere is a form of pure force, a disturbance of motion, and although without weight it induces, or conserves, gravity. It is invisible to mortal eyes, and is frictionless, but really is the bone of the earth. ”

“ The spheres, in many parts of the unfathomable ocean, is believed to be water quite through from the concave or convex surfaces to the great mid-plane-space, and probably the earthy or solid matter of the sphere, may in many places extend quite through from one surface to the [94] other, tending, like ribs or braces, to support the sphere in its proper form. Such a formation of spheres appears to be supported by various facts and phenomena; amongst the most prominent of which are Volcanoes and Earthquakes. ”