Plank

“ Inclined plane.—If a plank twelve inches long has one end on the ground and the other on a cart four inches high, one man can roll up the plank the same weight that would require three men to lift, but he has to move the object three times as far. ”

“ Then, taking the planks at each edge of the centre, by the same law their change and behavior will be quite different: they will still retain their original thickness at the centre, but will be a little reduced on each edge throughout, but the side next to the heart of the tree will be pulled round or bent convex, while the outside will be the reverse, or hollow, and the plank will be considerably narrower throughout its entire length, more especially on the surface of the hollow side. ”

“ I stepped from plank to plank
So slow and cautiously;
The stars about my head I felt,
About my feet the sea.
I knew not but the next
Would be my final inch, —
This gave me that precarious gait
Some call experience. ”

“ Those who have cruised in the Mediterranean Sea must have lively recollections of the calms which have stopped their onward progress—the slow rolling of the vessel without any apparent cause, the loud flapping of the canvas against the masts seemingly feeling anger at its inaction, the hot sun striking down on the decks and boiling up the pitch in the seams between the planks, the dazzling glare too bright for the eyes to endure from the mirror-like surface of the water, and, above all, the consequent feelings of discontent, lassitude, and weariness. ”

“ For in a right sphere the needle is parallel to the plane of the horizon; but when the cœlestial pole is vertically overhead, or when the pole of the earth is itself the place of the region, then the needle is perpendicular to the horizon. ”

“ The solid part of the earth is therefore composed of (1) a thin layer of unconsolidated or earthy material, a few feet to a few hundred feet in thickness, covering (2) a layer or zone many thousands of feet, and probably many miles, thick, composed of solid rock comparable to that exposed at numerous points on the surface, and (3) a central mass, to which the preceding layers are but a shell, composed of hot, dense, and rigid rock, the real nature of which is not known by observation. ”

“ 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. ”

“ Substances of the greatest specific gravity are susceptible of the greatest projectile force; and hence we find that mountains are composed of heavy masses of rock, mineral substances, and heavy earths; hills, or the next highest eminences, of earth of the next specific gravity; and plains, or level lands, of lighter substances. Had the earth originally been composed of one uniform substance, sand, for example, of equal fineness and weight, the whole surface of the globe would have presented one uniform level or unbroken plain. ”

“ If you imagine a cylindrical mass, with a cavity dug in the centre, whose edge conforms to the exterior edge; and if you place in this cavity another cylinder, higher than that which surrounds it, but so small as to leave between its sides and those of the cavity a hollow space, you will gain as distinct an image of this hill as words can convey. The summit of the inner rock was rugged, and covered with trees of unequal growth. ”

“ A flat plate of any uniform substance, and which has in every part an equal thickness, has its centre of gravity at the middle of its thickness, and under a point of its surface, which is to be determined by its shape. ”

“ 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. ”

“ The tangents drawn from a point P to a quadric surface form a cone of the second order, for the polar plane of P cuts it in a conic.
6. If the pole describes a line a, its polar plane will turn about another line a′, as follows from 2. These lines a and a′ are said to be conjugate with regard to the surface.
§ 100. The pole of the line at infinity is called the centre of the surface. If it lies at the infinity, the plane at infinity is a tangent plane, and the surface is called a paraboloid.
The polar plane to any point at infinity passes through the centre, and is called a diametrical plane. ”

“ Seeing that the foregoing reasoning forces us to look upon the earth as a hollow sphere, or shell, in which the whole of the matter composing it is divided into two equal parts, attracted outwards and inwards by each other to a common plane, or region of meeting, we shall divide its whole volume into two equal parts radially, that is, one comprising a half from the surface inwards, and the other a half from the centre [170] outwards—that is to say, each one containing one-half of the whole volume of the earth. ”

“ Accordingly, a body hanging by a line, which over a level surface would be drawn by the earth's attraction into a direction with reference to its point of suspension, the prolongation of the line of which would pass through the center of the earth—that is, would be perpendicular, or plumb—would be attracted and turned away from the perpendicular by a mass like a mountain in the neighborhood. ”

“ Let us further assume that, owing to the attraction of some immense stellar body, this huge mass has what we would call a weight corresponding to that which a plate of the same material would have at the surface of the earth, and let it be required to calculate the length of the side of a square plate of the same material and thickness and which shall be exactly equal to the circular plate. ”

“ 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. ”

“ 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 you have thus made a sphere for yourself, or, with an artificial globe before you, if you have access to one, proceed to point out on it the various arcs of azimuth and altitude, right ascension and declination, terrestrial and celestial latitude and longitude,—these last being referred to the equator on the earth, and to the ecliptic in the heavens.
When the circles of the sphere are well learned, we may advantageously employ projections of them in various illustrations. By the projection of the sphere is meant a representation of all its parts on a plane. ”

“ 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. ”

“ 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 ”

“ We have then to consider that, whatever the form of the earth may be, using the expression as applying to the fluid part of the earth, we must suppose also from the nature of a fluid, that the direction of a plumb-line is perpendicular to the surface, and therefore, if we suppose the earth to be fluid, the plumb-line will be always perpendicular to its surface. ”

“ Every part of the depth of earth in a given space is composed of layers, and each layer is composed of heavier or lighter materials, the lowest being the heaviest. And this can be proved, because these layers have been formed by the sediment from water carried down to the sea, by the current of rivers which flow into it. ”

“ Extract its contents, and then you will have a perfect representation of Olaf Jansen's earth. The distance from the inside surface to the outside surface, according to him, is about three hundred miles. The center of gravity is not in the center of the earth, but in the center of the shell or crust; therefore, if the thickness of the earth's crust or shell is three hundred miles, the center of gravity is one hundred and fifty miles below the surface. ”

“ And the parts of the envelops of the rolling plane between these lines, although a continuation of the developable surfaces which have been described, and representing states of the body, of which some at least may be realized, are of minor interest, as they form no part of the surface of dissipated energy on the one hand, nor have the theoretical interest of the primitive surface on the other. ”

“ But if we limit ourselves to {218} surfaces of revolution (that is to say, to surfaces symmetrical about an axis) , we find, as Plateau was the first to shew, that those which meet the case are very few in number. They are six in all, namely the plane, the sphere, the cylinder, the catenoid, the unduloid, and a curious surface which Plateau called the nodoid. ”

“ Here the science of geology takes its start with the metamorphic rocks, and it is the dividing line between the inner, smaller, and the outer, larger, planets.
IV. The Terraqueous Stage, when the surface has become substantially stable, there are great oceans gradually diminishing in size, and land gradually increasing. This is the stage of the sedimentary rocks, the time when the planet passes from its own supply of heat to dependence upon that of the sun; the stage when life begins, and the one in which the Earth is now. ”

“ In investigating the interior of the earth we did not find a central shaft running from pole to pole, such as has been described by some mediums, nor did we find a number of concentric spheres resting upon cushions of steam. ”

“ Here the radius, a straight line, is clearly the determining factor.
We now move to the other pole of the primary polarity, that is to the plane, and let the sphere arise by imagining the plane approaching an infinitely distant point evenly from all sides. We view the process realistically only by imagining ourselves in the plane, so that we surround the point from all sides, with the distance between us and
the point diminishing gradually. ”

“ Near the lithosphere surface the rocks support by their strength the load of rock above them, but at greater depths they are unable to do this, for the load bears upon each portion of the rock with a pressure equivalent to the weight of a rock column which extends upward to the surface. ”

“ Follow with your eye any two adjacent lines, and you will see that where they are close to each other the surface has an abrupt change of level; where they are further apart the surface is nearly horizontal. Where the surface approaches the perpendicular, as on the sides, the dark line showing the separation of the strata is thin, because it has been cut through nearly at right angles. Where the surface is more horizontal the dark line is broader, because it has been cut through obliquely, the breadth varying steadily with the angle of inclination. ”

“ All rocks are traversed by divisional planes of less or greater width and frequency, and thus divided into masses of definable shapes and proportions. These "joints," as they are often called, present themselves under a great variety of appearances, but almost always such as to be intelligible on the supposition of the mass of the rock having been contracted, so as to separate into prismatic and other forms, as clay, starch, &c. ”

“ The laws of conservation may not be violated: the earth will respond.
How are the Spheres constructed?
The constitution of these two retro-acting spheres, and consequently of all the others of [Pg 26] the heavenly host, [3] at this point demands our attention. How are the spheres made up? How speaks the earth? The earth with which we are familiar—our sample—is formed of a slight crust, a core, to a greater or less extent and degree incandescent, and measuring 250,000 millions of cubic miles in dimensions, also an envelope which we call the atmosphere. ”

“ A wooden globe, sixteen inches in diameter, was made hollow, for the purpose of reducing its weight, and while still in the lathe, grooves one-eighth of an inch deep and broad were cut to represent an equator, and parallels of latitude at every four and a half degrees each way from the equator to the poles. ”