Surface area

“ The surface of the sun—how much more the interior!—is an appalling cauldron of incandescent matter from pole to pole. Every yard of the surface is a hundred times as intense as the open furnace of a Titanic. ”

“ The effect of the distance of the surface of the solid rock from the under surface of productive soil may be both direct and indirect, and may vary much, not only with reference to the species of rock, but also to the vegetables. ”

“ In the stricter sense, physical geography is that part of geography which involves the processes of contemporary change in the crust and the circulation of the fluid envelopes. It thus draws upon physics for the explanation of the phenomena with the space-relations of which it is specially concerned. Physical geography naturally falls into three divisions, dealing respectively with the surface of the lithosphere—geomorphology ”

“ In earlier times geography was simply a catalogue of facts, and the earth's surface an ultimate datum; but nowadays we are beginning to regard the superficies of our planet as a result, to investigate the relations between its separate parts, and to note the changes which occur in it. ”

“ 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. ”

“ 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. ”

“ If at each point of the given surface we measure off along the normal one and the same distance at pleasure, then the locus of the points thus obtained is a surface cutting all the normals of the given surface at right an les, or, in other words, having the same normals as the given surface ”

“ I represents the surface of the Earth divided into land and water. Were all land on our Earth put together in a circle, and the water placed round it, then the land would only fill the inner circle, the water occupying the surrounding ring, a space nearly four times as large as the circle. Fig. II, III, IV, V and VI represent the comparative surfaces of America, Europe, Asia, Africa and Australia. ”

“ In considering alterations of this kind, brought about in the physical geography of particular tracts, we are too apt to think exclusively of that part of the earth's surface which has emerged from beneath the waters, and with which alone, as terrestrial beings, we are familiar. ”

“ It follows from this that if we want to make a simple model of a set of antlers, we shall be very greatly helped by taking some appropriate spheroidal surface as our groundwork or scaffolding. The best form of surface is a matter for trial and in­ves­ti­ga­tion in each particular case; but even in a sphere, by selecting appropriate areas thereof, we can obtain sufficient varieties of surface to meet all ordinary cases. ”

“ A natural extension of either of the methods already described will give us a series of surfaces in which every one is the surface, or every one the surface for a body of constant composition, the proportion of the components varying as we pass from one surface to another. But for a simultaneous view of the properties which are exhibited by compounds of two or three components without change of temperature or pressure, we may more advantageously make one or both of the quantities or constant in each surface. ”

“ That phase which treats of the outer relations of the earth is Cosmic or Astronomic geology; that which treats of the constituent parts of the earth and its material is Geognosy, of which the most important branch is Petrology, the science of rocks. That branch which investigates the structural arrangement of the material, or “the architecture of the earth,” is Geotectonic, or Structural geology; while that which deals with the surface changes and topographic forms, that is, with the face of the earth, is Physiographic geology. ”

“ And to the practised eye of the geologist, a fine landscape is not simply a pleasantly or grandly diversified surface, but it has depth; for he reads in the superficial lineaments the structure of the rocks out of which they are carved. ”

“ Then, when we come to examine further, I refer you to this sectional diagram of the geological strata of the earth, in which there is a more elaborate view of what is beneath the surface of our globe. ”

“ Let’s see from what you would define a mirror—from a surface per se, in quantum est superficies, or from a substance that forms the surface, or from the substance upon which the surface rests, the raw material, modified by the attribute ‘surface,’ since it is clear that, surface being an accidental property of bodies, it cannot exist without substance. ”

“ Fig. 56 shows the manner of holding the smooth plane in releasing the wedge, as well as when the cutting edge projects too much.
[35]
26. Planing First Surface True. —A true surface is one which is straight as to its length and width and which has its surface at the four corners in the same plane. Select for this first surface, which we shall call the face side, the better of the two broad surfaces. Knots, sap, wind, shakes, etc., should there be any, must be taken into account when passing judgment. Often the two sides are so nearly alike that there is little reason for choice. ”

“ The sun’s rays, striking at all angles a sphere, that from moment to moment presents and withdraws different parts of its surface, and each of them for a different time daily throughout the year, would produce a considerable variety of changes even were the sphere uniform. ”

“ A truly level surface is a segment of any spherical substance, which is concentric to the globe of the earth. A true line of level is an arch of a great circle which is imagined to be described upon a true level surface. ”

“ The fundamental basis of geography is the vertical relief of the earth’s crust, which controls all mobile distributions. The grander features of the relief of the lithosphere or stony crust of the earth control the distribution of the hydrosphere or collected waters which gather into the hollows, filling them up to a height corresponding to the volume, and thus producing the important practical division of the surface into land and water. ”

“ The answer seems to be this:—We have learnt by indirect methods that the Earth is a sphere; we have formed models approximately representing its shape and the distribution of its parts; generally when the Earth is referred to, we either think of an indefinitely extended mass beneath our feet, or else, leaving out the actual Earth, we think of a body like a terrestrial globe; but when we seek to imagine the Earth as it really is, we join these two ideas as well as we can—such perception as our eyes give us of the Earth’s surface we couple with the conception of a sphere. ”

“ Three-fourths of the surface of the earth is sea. Over the surface of the remaining fourth, excepting in mountainous places, is a layer of soil, varying from a few feet to a few hundred feet in depth. ”

“ A surface is defined to be length and breadth without depth; a line to be length without breadth or depth; a point to be what has neither length, breadth, nor depth. 'Tis evident that all this is perfectly unintelligible upon any other supposition than that of the composition of extension by indivisible points or atoms. How else could any thing exist without length, without breadth, or without depth? ”

“ But if I have got so far as to know that the earth is a sphere, and that its surface is spherical, I can cognize a priori and determine upon principles, from my knowledge of a small part of this surface—say to the extent of a degree—the diameter and circumference of the earth ”

“ The Surface Plate.—Planing to a flat surface requires some device to guide the eye. If the surface be very uneven at first, a beginning may be made in the planing without much assistance; but a point will finally be reached when neither the unaided eye nor the hand can determine whether or not a surface is flat. ”

“ Half a sphere is called a HEMISPHERE. 2. A body or the space bounded by a spherical surface. For most practical problems of navigation, the earth is considered a sphere, called the terrestrial sphere. ”

“ Every other part of the earth’s surface has at some time its running water coursing in valleys which it has itself etched into the surface. It is this etching out of the continents in an intricate pattern of anastomosing valleys which constitutes the chief difference between the land surface and the relatively even floor of the oceans. ”

“ To obtain a general idea of the nature and method of our science before beginning its study in detail, we may visit some valley, such as that illustrated in the frontispiece, on whose sides are rocky ledges. Here the rocks lie in horizontal layers. Although only their edges are exposed, we may infer that these layers run into the upland on either side and underlie the entire district; they are part of the foundation of solid rock which everywhere is found beneath the loose materials of the surface. ”

“ The level of its surface, however, is varied by hills and mountains, which, though insignificant in comparison with the size of the whole earth, are enormous when compared with the structures of human hands. ”

“ 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 it so happens that the whole surface of our [21] skin is sensitive in yet another way, and a small portion of it is astoundingly and beautifully sensitive, to an impression of an altogether different character—one not necessarily associated with any form of ordinary matter—one that will occur equally well through space from which all solid, liquid, or gaseous matter has been removed. ”

“ The surface of the earth surrounding such buildings should have a grade of at least one-half inch to the foot, for the distance of 50 feet in every direction, to insure the turning away of all surface water from the walks and grounds. ”

“ So in successive strata the present surface of the world was built, and sometimes in throes of uplifting, some long-buried stratum was doubled upon itself, and having been thrust up through deposits lying above it, once more reached sunlight. ”

“ 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. ”

“ In the case of the Ordnance Survey map, on the scale of 1 inch to a mile, the varying forms of the surface are so faithfully delineated as frequently to indicate to a trained observer the nature of the rocks and the geological structure of the ground. ”

“ Thus all the surface of this earth is formed according to a regular system of heights and hollows, hills and valleys, rivulets and rivers, and these rivers return the waters of the atmosphere into the general mass, in like manner as the blood, returning to the heart, is conducted in the veins. ”

“ It has been seen that igneous and aqueous agents have remodeled, from time to time, the physical geography of the globe. Can it admit of a doubt that changes in the physical structure of the earth’s surface will be accompanied with other changes in the organic productions of extensive areas? ”

“ In this cooling down and solidification of the Earth’s surface, we have one of the simplest, as well as one of the most important, instances, of that change from a uniform to a multiform state which occurs in any mass through exposure of its different parts to different conditions. To the differentiation of the Earth’s exterior from its interior thus brought about, we must add one of the most conspicuous differentiations which the exterior itself afterwards undergoes, as being similarly brought about. ”

“ We conclude from all these evidences that there exists on the surface of solid bodies an extremely thin layer, the density of which diminishes the more nearly we approach the free surface. Let us assume, consequently, such a special constitution for the superficial layer of solids, and, by a new effort of our imagination, witness the unrelaxing work of our particles of air in the immediate vicinity of some solid body ”

“ The outer surface of a pencil line represents the surface of the earth; the inner surface of the line represents the depth of man's explorations; the highest mountain would be represented by a comma resting on the line. ”

“ The very action of the physical forces determining the configuration of the earth's surface tends to produce a bilaterally symmetrical arrangement, as we may see by the simple experiment of throwing down a heap of pebbles or sand on the ground. ”