Verticality

“ Having the horizontal sections given, we may obtain a complete knowledge of the direction in which the ground slopes by drawing perpendicular to them any number of lines of greatest descent; the degree of declivity is expressed by purely conventional means. The means adopted for this purpose are of two kinds. One depends upon the principle of vertical illumination, in which the maximum quantity of light is reflected upwards to the eye by a horizontal surface, and a minimum by a surface inclined 45° to the horizon. ”

“ It will be seen that if a horizontal line is drawn from the foot of one of these figures, say G, to point O on the edge of the incline, then dropped vertically to o·, then again carried on to o·· where the other figure g is, we find it is the same height and also that the other vanishing scale is the same width at that distance, so that we can work from either one or the other. In the event of the rising ground being uneven we can make use of the scale on the level plane. ”

“ The superior importance of the vertical and horizontal directions, the specially restful character of the horizontal, and the aspiring aspect of the vertical, the voluptuous nature of the curve as opposed to the severity of the straight line, point to the deeper and fuller experiences of movement, muscular exertion, and repose, which we obtain apart from the eye. Even the value of bilateral symmetry for the eye may owe something to that well-marked rhythmic contrast of right and left, which the movements of the tactual organ yield to us. ”

“ When the elevation is determined by sights the angle of elevation is the angle between the line of sight and the axis of the piece, when these lines are in the same vertical plane,—or the angle between the line of sight and a plane containing the axis of the piece and a horizontal line intersecting it at right angles, when they are not. The graduations of tangent scales and fixed breech-sights give this angle in degrees. The graduation of the pendulum hausse gives the angle correctly only when the line of sight is horizontal. ”

“ Try it and see if it is not true that lines in one direction never indicate any other direction; the vertical can never be mistaken for the horizontal, or the reverse. For the representation of a level plain, make simple strokes in the horizontal direction with the side of the crayon, and to represent a vertical surface as a cliff, make a stroke in the vertical direction with the same broad side of the crayon. Oblique surfaces, as slopes, are to be drawn with oblique strokes, and curved surfaces like rounded hills, represented by continuous upward and downward strokes. (See Fig. 1.) ”

“ The principle on which the horizontal lines converge is already known, but the principle on which the vertical lines cut these at certain determinate distances is not yet known. It is easy taking the latitudes of the art, if we may so speak, but its longitudes are still to discover. At length, however, have we the lines of discovery indicated: in the architectural drawings of the calotype the perspective is that of nature itself; and to arrive at just conclusions, we have but to measure and compare, and ascertain proportions. ”

“ The accompanying charts comprise a series of projections formed on the following principle; A vertical line, one inch long, is divided by horizontal lines into eight parts, representing as many decades. The angle to the left of the vertical line is supposed to represent males, and that to the right, females; and the shading of either angle indicates the predomination of the sex it stands for. Figures attached to the ends of the horizontal lines indicate by thousandths the number of individuals in each decade of life. ”

“ For example, the horizontal interval for a slope of 1⁄20, corresponding to a vertical interval of 25 feet, will be 20 × 25 = 500 feet, which, on a scale of six inches to a mile, will be represented by a length equal to 500⁄5280 × 6 = 0·566 inches. In this case, therefore, supposing the slope of the ground to be uniform between two given contours 25 feet apart, we should represent it by means of the hachures shown opposite a slope of 1⁄20, continued over a space of 0·566 inch. ”

“ In sketching hills endeavour to project as many horizontal curves as possible, which should be lightly put in, and then the shading lines may be drawn over them. The degree of slope should be frequently written down in numbers upon the sketch. The names of localities, streams, hills, farms, &c., should also be entered.
Thus far we have supposed a measured line upon the ground, to which the situation and dimensions of objects might be referred. It is much more difficult to embody the relative positions and dimensions, where all is left to the eye. ”

“ To get a plan we make a horizontal section at any determined height, which gives us the thickness of the walls and the area of the spaces which they inclose. An elevation shows us one of the faces of the building in all its details, while the transverse or longitudinal section allows us to lay the whole of the structural arrangements open to the spectator. Plan, elevation, and section, are three different things by the comparison of which a just idea of the whole building and of the connection of its various parts may be formed. ”

“ 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. ”

“ As the horizontal contours of any portion of the earth's surface must depend on the vertical, or, in other words, the various features which are marked on the map—the coast line, plains, rivers, vallies, lakes, hills, mountains, &c., being consequent on the different elevations of the various portions of the surface above the level of the sea ”

“ Given a vertical height joining two horizontal parallel lines; given also a distance greater than once and less than twice this vertical height, it is required to pass through the foot of the given perpendicular an inclined plane such that, after fall through the given vertical height, a body whose motion is deflected along the plane will traverse the assigned distance in a time equal to the time of vertical fall. ”

“ To sum up, the eye, owing to the laws of its mechanism, follows a line much more easily in the central than in the peripheral parts of the field, and in the central parts it follows a vertical line more easily than an oblique, and an horizontal more easily than a vertical. ”

“ If a point lies in the horizontal plane, its elevation lies in the axis and the plan coincides with the point itself. If a point lies in the vertical plane, its plan lies in the axis and the elevation coincides with the point itself. ”

“ The angle of slope on either side is a little more than fifty-one degrees, a slope which is often called perpendicular, and, moreover, as the strata are horizontal, there are several vertical walls of rock, which sweep around the entire north and west faces, and apparently make impassable barriers. ”

“ The apparent vertical indicated by the plummet-line or determined at the level of the sea, is simply the direction of weight, which may be materially affected by local attractions due to an irregular distribution of the masses composing the soil. ”

“ A space that is arched looks wider than it actually is, for the eye unconsciously follows the lines of the arch, and a distance or width effect is the result. The same space treated with a straight line is quickly bridged. The same space treated with lines that come to an angle looks narrower, for the reason that the eye becomes focused by the apex of the angle, and a height effect, not a breadth effect, is the result. ”

“ The horizontal map distances should be related to the other horizontal distances of the map, and the altitudes to other altitudes, and these with reference, also, to the tabulated lists found in every geography, of the heights of mountain peaks and lengths of rivers.
“All knowledge of external things comes through observation, comparison, and judgment.” To judge of great altitudes, one must have a knowledge of the heights within experience. ”

“ From these two data the length of an arc of a meridian corresponding to a difference of latitude of 1° at once follows. The latitude of a place is the angle which the vertical at the place makes with the equator, or, expressed in a slightly different form, is the angular distance of the zenith from the celestial equator. The vertical at any place may be defined as a direction perpendicular to the surface of still water at the place in question, and may be regarded as perpendicular to the true surface of the earth, accidental irregularities in its form such as hills and valleys being ignored. ”

“ The height of the stick divided by the length of the shortest shadow is the tangent of the complement of the latitude.
If the earth be considered a rigid body and the axis upon which it rotates be fixed within the body of the earth, the latitudes of all places upon its surface will remain always the same. If, however, the axis should shift its position within the earth, then the equatorial plane, which must be always perpendicular to the axis, must shift and consequently the latitudes of all places on the earth's surface must change accordingly. ”

“ Without counting that if a vertical descent of sixteen leagues costs us a horizontal of eighty-five, we shall have to go about either thousand leagues to the southeast, and we must therefore come out somewhere in the circumferences long before we can hope to reach the center. ”

“ If one and the same body, starting from rest, falls along an inclined plane and also along a vertical, each having the same height, the times of descent will be to each other as the lengths of the inclined plane and the vertical. ”

“ Hence we are peculiarly inclined to think that a line which we perceive to be in such a plane is a vertical line. But to see a whole lot of lines at once, all ready to throw their images upon the vertical meridian, is a thing that has hardly ever happened to us, except when they all have been vertical lines. Hence when that happens we have a still stronger tendency to think that what we see before us is a group of vertical lines. ”

“ In level countries, as might be expected, the disposition of the layers is nearly horizontal. In approaching mountainous countries, this horizontality, generally speaking, ceases; finally, on the sides of mountains, some of these layers are very much inclined; they even sometimes attain a vertical direction.
"May not the inclined deposits that we see upon the slopes of mountains, have been deposited in inclined or vertical positions? ”

“ For the same reason, the horizontal line, in which innumerable objects intervene between the eye and the horizon, appears so much longer than the line of altitude of the meridian, that the vault of the sky does not seem a hemisphere, but a far smaller segment of a great sphere. ”

“ In fact, the sea horizon lies below the rational horizon by an amount varying with the elevation of the eye above the surface. Geometry enables us to determine just what the dip of the horizon must be for any given elevation of the eye. A rough and ready rule, which may serve for many purposes, is that the square root of the elevation of the eye in feet equals the dip of the horizon in minutes of arc, or of angular measure. ”

“ The horizontal dimension represents the downward and outward force of the weight; the vertical dimension, the upward forces, which prevent the wall from collapsing in itself and hold it upright; while the lateral boundaries give evidence of the inward tension that keeps the mass together. ”

“ The distinction between horizontal and vertical is not an illusion; and the man who thinks it can be disregarded is likely to come to an untimely end. Yet we cannot arrive at a comprehensive view of nature unless we combine horizontal and vertical dimensions into a three-dimensional space. ”

“ Contour and surface enrichment should never appear to compete for attention in the same design.
Fobs
Plate 54 shows flat planes, the service of which suggests vertical inceptive axes. Figure 380 is noted as an exception to this vertical inceptive axis as it possesses a vertical primary mass but with radial inceptive axes. The interesting manner by which the dynamic leaves of the outer border transmit their movement to the inner border, which in turn leads toward the point of concentration, is worthy of attention. ”

“ To render the differences of altitude more apparent, these vertical distances are plotted to a much larger scale than the horizontal, as explained in a preceding Section. To erect the perpendiculars, the T and set square furnish the most convenient means. The detail points thus determined upon the perpendiculars represent [94] the points in the surface of the ground at which the levels were taken, and by joining these points we obtain the surface line. An example will clearly show the method pursued. Let it be required to lay down the section from the following level-book:—
Fig. ”

“ If from any line A or B or C (Fig. 18) , &c., we drop perpendiculars from different points of those lines on to a horizontal plane, the intersections of those verticals with the plane will be on a line called the horizontal trace or projection of the original line. ”