Horizontal

“ 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. ”

“ 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. ”

“ Extremes meet, and so the attempt to avoid absolute horizontal lines has completely failed, because in their place we have a succession of vertical members placed side by side in such endless numbers that we really think more of the horizontal arrangement of these members, slight though they are, than we should of the simplest defined horizontal line. ”

“ By tracing parallel lines and finding vanishing points of planes and surfaces, much that bewildered you in the past will become clear and reasonable.
Planes, horizontal planes and perpendicular planes, are terms constantly used with regard to perspective.
A horizontal plane is a plane parallel with the earth; a perpendicular plane is one perpendicular to the earth. The top of a table and the ceiling of a room are horizontal planes; the walls of the room are perpendicular planes. ”

“ 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. ”

“ 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. ”

“ 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. ”

“ 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. ”

“ 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. ”

“ 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. ”

“ 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. ”

“ 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 two horizontal planes cut by a vertical line, it is required to find a point on the upper part of the vertical line from which bodies may fall to the horizontal planes and there, having their motion deflected into a horizontal direction, will, during an interval equal to the time of fall, traverse distances which bear to each other any assigned ratio of a smaller quantity to a larger. ”

“ But there is nothing to prevent us from assuming that between the verticals and horizontals we have mentioned there lie an indefinite number of other similar lines, to which intermediary fractional numbers will be assigned. Henceforth every point of the plane can be regarded as defined by the intersection of some particular horizontal and some particular vertical. ”

“ As horizontal surfaces can be planed very much quicker than vertical ones, it frequently occurs that it will pay to take extra trouble in order to chuck the work so as to plane it horizontally, an excellent example being the planing of the faces of the two halves of a large pulley, the chucking of which is illustrated in Fig. ”

“ The tendency of the primary strata to remain straight in the horizontal direction, and to be bent in the vertical, is a phenomenon which points very directly to the causes from whence it has arisen. A surface of simple curvature, or a surface straight in one direction, is - 231 - what the application of forces to different points of a plane, which is flexible, though with a certain degree of rigidity, will naturally produce. ”

“ Now it is evident, that whatever the actual angle of elevation of the mountain may be, every exhibition of this horizontal distance between us and the summit is an addition to its height, § 19. And consequent expression of horizontal distance in their ascent.and of course to its impressiveness; while every endeavor to exhibit its slope as steep and sudden, is diminution at once of its distance and elevation. In consequence nature is constantly endeavoring to impress upon us this horizontal distance, which, even in spite of all her means of manifesting it, we are apt to forget or underestimate ”

“ 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. ”

“ Fig. 6.
As outlines are composed of profiles, the same laws govern. That the curved line is the line of beauty stands out most evidently in the study of antique designs. Vertical lines and horizontal lines are the lines of support and strength, and must always have proper consideration; but in pure ornament the office of straight lines seems to be confined to connecting curves and to emphasizing their contrasts. ”

“ The quantity of the horizontal parallax of any object is in proportion to its distance from the place of observation, being greater or less as the object is nearer to or farther removed from the spectator. ”

“ No one, I presume, will doubt the truth of this proposition, who reflects, that it is much easier to move any spherical body on an horizontal plane, than to raise the same body up against a perpendicular wall. ”

“ If our picture plane is a sheet of glass, and is so placed that we can see the landscape behind it or a sea-view, we shall find that the distant line of the horizon passes through that point of sight, and we therefore draw a line on our picture which exactly corresponds with it, and which we call the Horizontal-line or Horizon.3 The height of the horizon then depends entirely upon the position of the eye of the spectator: if he rises, so does the horizon; if he stoops or descends to lower ground, so does the horizon follow his movements. ”

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

“ The vertical dimensions—the physical limitation—are defined by the elevation of terraces and highlands, and they exhibit the greatest diversity of phenomena.
The horizontal dimensions supply most of the material for our elementary compends for political geography, which seldom make much account of vertical dimensions, and which, by no means, penetrate to their real value. They are commonly held to be a side-matter, to be touched lightly upon, or wholly cast aside. But both must be thoroughly studied; for they are mutually dependent, and are never found divorced in nature. ”

“ Appearances.We have to deal with appearances rather than realities. The edges we know to be horizontal, no longer appear so; we compare them with the pencil held horizontally until we realise the angle they make with it. The width has apparently grown much less and must be compared with the front edge. ”

“ Thus, for example, it has lately been shown that we habitually draw geometrical forms too large in the horizontal dimension as compared with their vertical dimension; we draw oblate ellipses where we intend to draw circles ”

“ The devices which aid the figure painter in disposing of one or many verticals have been briefly viewed. A consideration of the horizontal will necessarily take us out of doors to earth and sky, where nature constructs on surfaces which follow the horizon.
The problem in composition which each of these lines presents is the same and the principle governing the solution of each identical; balance by equalization of forces. [pg 117] Given a line which coincides with but one side of the picture it becomes necessary for the poise of the quadrilateral to cross it with an opposing line. ”

“ The angles of inclination should be frequently noted down in numbers; all accidents of ground, such as ravines, rocks, &c., should be carefully placed, and all other objects, such as houses, fences, trees, &c., should be put down in their proper relative positions and dimensions. Having thus prepared a skeleton of horizontal curves, numbered as to inclination and heights, the sketch will always serve a useful purpose without any lines of greatest descent. ”

“ In prison.—My eye, however strong and weak it may be, only encompasses a certain distance, and within this distance I move and live; this horizontal line is my immediate greater and lesser fate, from which I cannot escape. Thus round every being a concentric circle is drawn, which has a centre and which is peculiar to him. In a similar way our car encloses its in a small space, and so does our touch. ”

“ The vanishing scale, which we shall find of infinite use in our perspective, is founded on the facts explained in Rule 10. We there find that all horizontals in the same plane, which are drawn to the same point on the horizon, are perspectively parallel to each other, so that if we measure a certain height or width on the picture plane, and then from each extremity draw lines to any convenient point on the horizon, then all the perpendiculars drawn between these lines will be perspectively equal, however much they may appear to vary in length. ”

“ All horizontal lines in nature that are parallel to {36} PEN DRAWING. By Jules Girardet. Showing a mantel a little below the eye. The student should practice drawing interiors with the purpose of learning the theory of perspective from every object drawn. The horizontal lines of the picture frame, for example, tip in the opposite direction to the mantel, because they are above the eye. Had the mantel been a few inches higher it would have been drawn as a perfectly horizontal line. {37} CRISPI AS CÆSAR IN HIS ROBE DE CHAMBRE. A political caricature from Don Chisciotte. ”

“ The perpendicularity of the one line, and the horizontality of the other, must not in any way be interfered with; in the sketch they should, in fact, meet and form a right angle, which should just be rounded off. ”

“ Whether the horizontality of the shelves or terrace-lines is really as perfect as has been generally assumed is a point which will require to be tested by a more accurate trigonometrical survey than has yet been made. ”

“ Independently of phenomena which we are still to study, and paradoxical as it may appear, we can say that, if there are bands or zones in a cascade, they are rather horizontal than vertical. Our design vi, Fig. 5, still false and incomplete in many respects, looks more like a real fall of water than the design v, Fig. ”

“ But if we consider the vertical force by itself, and bring it into the form so that satisfies the above-mentioned partial differences, then and, consequently, Thus, by the combination of the horizontal force with the vertical, we obtain the means of dividing into its constituent parts and , and thus of learning whether a sensible value must be assigned to the latter. Only the constant part of , namely, , is left wholly undetermined by the observations, the reason of which is plain from Art. ”