Vertical

“ 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.) ”

“ 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. ”

“ 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. ”

“ So accustomed is the eye to vertical lines in tree trunks, tall buildings, and thousands of other examples that the upward eye movement in viewing an object, having a predominance of vertical elements, seemingly adds to its height. ”

“ And in this he first explained the distinction between two styles, which have been called the “ horizontal and vertical systems, ” the “ horizontal system ” being that by which the older contrapuntists regulated the onward motion of their several' parts, and the “ vertical system ” that which constructs an entire passage out of a single harmony. ”

“ If a vertical line, drawn through the centre of the trunk, be taken as a median line in a simple design of the human figure, all subsequent patterns which are drawn will be grouped symmetrically about it. ”

“ 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. ”

“ 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. ”

“ 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. ”

“ 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. ”

“ 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. ”

“ 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. ”

“ 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 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. ”

“ 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. ”

“ But imagine a vertical plane from the highest point of which are drawn lines inclined at every angle and extending indefinitely; imagine also that heavy particles descend along these lines each with a naturally accelerated motion and each with a speed appropriate to the inclination of its line. ”

“ 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. ”

“ In proof of the fact that the half balance, or that on either side of the vertical is sufficient in many subjects, see such portraits in which the head alone is attractive, the rest being suppressed in detail and light, for the sake of this attraction.
It is rarely that figure art deals with balance over the horizontal central line in conjunction with balance over the vertical. ”

“ How many pairs of vertical angles are formed by the intersection of two lines?
Read all the pairs of vertical angles formed by the lines l m, n p.
LESSON NINTH. KINDS OF ANGLES. RIGHT ANGLES. What do we call the angles a o c, c o b? (Diagram 9.)
Are they equal to each other?
Then they are called right angles.
A right angle is one of two adjacent angles that are equal to each other.
Are the adjacent angles c o b, b o d equal to each other?
Then what are they called?
Read the right angles below the line a b. On the left of c d.
Read three right angles whose vertices are at p.
24
Diagram 9. ”

“ 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 ”

“ Without reckoning, too, that if a vertical depth of sixteen leagues can be attained only by a diagonal descent of eighty-four, it follows that we must go eight thousand miles in a south-easterly direction; so that we shall emerge from some point in the earth's circumference instead of getting to the centre! ”

“ 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. ”

“ The GROUND-PLANE is the plane on which we stand; the base-line is an imaginary line passing through the middle of the feet as we stand square and erect; and the vertical plane is supposed to stand on the base-line and perpendicular to it. ”

“ We have seen that a film tends to set itself at equal angles to the surface which it meets, and therefore, when that surface is a solid, to meet it (or its tangent if it be a curved surface) at right angles. Our vertical partition is, therefore, everywhere normal to the original cell-walls, and constitutes a plane surface. ”

“ For if a shaft is vertical, there is a triangle with a right angle, which the Greeks call ὀρθογώνιον and this, according to the inequalities of the mountain slope, has either two equal sides or three unequal sides. ”

“ If the base and the difference of the base angles of a triangle be given, the rectangle contained by the perpendiculars from the vertex on two lines through the middle point of the base, parallel to the internal and external bisectors of the vertical angle, is constant. ”

“ Thomas Young explained the parhelic circle (P) as due to reflection from the vertical faces of the long prisms and the bases of the short ones. If these vertical faces become very numerous, the eye will perceive a colourless horizontal circle. ”

“ When the expression perpendicular to the surface of the glass is used, it means what a workman would probably call square to the surface of the glass. The vertical direction at any place is that of a plumbline hanging there, or perpendicular to the surface of still water. ”

“ 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 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. ”

“ The upper horizontal Figures shew the Number of Parts into which the Tenth of an Inch has been divided.
2. The Figures in the left vertical Column express the Height in feet, (above the imaginary Level, at 32 Inches of the Barometer,) or Expansion corresponding to a single Tenth of an Inch of Quicksilver.
3. The feet in the Place of Meeting are called tenths: thus, 90 Feet are 9 Tenths of 100 Feet. ”

“ The vertical circle passing through the east and west points is called the prime vertical, and has a distinction above other vertical circles by virtue of its being the most favorable position for a body in observations for longitude. The heavens are further swept by an infinite number of parallels of altitude which are, as their name implies, parallel to the horizon. ”

“ 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. ”

“ The reason why we prefer vertical symmetry and regard it as something special in its kind, whereas we do not recognise horizontal symmetry at all immediately, is due to the vertical symmetry of the muscular apparatus of the eye. ”

“ He has shown, for example, that vertical distances appear greater than equal horizontal distances in the proportion of 4·8 to 4, and that the same proportion exists between the muscular forces which move the eye vertically and those which move it horizontally; that the minimum of movement of the eye capable of exciting consciousness of contraction and the smallest perceptible distance are in exact agreement, both answering to an angle of one sixtieth of a degree ”

“ Thousands of cases are to be found in every group, of rocks and lines horizontal at the top of the mountain and vertical at the bottom; but they are still the exceptions, and the average out of a given number of lines in any rock formation whatsoever, will be found increasing in perpendicularity as they rise. ”

“ 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 ”

“ 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. ”

“ 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. ”