Grid

“ Moreover, the appearance of the surface varies with the projection and with the relation of that surface area to the point of tangency. One may want to identify a location or area simply by alpha-numeric rectangular coordinates. This is accomplished with a grid. In its usual form this consists of two series of lines drawn perpendicularly on the chart, marked by suitable alpha-numeric designations. ”

“ Universal Transverse Mercator (UTM) Grid The Universal Transverse Mercator (UTM) grid is a military grid superimposed upon a transverse Mercator graticule, or the representation of these grid lines upon any graticule. This grid system and these projections are often used for large-scale (harbor) nautical charts and military charts.
309. Oblique Mercator Projections A Mercator projection in which the cylinder is tangent along a great circle other than the equator or a meridian is called an oblique Mercator or oblique orthomorphic projection. ”

“ If we could get the sand away, we could finish the grid. If we could finish the grid, we’d have power enough to get the sand away—in a few years, and if we could replace the machinery that wore out handling it. ”

“ A subdivision of YOUNG ICE l5 to 30 centimeters thick. Gray-white ice under pressure is more likely to ridge than to raft.
grid. , adj. Pertaining to a grid or related to grid north.
grid. , n. 1. A series of lines, usually straight and parallel, superimposed on a chart or plotting sheet to serve as a directional reference for navigation. See also FlCTlTlOUS GRATICULE, GRATICULE, definition 1. 2. Two sets of mutually perpendicular lines dividing a map or chart into squares or rectangles to permit location of any point by a system of rectangular coordinates. ”

“ It was as though the real sky, the real flowers, the real earth were forbidden her for all time and she condemned to breathe no other air than that of the theater. An occasional fireman passed, watching over their melancholy idyll from afar. And she would drag him up above the clouds, in the magnificent disorder of the grid, where she loved to make him giddy by running in front of him along the frail bridges, among the thousands of ropes fastened to the pulleys, the windlasses, the rollers, in the midst of a regular forest of yards and masts. ”

“ Just as the circle may be defined either as a plane surface or as the bounding line which is the locus of a point in a plane at a given distance from a fixed point, so a sphere may be defined either as a solid or as the bounding surface which is the locus of a point in space at a given distance from a fixed point. In higher mathematics the circle is defined as the bounding line and the sphere as the bounding surface; that is, each is defined as a locus. ”

“ Engineers surveying for a railway lay down the line level, or as nearly level as the configuration of the surface will permit; but an engineer’s level is not a straight line; it is the segment of a circle,—that circle being the circumference of the globe. The line which practically constitutes a level bends downwards continually as it goes forward, following the form of the earth, and at every point being at right angles to the radius. ”

“ If the region has one bounding surface, we may suppose that surface to contract inwards without breaking its continuity or cutting itself. If the region is one of simple continuity, such as a sphere, this process may be continued till it is reduced to a point; but if the region is like a ring, the result will be a closed curve; and if the region has multiple connexions, the result will be a diagram of lines, and the cyclomatic number of the diagram will be that of the region. The space outside the region has the same cyclomatic number as the region itself. ”

“ The form of a circle is familiar to all; and we proceed to define certain lines, points, &c., which constantly occur in studying its geometry. The fixed point in the preceding definition is termed the “centre” (C in fig. 1) ; the constant distance, e.g. CG, the “radius.” The curve itself is sometimes termed the “circumference.” Any line through the centre and terminated at both extremities by the curve, e.g. AB, is a “diameter”; any other line similarly terminated, e.g. EF, a “chord.” Any line drawn from an external point to cut the circle in two points, e.g. ”

“ We read how the truths have appealed to his own consciousness. It stands where the relief map itself stands, as representing the delineator’s own mental image of such structure.
There are no lines drawn in this map that contradict or confuse the meaning; all is direct, truthful and clear in statement of fact. Each line has its own particular meaning. If represents direction. Applied to land surface, a vertical line means a perpendicular mountain or side wall of plateau, horizontal lines indicate level areas, and oblique lines a sloping surface. ”

“ Square after square I passed through, and building after building. The cylinders were everywhere but did not interfere with my movements. A group of them constantly accompanied me, but whether always composed of the same cylinders I could not tell. Their incessant whispering was a nerve-wracking thing, and I often felt like turning on them and shooting.
I wish I could tell you all I saw: buildings full of toiling machinery and now and then a score or so of beast-men; squares and radiating arteries without a blade of grass or a tree, and never an animal, a bird, or an insect. ”

“ When more than three surfaces of discontinuity in a fluid system meet in equilibrium along a line, with respect to the surfaces and masses immediately adjacent to any point of this line, we may form a polygon of which the angular points shall correspond in order to the different masses separated by the surfaces of discontinuity, and the sides to these surfaces, each side being perpendicular to the corresponding surface, and equal to its tension. ”

“ The circle being drawn, a line A, 179, is drawn through its centre, and from its intersection with the circle as at b, here a step on each side is marked as c, d, then lines c to d, and c and d to e, where A meets, the circle will describe a trigon. If the figure is to stand vertical, all that is necessary is to draw the line a vertical, as in Figure 180. A ready method of getting the dimension across corners, across the flats, or the length of a side of a given polygon, is by means of diagrams, such as shown in the following figures, which form excellent examples for practice. ”

“ Evolution of Geometric Land-measures While smaller units, such as the superficial rod, can easily be conceived as square, the larger arable units have, or have had, a peculiar form which still attaches to them. The peasant, whose mind’s eye 67can perceive the square rod or toise or verge, refers the rood or the acre, the vergée or the arpent, to the familiar length of the furrow and to the breadth of the rod or of the four-rod acre-breadth equal to a cricket-pitch. ”

“ If the reader will imagine this series of squares to represent a portable piece of open trellis-work, which might be set up at a window or in the open field, between the spectator and any object of interest at a distance—each square representing a number corresponding with a code in universal use—it will be obvious, that by noticing the squares which the outline of a hill would cover, and telegraphing the numbers of the squares, something in the way of form and outline may be quickly communicated from the other side of the world. ”

“ The circle was undoubtedly known to the early civilizations, its simplicity specially recommending it as an object for study. Euclid defines it (Book I. def. 15) as a “plane figure enclosed by one line, all the straight lines drawn to which from one point within the figure are equal to one another.” In the succeeding three definitions the centre, diameter and the semicircle are defined, while the third postulate of the same book demands the possibility of describing a circle for every “centre” and “distance.” ”

“ We also represent every stress twice over, for it appears as a side of both the polygons corresponding to the two joints between which it acts. But if we can arrange the polygons in such a way that the sides of any two polygons which represent the same stress coincide with each other, we may form a diagram in which every stress is represented in direction and magnitude, though not in position, by a single line which is the common boundary of the two polygons which represent the joints at the extremities of the corresponding piece of the frame. ”

“ If we draw a circle about this pole on a common terrestrial globe, and intersect it by spirals to represent the direction of the wind, we shall see that the wind enters all parts of this circle from the southwest, and, consequently, that a whirl ought to be created thereby, in which the ascending column of air revolves from right to left, or against the hands of a watch. ”

“ A system coaxal with the two given circles is readily constructed by describing circles through the common points on the radical axis and any third point; the minimum circle of the system is obviously that which has the common chord of intersection for diameter, the maximum is the radical axis—considered as a circle of infinite radius. ”

“ If from any point without a circle there he drawn two straight lines, one of which cuts the circle, and the other meets it, and if the rectangle contained in the whole line which cuts the circle, and the part of it without the circle, be equal to the square on the line which meets the circle, the line which meets the circle shall touch it. ”

“ Where it extends over upon the next page or plate, it is always to be understood that the one which precedes is to have its left margin placed to the right margin of that which follows, and that the day column at the left of a division refers to all that stand to the right of it, when thus placed, until another day column is reached. In order to make this clear, let me illustrate by an example. On the middle division of Plate V we find a day column with two figures to the right of it. Turning to Plate IV, we find other figures of a similar character, but no day column. ”

“ These arcs on a solid globe would be parallel to the equator, but do not appear so on a plane or flat surface. In geography, they are called Parallels of Latitude.
If an apple be taken and sliced from side to side, it will exactly represent the circles, which are planes cutting a sphere perpendicular to its axis. ”

“ But after driving over a circuit of several miles embracing the remarkable group of earthworks of which this is only a single feature, and satisfying myself by personal observation of the existence of parallel avenues which have been traced for nearly two miles; and of the grand central oval, circle, and octagon, the smallest of which measures upwards of half-a-mile in circumference: all idea of mere combined labour is lost in the higher conviction of manifest skill, and even science. ”

“ Whether a Branch (suppose) of three Circles, cut at Spring, the sap ascending, or another of the same bigness, will at Michaelmas following, if cut again, be found to have increased one or more Circles than it had in the Spring: and whether at Spring or Fall, or at other season, it be found to have a Circle or half a Circle of Pricks next or betwixt the Barks, or a Circle of Wood next the inner Bark onely, or both? But here the Comparison is to be made with distinction, For it must be inquired, Whether some Trees shoot new Tops every year until a certain Age, and after not? ”

“ We give a diagram to make the points clear.
As the chimney top does not move from its place on the window, it is clear that the train is running on a segment of a circle having the chimney for its centre. It follows that the observer’s distance throughout is equal to the radius of that circle, and the radius of a circle of which the quadrant measures 51⁄2 miles is 31⁄2 miles within about 11 ft. ”

“ Whether some have the Circles in their Branches decreased from their Body to the extremity of the Branch in such order, that (e. g.) an Apple-tree shoot of this year hath one Circle of Pricks or Wood plac'd in the Graft of two years old, and that of two years growth will the next year have one Circle more then it had the year before? And whether this onely be till the Branch shoot no more Grafts, and whether then the utmost Twig get any new Circles, or stand at a stay, being nourish'd onely, not augmented in bulk as to the appearance of the Circles? ”

“ The third general method of attack applies chiefly to problems where some point is to be determined. This is the method of the intersection of loci. Thus, to locate an electric light at a point eighteen feet from the point of intersection of two streets and equidistant from them, evidently one locus is a circle with a radius eighteen feet and the center at the vertex of the angle made by the streets, and the other locus is the bisector of the angle. ”

“ For any ordinary man may much sooner and more accurately find a strait line equal to the perimeter of a circle, and consequently square the circle, by winding a small thread about a given cylinder, than any geometrician shall do the same by dividing the radius into 10,000,000 equal parts. ”

“ In any triangle, the radius of the circumscribed circle is to the radius of the circle which is the locus of the vertex, when the base and the ratio of the sides are given, as the difference of the squares of the sides is to four times the area. ”

“ Each component part of a border should be strongly dynamic and, if possible, partake of the main movements of the border.
Any form which causes the eye to move in a given direction is strongly dynamic, and is opposed to the static form which does not cause a marked eye movement. A circle is symbolic of the static form, while a triangle is dynamic. ”