DRAWING 251 cally are simple and well established. The supposed transparent plane is called the plane of projection or plane of the picture. The ho- rizon of the picture is the horizontal line re- sulting from the intersection of the plane of the picture by a horizontal plane passing through -Vanishing Point. FIG. 3. the eye. Point of view or point of sight is the point where the eye is supposed to be placed. Vanishing points are points in a picture to which all lines converge that in the object are parallel to each other. An object is said to be in parallel perspective when one of its sides is parallel to the plane of the picture (fig. 3) ; in angular perspective when none of its sides are so. Isometrical drawing implies that the mea- sures of the representations of the lines forming the sides of each face are equal. The principle of isometrical projection consists in selecting for the plane of the projection one equally in- clined to three principal axes at right angles to each other, so that all straight lines coincident or parallel to these axes are drawn in projection to the same scale. To draw a cube in isomet- rical projection (fig. 4), with a radius equal to one side of the cube, describe a circle, inscribe FIG. 4. a regular hexagon, and draw lines from alter- nate angles to the centre; the hexagon will be divided into three parallelograms, each of which will represent a face of the cube ; all the lines will be equal, and equal to the side of the cube. On these lines can be set off dis- tances as in orthographic projection, but only upon these lines, or those parallel thereto. Curved or inclined lines are therefore to be established by reference to these lines, and not by direct measure of the lines themselves. Isometrical drawing is especially valuable to the mechanical draughtsman, as it embraces the applicability of a scale with pictorial rep- resentation. In drawings for the patent office it is of very general application. Topograph- ical drawing is the delineation of the surface of a locality (fig. 5), with the natural and artificial objects, as houses, roads, rivers, hills, &c., upon it, in their relative dimensions and positions; giving in miniature a copy of the field, farm, district, &c., as it would be seen by the eye moving over it. Many of the objects thus to be represented can be defined by regular and mathematical lines, but many other objects, from their irregularity of outline and their in- significance in extent, would be very difficult to distinguish. Certain signs have therefore been adopted into general use among draughts- men, some of which resemble in some degree the objects for which they stand, while others are purely conventional. Sand is represented by fine dots, gravel by coarser dots ; meadow or grass land is represented by tufts of little per- pendicular lines ; trees, although not consonant with the other parts of the plan, are represent- ed often in elevation, at other times by clumps of foliage in plan, sometimes distinctive in their foliage ; dwellings and edifices usually in plan, made distinctive by some small prefix, as a pair of scales for a court house, a sign post for a tav- ern, a horse shoe for a smithy, a church with a cross or steeple, &c. The localities of mines are represented by the signs of the planets which were anciently associated with various metals, and a black circle or dot for coal. Hills are represented by two methods, the vertical and the horizontal. In the first the strokes of the pen follow the course the water would take in running down the slopes, the strokes being made heavier the steeper the inclination ; and systems have been proposed and used by which the inclination is defined by the comparative thickness of the line and the intervening spaces. In the system proposed for the United States coast survey, slopes of 75 are represented by a proportion of black to white of 9 to 2, and so down by nine grades to a slope of 2|-, in which the proportion is 1 black to 10 white. By the horizontal method, or by contours, hills are represented by horizontal lines traced round them, such as would be shown on the ground by water rising by equal vertical stages. The choice of a scale for a plot depends in a great measure on the purpose for which the plan is intended. Plans of house lots are usually named as being so many feet to the inch, plots of surveys so many chains to the inch, maps or surveys of states so many miles to the inch, and maps of railway surveys as so many feet to the inch, or so many inches to the mile. In the coast survey all the scales are expressed frac-
