Chap. VIII.

GEOMETRY.

791

point of convergency that two or more lines will have, which are the representations of twoor more parallel lines in an original object, placed inclined to the plane of delineation.

Vanishing line is a line on the picture or plane of delineation supposed to be obtained bya plane passing through the eye parallel to any plane in an original object, and produceduntil it cuts the picture : the horizontal line is, therefore, the vanishing line of all horizontalplanes, and all horizontal lines have their vanishing points in the horizontal line.

To find the vanishing point of a line as well as all the others, the diagram introducedmay be sufficient.

The plan of a church is shown at ABCDE, and at the side an elevation on which theseveral heights are drawn: it is required to put this in perspective on a plane or sheet otpaper, standing vertically on its edge upon the ground line, li T, the situation of the draughts-man being at S, the station point. ST and S R are drawn parallel to the ends of thebuilding through the station point S : and where they cut the ground line, RT, they fixthe extent of the vanishing point. The line VZ is the horizontal line, and perpendicularsdropped upon it from the points R and T determine the vanishing points V, Z.

On the plan, FE and FA are prolonged to the ground line ItT: these dropped serveto set out the heights of the several parts : X Y is the height O P, which, when drawnthrough to its vanishing point, V, marks um, as the perspective height of the same line:X \V shows the height O N, which is also drawn through the vanishing point in the samemanner, and where it cuts the prolonged perpendiculars um at v, a line is drawn to itsvanishing point z, and at o is found the point of the gable of the roof.

Lines having been drawn from the points A,B,C,D,E,F,G,H, of the plan to the stationpoint S, the corresponding small letters on the ground line R T show where the perpen-diculars arc to be dropped, on which the several heights are to be perspcctively marked off.mopqu show the end ED: ikmu the side E F, rski the side A F, rsyt the end A 13. O Ois the height of the spectator, wliich, of course, may be varied at pleasure, and were thehorizontal line V Z dropped to half the height, the perspective representation would bevaried materially : the top of the tower hue, as well as the ridges wx and oz , would thenall incline downwards towards the vanishing points, Z, V, which are supposed to be imme-diately over the points RT of the ground line.

Sometimes, to enlarge the perspective representation, the lines are not drawn immediately tothe station point, but are prolonged upon the ground line, and then crossed to the vanishingpoints which have been previously found. In this example we have the effect of thecapital above and below the horizontal line, and the small letters show the position on theplan, and the corresponding large ones; those of the plan above and elevation are shownin perspective.

For convenience the plan to be put into perspective may be placed either above or belowthe line, and in the diagram three systems are shown of drawing a figure; the angle ofvision or angle of view being the same in all.

'The Young Painter’s Maulstick contains, among many other valuable hints, one withregard to the best angle for vision, or that within which objects should be viewed, so as toobtain the most agreeable representation ; for as the angle of vision is enlarged or lessenedby viewing the objects near or remote, their appearance will be altered. Objects may beplaced too near the eye for their proper observance, and as the eye can contemplate only apoint at one time, it is by its celerity and continual motion that it becomes perfectlysensible of a whole or of many forms; but when an object, or many objects widely ex-tended, are placed too near the traverses of the eye, to contemplate them becomespainful. In taking a view of a building turning the head should be avoided, as no viewshould comprise a greater extent than the eye can agreeably contemplate at one glance, orthat can be seen by a pleasing and satisfactory traverse of the eye alone, which necessarilyconfines the extent of the matter, and of course the angle of vision, to certain limits. Theeye rests with composure on what it can contemplate with little trouble; not only too greatan extent, but too many objects, however they may interest and delight at first, soondistract and tire the organ of vision. Smallness of object has nothing to do with theangle of view’; a cube or miniature being placed too near the eye may form a largeangle of view’, and cause pain in observing it: a large extent of view’, or a large picture,may be contemplated w'ith as much ease as a small one ; it is only to place the observerat a greater distance.

Isometrical Perspective is sometimes used to represent buildings, and is of great use indiagrams and drawings of machinery, as all perpendicular lines in them may be measuredby a scale; the principles may be explained in the representation of a cube, into whichfigure all others may be resolved.

The square or side of the cube is crossed by diagonal lines, ar.d then another, as A C, isset out from A D, at an angle of thirty degrees ; and w’here this cuts the other diagonal, asat B, you have the length of the side, as A B, for the radius of a circle which is to containthe isometrical cube ; and if on this a scale is marked, all other parts may be measured by it.'The sides, as well as radius and height in the figure, all exactly correspond in length, and,

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