Chap. VIII.

GEOMETRY.

789

When the abacus is circular, then the cylinder beneath it will receive its shadow inthe same manner ; the process of projecting it is the same as in the preceding example.A prism with a polygonal base and a projection breaking round its top, when attachedto a wall, will cast a similar shadow; it will not be difficult to cast the shadow uponthe base, shaft, and capital of a column, if we suppose them to be cut into planes parallelwith its axis, for the purpose of marking the points which receive the shadows; for itmust be evident that if a ray of light enter any of these planes, every part of that raywill be in that plane, and the projecting parts upon the edges of those planes willcast a shadow at the several points of intersection.

In shading mouldings, it must be remembered that where the end or side of a buildingon which they occur is in shade, they will not receive any reflected light, either from theground or the surface of the building: and such mouldings will have a contrary effect toothers in shadow, situate on the light side of an object.

An ovolo laid level, whose greatest projection is above, when on the dark side of abuilding, will be lightest above, and gradually becoming darker towards its lowest edge.

The cavetto will be the reverse of this when in the same situation; it will be continuallylighter and lighter towards the under edge.

Perspective is the art of drawing the forms of objects as they are seen : this method ofdelineation differs materially from that called geometric, and is in fact the section of apyramid of rays, proceeding from the object to the eye; suppose for example a line drawnfrom every point or angle of a cube to the eye, or threads substituted for such lines,and that they in their passage pass through a transparent plane, as a sheet of glass orpaper ; the holes made in this plane will indicate the boundary and form of the object,and consequently its perspective representation.

Vignola , Seragatti , Brook Taylor , Priestley , and the Mahons , have by their writingsrendered this subject perfectly clear, and the Young Painter’s Maulstick by James Maitonis an admirable practical treatise ; and Sir Joshua Reynolds , in the first Discourse hedelivered at the Royal Academy , showed its importance : for it had been by many supposedto bound the artist with laws that might cripple the beauty of the forms he was called uponto draw, but the President emphatically stated that “ Every opportunity should be taken todiscountenance that false and vulgar opinion, that rules are the fetters of genius ; they arefetters only to men of no genius; as that armour, which upon the strong is an ornamentand defence, upon the weak becomes a load, and cripples the body which it was made toprotect. How much liberty may be taken to break through these rules, and as the poetexpresses it, * To snatch a grace beyond the reach of art,’ may be a subsequent considerationwhen the pupils become masters themselves : it is then where their genius has received itsutmost improvement, that rules may possibly be dispensed with : but let us not destroy thescaffold until we have raised the building.”

To the civil and military engineer a knowledge of the rules of perspective is highly im-portant, to enable him correctly to delineate all the objects within his sight, and to all it isthe principles of the art of seeing, and should be generally understood.

Drawing is as useful as the art of writing, and oftentimes the pencil in the hand of anexperienced draughtsman can explain more than the pen of a ready writer : and in givingdirections to a workman, a drawing accurately made is often all he requires; to those whoare desirous of forming a clear and distinct notion of form, the study of perspective is neces-sary, for every thing we see is seen perspectively, and no object appears as it really is fromany one point of view except it be the sphere.

In the geometrical representation of a building all the forms are drawn exactly as theyare, and it is necessary that such drawings should be made before we can exhibit its per-spective effect.

A visual rav is an imaginary line extended from the eye to any particular point, and a

3 e 3