784
THEORY AND PRACTICE OF ENGINEERING.
Book II.
sphere into a potyedron, and these bands can be made to exhibit the faces of the truncatedpyramids of which they are a portion.
The mineralogist has taken the regular tetraedron, the cube, the rhombic dodecaedrmi, theoctaedron , the six-sided prism, and the parallelopiped, as the primary forms upon which theseveral crystals are found : in the first four, which arc called the regular geometrical solids,we find all the planes of each equal and similar ; the cubical crystal of floors may have eachof its solid angles removedeasily, when its figure willexhibit eight triangularsmooth planes instead, andthen continuing to removethe several layers whichcompose these eight trian-gular planes, we arrive atthe eight triangular planes : -_r.
of a regular octaedron. By '*-. n
a study of the structure ofa mineral substance, weshall arrive at a tolerablygood idea of the principlesof descriptive geometry :the sphere may be in thepresent instance consideredthe nucleus upon whichthe parallel deposits areformed.
The sphere is a polyedron, having a great number of plane faces, formed by trun-cated pyramids whose base is a polygon, and its development by conic zones is obtainedin the same manner as for truncated pyramids, with this difference, that all the arrises aiearcs of circles, described from the summits of cones, instead of being polygons.
Ftg. m.
mn
On Shadows _That part of a body from which light is intercepted by any object inter-
vening is said to be in shadow. The rays of light, which we receive from the sun, proceedin straight lines, and opaque objects, not transmitting through them the light they receive,necessarily have their opposite sides to the luminary in shadow: a shadow becomesapparently darker as the illuminating powers which produce it are increased. A stream otlight may be supposed to proceed from every luminous body which falls on all the objectsaround, and is again reflected by them to others, until it is entirely imperceptible.
Shadows are produced by depriving the object of the direct rays of light, and the artistgenerally represents on his drawing a shadow equal in depth to the projection of the ob-ject which casts it, or at an angle of 45°.
Light is either transmitted, absorbed, thrown back, or reflected, and the latter is alwaysso thrown that the angle of reflection is equal to the angle of incidence.
Some colours reflect light stronger than others, and on this subject the painter mustcarefully study nature to obtain his knowledge : in a lofty building those parts nearestthe ground receive the greatest portion of reflected light, and the upper the less, consequentlythey are darker : and the strength of colours is heightened or lessened from this cause.All shadows thrown from one object to another are darker than the object itself, and thoseparts which do not receive the direct light receive their brightness from reflection, and theshadow gets no reflection except from the object in shade.
The cornice of a building, which casts a shadow on its perpendicular face, receives on itsunder side or soffite a proportionate quantity of reflected light, either from the ground be-neath it or the upright face of the wall; consequently it is not so dark as the shadow it casts,and hence the beautiful relief between one and the other : there is the positive light, theintermediate, and the shadow.