756

THEORY AND PRACTICE OF ENGINEERING.

Book II

actual dimensions, we may obtain the requisite measuresfrom the properties of similar triangles; for instance, tofind the position of the image of either of the right lines inthe cube, we must determine the point in which a lineparallel to it, passing through the place of the eye, cutsthe plane of the picture; this, which is called the vanishingpoint, is shown at X, and all the lines which are under thesame parallel will tend to it; when the lines are, however,parallel with the plane of the picture, the distance of theirvanishing point becomes infinite, as we shall see whentreating of the laws of perspective. In treating diagrams,geometricians usually make all lines which are on thereturn of a cube, or which represent its sides, tend to onepoint, and draw the face in front, as D, perfectly square.

When a cube is represented with its sides equal, it issaid to be geometrically drawn, but when shown as atK it is in perspective.

A Sphere is a body comprised within a single super-ficies, in which all the lines drawn from a central pointequal one another.

LMNO is an hemisphere or half globe; a segmenteither less than a portion cut off, as at Q, or greater,as that part of the sphere at R.

The zone is a portion taken out of the middle, asshown at S.

The sector of a sphere has a portion of the outersurface, and terminates in a point as at T.

The globe R, when cut in two, has the parts or planesshown as at T, V, which are called its sections, and S is anhemisphere.

B is an armillary sphere, and used by astronomers toshow the motion of the earth, and the relative positionof the sun, moon, and stars, &e. This is an ancient astro-nomical machine composed of an assemblage of hoops orcircles, representing the different circles of the system ofthe world, as the equator, the ecliptic, the colures , &c.,arranged in their regular position.

D shows the mounting of the sphere used to representthe earth, which is usually represented as round, or a trueglobe ; this was inferred from the figure of its shadow, asseen on the moon’s disc in lunar eclipses. The hypothesisof its being a true sphere is sufficient to explain the generalappearance of the heavens as seen from different points ofits surface: Eratosthenes , upwards of 2000 years ago,made the attempt to ascertain its diameter : he knew thaton the day of the summer solstice the sun illuminated thebottom of a well at Syene ; at the same instant he observedat Alexandria that the sun was 7° 12' from the zenith, andit was supposed that Syen6 was due south from that, place,and, therefore, that both were under the same meridian.Having determined the distance between the two places tobe 5000 stadia, and accurately measured the sun’s altitude,he found the earth’s circumference to be 250,000 stadia:this method, which is not accurate, was afterwards adoptedby many other philosophers.

Artificial globes are used for explaining the rotation ofthe earth, the latitude and longitude, and the situation ofplaces with respect to each other; they are, however,limited to general explanation : it is often highly necessaryfor the engineer to determine the meridian, or to draw ameridian line, and this requires the aid of a good telescope,a well-regulated clock, and the sextant, or an instrumentfor determining the altitude of the sun or star. By thesextant we can determine two instants of time; when thestar has the same altitude, the clock will give the intervalof time between them, and half this interval will be thetime between each observation and the passage of the starover the meridian. If we next day note the time of the

Fig. 754.

Fig. 755.

Fig. 757.

Fig. 75*.

B

F>

Fig 760.