758

THEORY AND PRACTICE OF ENGINEERING.

issues from a hole made in the side of a cistern or reservoir,and it forms the best curve for the reflection of light.

The mouldings found in Greek temples, so worthilyadmired, are all of this form; they result from the inter-section of conic surfaces by planes parallel to the side ofthe cone in general.

VX is the base of the parabola Y. The parabola is acurve consisting of two similar sides, which may be producedindefinitely, by being drawn in such a manner with regardto the axis passing through the vertex, that the abscissa; areto each other as the squares of the ordinates ; so that if theformer be 1, 4, 9, the latter will be 1, 2, 3, &c. When abody or projectile is thrown in a horizontal direction,its path through the air will be half of a parabola, whosevertex lies in the point of projection.

When a body is thrown obliquely upwards, its path isthat of a complete parabola, whose vertex will be thehighest point reached by the body, which ascends one sideand descends by the other: if the projectile forms anyangle whatever with that of gravity, a body set in motionby these forces will not follow the direction of either ofthem, but will adopt a middle course proportional to boththe forces; the course of the body, which is determined bythe laws relative to the parallelogram of forces and theearth’s attraction, will be that of a curved line resemblingthe parabola.

The base of a paraboloid, as Z, is its circular end ; in thefrustum of a cone it is at 8, and the top at 2 shows thebase of the part cut off, and 1 the slant height.

In the parabola NOP the superficial content may beobtained by considering it as the portion of an oval.

A Cone is a body comprised within two superficies, andis formed by revolving a right-angled triangle on its axisas that at X. So is formed the paraboloid C when oneside of the figure is curved.

The base of a cone is the circle on which the figurestands : N O is the slant height.

If a body be thrown vertically upwards, it will be re-tarded in an uniform manner, and not arrive either per-pendicularly or at the apex of the cone, but will, by theinfluence of gravity, assume the parabolic curve, which isone of the sections of the coue. This is in consequence ofthe effect of the projectile force becoming every momentless powerful by the earth’s attraction on the ascendingbody, and which is exactly in the same ratio as it accele-rates its descent. The laws which regard the latter are ininverse application; a body will therefore lose its velocityafter a certain time, and return to the surface of the earthiu precisely the same time as was occupied by its ascent;the projectile force is momentary, and the action of gravitypermanent; the motion is consequently a compound one,the forces acting sometimes in the same vertical, and some-times in an opposite or oblique direction.

When a ball or other body is projected, its force as wellas angle may be ascertained by using a spiral steel spring,which may be strained according to various degrees oftension; this spring, placed in a tube, and made movableabout a pivot, may be made to act at any required anglesby means of a graduated scale.

The base of an angle is D C : B is the summit ofthe angle A.

The base of any solid is the side on which it rests:L M is the base of the figure K.

The amount of the weight of such a body is proportionalto the mass, the measure of which, estimated by that ofsome other body which serves as an unit, is termed its ab-solute weight. Gravity and weight in mechanics alwaysare to each other in the relation of action and re-action.

Fig 769.

Fig. 770.

Fig. 771

Fig.772.

Fig. 773.

L_-

Fig. 77-1.

z

Fig. 777*.