quires no description, and the latter will be explained further on. From these machines, as elements, are formed by combination, the pulley, the wheel and axle, the screw, and the wedge. These seven make up what are commonly called the Mechanical Powers, and from them may be constructed every machine, however complicated. For a more detailed account of the general principles of Mechanism and Machines, the reader is referred to Chapter XI.

III.--PRINCIPLES DEPENDENT ON THE ATTRACTION OF GRAVITATION.

Universal Gravitation.

34. THE earth exerts a force of attraction upon all bodies near it, tending to draw them towards its centre. This force, called the Force of Gravity, when unresisted imparts motion, and the body is said to fall; when resisted it gives rise to pressure, which is called Weight.

NEWTON showed that the force of gravity, as exhibited at the earth's surface, is only a particular case of a general attraction extending throughout the Universe, and continually tending to draw bodies together. This general attraction he called Universal Gravitation. It is mutually exerted between any two bodies whatever, and it is by virtue of it that the heavenly bodies are retained in their orbits.

The law of universal gravitation may be easily explained. If we take the mutual attraction of two units of mass, at a unit's distance from each other, as 1, then will their mutual attraction at any other distance be equal to 1 divided by the square of that distance; thus, if the distance is 2, their attraction will be of what it was at the

What machines are formed by combinations of simple machines? Name the seven mechanical powers. (34.) What is the Force of Gravity? What is its effect when unresisted? When resisted? What is Universal Gravitation? Explain the law of Universal Gravitation.

distance 1; if their distance is 3, their attraction will be of what it was at the distance 1, and so on. If one of the masses contains m units of mass, and the other one unit, the force will be m times as great as though they were both units of mass; that is, the attraction will be equal to m, divided by the square of the distance between the bodies. If the second body contain n units of mass, the attraction will be n times as great as before; that is, it will be mn, divided by the square of the distance between the bodies.

This law, discovered by NEWTON, may be expressed as follows: Any two bodies exert upon each other a mutual attraction, which varies directly as the product of their masses, and inversely as the square of their distance apart.

Effect of Gravitation on the Planets.

35. It is by the influence of gravitation that the planets are retained in their orbits. Their motion is the same as though they had been projected into space with an impulse, and then continually drawn from the right lines along which inertia tends to carry them, by the attraction of the sun. The planets also attract the sun, but their masses being exceedingly small in comparison with that of the sun, their effects in disturbing its position are exceedingly small. The orbits of the planets are ellipses differing but little from circles.

Force of Gravity.

36. The FORCE OF GRAVITY is that force of attraction which the earth "exerts upon all bodies, tending to draw them towards its centre.

As has been stated, it is only a particular case of Universal Gravitation. It is, therefore, subject to the same law, that is, it varies directly as the mass of the body acted

Enunciate NEWTON's law. (35.) What is the effect of gravitation on the planets? What are the orbits of planets? (36.) What is the Force of Gravity? How does it vary?

upon, and inversely as the square of its distance from the centre of the earth.

The shape of the earth has been shown by careful measurement to be that of a spheroid; that is, of a sphere slightly flattened at the poles. The mean radius is a little less than 4000 miles. On account of the flattening of the earth at the poles, different points are at slightly different distances from the centre, and consequently the force of gravity varies slightly at different places on the surface. For ordinary purposes, however, we may regard the earth as a perfect sphere, and the force of gravity as constant all over its surface.

37.

Vertical and Horizontal Lines.

A VERTICAL LINE is a line along which a body falls freely. All vertical lines are directed towards the centre of the earth, but for places near together they may be regarded as parallel.

In Fig. 21, the lines ao and bo are verticals, but if they are not far apart, their convergence is so small that they may be taken as

parallel. If, however, their distance apart is considerable, they can not be regarded as parallel. A man standing erect has his body in

What is the shape of the earth? (37.) What is a Vertical Line? Where do verticals meet? When may they be considered parallel? When not parallel? Illustrate.

a vertical, and it may happen that two persons on opposite sides of the globe, as at E and E', may both stand erect, and yet their heads be turned in exactly opposite directions, their feet being turned towards each other. Points where this may happen are said to be antipoles.

A HORIZONTAL LINE, or PLANE, at any place is one which is perpendicular to a vertical line at that place. The surface of still water is horizontal, or level. For small areas this surface may be regarded as a plane, but when a large surface is considered, as the ocean, it must be considered as curved, conforming to the general outline of the earth's surface.

Upon the principle of verticals and horizontals, all of our instruments for levelling and making astronomical observations are constructed.

The Plumb-Line.

38. A PLUMB-LINE, is a line having a heavy body, usually of lead, suspended at one of its ends. When the other end is held in the hand, the lead, tending towards the centre of the earth, stretches the string in the direction of the force of gravity.

It is used for indicating a vertical line. In Engineering and Architecture it is of continual use. For determining whether a wall is vertical, it is accompanied by a square plate, whose length is just equal to the diameter of the cylindrical leaden weight, and which has a hole at its middle point, just large enough to admit the passage of the string. The edge of the plate is applied to the masonry, as shown in Fig. 22, and if the plumb-bob just touches the wall, it must be vertical.

Weight.

39. The WEIGHT of a body is the pressure which it

What are antipodes? What is a Horizontal Line, or Plane? Level? Applications to instruments. (38.) What is a Plumb-Line? Describe it and its use. (39.) What is Weight?

exerts upon any body that prevents it from falling towards the earth.

The weight of a body is due to the force of gravity, acting upon all of its particles, but it must not be confounded with the force of gravity. Weight is only the effect of gravity when resisted; when gravity is unresisted it produces quite another effect, that is, motion.

At the same place the weights of bodies are proportional to their masses, or the quantities of matter which they contain We shall see hereafter that the weight of bodies may be determined by means of the balance; the force of gravity is determined by the velocity which it can impart to a body in a certain time, as will be shown more fully hereafter.

Centre of Gravity.

40. The CENTRE OF GRAVITY of a body is that point through which the direction of its weight always passes.

We have seen that the weight of a body is the resultant of the action of gravity upon all of its particles. It is shown

Is weight the same as gravity? How is weight determined? measured? (40) What is the Centre of Gravity?

How is gravity