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THE ELEMENTS

OF

MECHANICS AND HYDROSTATICS.

THE few explanatory articles and paragraphs that are enclosed in brackets form no part of the Course required to be read by the Candidate for the degree of B.A. Those in smaller type are illustrative of the Definitions and Propositions which they immediately follow. The whole of the extra matter so introduced forms but a very small, and a very easy, portion of the book; and they who come to this subject for the first time will do well not to omit it.

MECHANICS.

CHAPTER I.

DEFINITIONS; EXPLANATION OF STATICAL FORCES; THE MANNER IN WHICH THEY ARE MEASURED, AND REPRESENTED.

1. THE science of MECHANICS investigates the causes that prevent or produce motion in bodies, or that tend to produce or prevent motion.

It is divided into two parts. The one, which investigates the conditions fulfilled when a body is in a state of rest, is called STATICS. The other, which treats of the causes and the effects of motion, is called DYNAMICS.

Thus it is the province of STATICS to shew how the roof of a building is supported by the cross beams and the walls. If the roof give way and fall, it would belong to DYNAMICS to account for the circumstances attending the fall;-to explain why the motion takes place in one direction rather than in another; to determine the time elapsed in falling, and the swiftness of motion at any instant.

The part of MECHANICS treated on in the following pages is THE ELEMENTS OF STATICS.

2.

DEF. Whatever the cause may be that produces or prevents motion, or that tends to produce or prevent motion, it is called a FORCE.

[If a heavy body, as stone, be laid on the open hand, experience informs us that to prevent the stone from falling the hand must make some effort. Again, to set a ball rolling along the ground requires some exertion. The effort, or exertion, is called in either case a FORCE; and though the effect be not great enough to prevent entirely the fall of the stone, or to communicate motion to the ball, yet it is still denominated a FORCE.

From the definition of STATICs given in Art. 1 it will readily be understood that in that branch of MECHANICS the conditions are investigated, which are fulfilled by those forces only that keep a body at rest.]

3. DEFS. (1) All bodies we are acquainted with, if left to themselves, would fall to the earth's surface. This power residing in the earth of drawing all substances to its surface is called THE FORCE OF

GRAVITY.

(2) The act of a body's pressing downwards when laid on any substance is called the GRAVITATION of the body.

(3) The precise amount of gravitation residing in any particular body is termed its WEIGHT.

4. [The WEIGHTS of bodies may be thus compared. If two bodies, when successively attached in the same manner to a spring, so that they may act upon it by their weights in the same way, produce the same effects,-(by bending the spring to the same extent), the weights of the bodies will be equal. Any other body that produces the same effect on the spring by its weight as both the former bodies when applied at the same time do by their weights, is double the weight of either. And by means of such a contrivance as this spring, bodies might be shewn to be three, four, or any number of times the weight of the first body.

The WEIGHT of any body is thus measured. The weight of a certain bulk of some particular substance is first fixed upon as a standard. Thus the weight of a piece of lead of a certain size is called a pound, and then any other body whose gravitation produces the same effect as four, or six, or ten such pieces of lead, is four or six or ten pounds in weight, as the case may be.]

5. DEF. The substance, or material, of which any body is formed, is called MATTER.

[As all bodies we are acquainted with have Weight, the property of having weight is to be considered as necessarily and inherently belonging to all matter; and it is with respect to its property of having weight that matter is made the subject of mathematical investigation. The existence of matter, under whatever form it may appear, is therefore tested by that form having weight; and in the same ratio or degree that one body has more weight than another, it is concluded that the former body contains more Matter than the latter does.]

6. DEF. THE QUANTITIES OF MATTER that different bodies contain are proportional to the weights of the bodies.

[Thus, if a body A weigh one pound, and another body B weigh three pounds, the quantity of matter contained in A is said to be to the quantity contained in B as 1 to 3; or B is said to contain three times as much matter as A does.

The exact quantity of matter contained in any body is measured by comparing its weight with the weight of some particular body. Thus if we take a cubic inch of water for the body to measure the quantities of matter contained in all other bodies by, and we call the quantity of matter in this cubic inch of water one, then the quantity of matter in any other body would properly be said to be five, if the weight of that body were five times as great as the weight of the cubic inch of water.]

7. DEF. When we speak of the DENSITIES of different substances, we refer to the closeness with which the matter composing them is packed, as it were, in the substances.

4.

To compare this closeness, let equal bulks of two different substances be taken;-suppose the substances to be water and lead. If the bulk of water taken weigh one pound, it will be found that the piece of lead of equal size will weigh 11 pounds. There is evidently, therefore, 11 times as much heavy matter in a piece of lead as there is in an equal bulk of water; and this is expressed by saying, that "the DENSITY of lead is to the DENSITY of water, as 11 to 1."

10

COR. 1. If the density of water be called 1,i. e. if water be made the measure of density,then the density of lead will be properly called 11

or 11.4.

10

[COR. 2. In the same manner as we have explained how the density of lead is estimated with respect to the density of water, the densities of any other substances, either solid or fluid, may be deterinined with respect to that of water.]

8. To explain how the precise amount of a statical force may be described; that is, To

SHEW HOW STATICAL FORCES ARE MEASURED.

The amount of a Statical Force is described by mentioning the number of pounds it would support if it acted in a direction opposite to the force of gravity. Thus if the weight of a body were P pounds, and it were prevented moving towards the earth's surface by a hand placed beneath it, the resistance offered by the hand to the communication of motion, (that is, the force exercised by the hand), is clearly P pounds,

SURES.

9. [FORCES are, in Statics, also called PRESIn whatever direction a force tends to produce motion, its magnitude is, as has already been stated, measured by the weight of the body which would exert the same effect to produce motion downwards, as the force under consideration does in the line in which it endeavours to produce motion. And that such a method of measuring Forces is allowable will readily appear from this consideration, viz., that the effect produced in consequence of a weight acting may be made to take place in any direction we choose;

horizontally, as in the case of a string being attached to an object lying on a table and kept stretched by a heavy body (W) that hangs over the side of the table; or vertically

upwards, as in fig. 1, by passing the string over a peg 4 and attaching the end to a ring B, so that BA may be vertical; or in any other direction (fig. 2), by the heavy body

OB

W

pulling the string in a direction BA inclined at any angle to that (AW) in which it acts itself.

10. (1) The point at which a force acts upon a body is called the point of application of the force.

(2) The line in which a force produces, or tends to produce, motion, is called the line of the force's action; and any line that is parallel to the line of a force's action is said to be in the direction of the force.

[When the direction of a force's action, or as it is generally called "the direction of the force," is indicated by a line, we have either the very line given in which the force acts, or some line parallel to it. "The line of a force's action”

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