70. PROP. VII. If M be the magnitude of a body, S its specific gravity, and W its weight, W = MS. 71, 72. To find the relation which exists between the weights, mag- nitudes, and specific gravities, of two substances, and of a 73. PROP. VIII. When a body of uniform density floats on a fluid, the part immersed the whole body :: the specific gravity of the body the specific gravity of the fluid. 74. PROP. IX. When a body is immersed in a fluid, the weight lost whole weight of the body :: the specific gravity of the 76. PROP. X. To describe the Hydrostatic Balance; and to shew how to find the specific gravity of a body by means of it, 1st, when its specific gravity is greater than that of the fluid in which it is weighed; 2ndly, when it is less. 77. PROP. XI. To describe the common Hydrometer; and to shew how to compare the specific gravities of two fluids by means 86. PROP. XVII. To explain the construction of the Common Barometer; and to shew that the mercury is sustained in it by the pressure of the air on the surface of the mercury in the 87. PROP. XVIII. The pressure of the atmosphere is accurately 92. PROP. XIX. To describe the construction of the Common 93. PROP. XX. To describe the construction of the Forcing- 94. PROP. XXI. To explain the action of the Siphon. 96. PROP. XXII. To shew how to graduate a common Ther- 97. PROP. XXIII. Having given the number of degrees on Questions on Chap. IV. MECHANICS. [The explanatory matter, printed in small type, forms no actual part of the UNIVERSITY COURSE ; but is illustrative of the particular Definition, or Proposition, which it immediately follows; and will be found useful for answering the Questions, and solving the Problems, which are usually given in the University Examinations.] CHAPTER I. DEFINITIONS; EXPLANATION OF STATICAL FORCES; THE MANNER IN WHICH THEY ARE MEASURED, AND REPRESENTED. 1. MECHANICS is the science, which treats of the causes that prevent, or produce, motion in bodies, or that tend to prevent, or produce, 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 beams and the walls. If the roof gave way, and fell, it would belong to DYNAMICS to account for the circumstances attending the fall-to explain why the motion took place in one direction rather than in another-to determine the time elapsed in falling-and the swiftness of the motion at any instant. The part of MECHANICS treated on in the following pages is STATICS. L. C. C. 1 2. Definition of FORCE. Whatever the cause be which produces, or prevents, motion, or which tends to produce, or to prevent, motion, in a body, it is called a FORCE. If a heavy body, as a stone, be laid on the open hand, experience shews that, to prevent the stone from falling, the hand must make some effort. Again, to set a ball rolling along the ground require» some exertion. The effort, or exertion, is called in either case a FORCE; and although the effect produced be not great enough to prevent entirely the fall of the stone, or to communicate motion to the ball, yet it is still called 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, which keep a body at rest. 3. Definition of WEIGHT. All bodies, if left to themselves, fall, or tend to fall, towards the earth's centre, through a power, which resides in the earth, of constantly drawing all substances towards it, called THE FORCE OF GRAVITY. Consequently, if any body be reduced to a state of rest, it exerts a certain pressure downwards upon that which sustains it. And the precise amount of this pressure for any particular body is called the WEIGHT of that body. 4. The WEIGHTS of different bodies may be compared thus :-Let two bodies be successively attached in the same manner to a spring, so that they may act upon it by their weights in the same way. If they produce the same effects, (by bending the spring to the same extent,) the weights of the bodies are equal. Any other body, which produces the same effect on the spring by its weight as both the former bodies when applied together do by their weights, has its weight double of that of either of them. 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 a given body. 5. The WEIGHT of any body is measured thus :-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 being called a pound, any other body, which by the force of gravity only, produces the same effect as four, or six, or ten, such pieces of lead, will be four, or six, or ten, pounds in weight, as the case may be. 6. Definition of QUANTITY OF MATTER. The substance, material, or stuff, of which any body is made, is called MATTER. And since all bodies have Weight, the property of having Weight is to be considered as necessarily belonging to Matter. Hence in the same ratio, or degree, that one body has more weight than another, it is concluded, that it contains more matter; that is, the Quantity of Matter in a body is proportional to its Weight. 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. 7. The exact quantity of matter contained in any body may be measured by comparing its weight with the weight of some particular body, which has been fixed upon for a standard. Thus, if a cubic inch of water be previously taken as the body by which to measure the quantities of matter contained in all other bodies, and the quantity of matter in this cubic inch of water be called 1, then the quantity of matter in any other body would properly be said to be 5, if the weight of that body were five times as great as the weight of the cubic inch of water. 8. Definition of DENSITY. The Density of a substance, or body, is the degree of closeness, with which the matter composing it is, as it were, packed; which closeness is measured, or compared in manner following: Let equal bulks of two different substances be taken, suppose Water and Lead. Then, if the bulk of water which is taken weigh one pound, it will be found, that the piece of lead of equal size with it 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 fact is expressed, or described, by saying, that The DENSITY of Lead is to the DENSITY of Water, as 11 is to 1"; or by saying, "The DENSITY of Lead is times that of Water. 11 66 |