By Professor Miller's kind permission, I have been allowed to make use of the Chapter on Instruments in his Hydrostatics: of this permission I have availed myself in many cases, and, in particular, I am entirely indebted to Professor Miller for the descriptions of the Piezometer and Stereometer, and for information and references having regard to those instruments. The slight historical notices appended to some of the Chapters are intended to mark the principal steps in the progress of the science, and to assign to their respective authors the exact values of the advances made at different times. I have given, in most cases, the answers to the examples and problems, and these will, I hope, sufficiently illustrate the subject, and form for the student a collection of useful and instructive exercises. W. H. BESANT. ST JOHN'S COLLEGE, For the present Edition the text has been carefully revised, answers to the Examples have been tested, and additional answers inserted. Attention has been particularly paid to the numerical answers, and it is hoped that all the answers given will be found to be free from error. TABLE OF CONTENTS. PAGE 95-121. The Diving Bell, Pumps, Bramah's Press, Air Pumps, Condenser, Manometers, 133-157. Mixture of Gases, Radiation, Conduction and Convection of Heat, Dew, Hygrometers, ELEMENTARY HYDROSTATICS. INTRODUCTION. THE object of the science of Hydrostatics is to discuss the mechanical properties of fluids, or to determine the nature of the action which fluids exert upon each other and upon bodies with which they are in contact, and to explain and classify, under general laws, the varied phenomena relating to fluids which are offered to the attention of an observer. To effect this purpose it is necessary to construct a consistent theory, founded upon observation and experiment, from which, by processes of deductive reasoning, and the aid of Geometry and Algebra, the explanations of phenomena shall flow as consequences of the definitions and fundamental properties assumed; the test of the theory will be the coincidence with observed facts of the results of such reasoning. We shall assume in the following pages that the student is acquainted with the elements of Plane Geometry, with the simpler portions of Algebra and Trigonometry, and of Statics, and, in the later chapters, with a few of the properties of Conic Sections, and certain results of Dynamics. In dealing with any mechanical science, we may take as the basis of our reasoning certain known laws, derived from experiment, or we may deduce these laws from a set of B. E. H. 1 axioms and definitions, the axioms being the result of inductive reasonings from observed facts. With our present subject it is generally necessary to rest upon empirical laws, but in some cases these laws can be deduced from the axiomatic definition of a fluid. For instance, in the first chapter we have stated as experimental laws the principles of the equality of pressure in all directions and the transmission of pressure, but this formal statement of fact is followed by a deduction of the laws, by strict reasoning, from the axiomatic definition. The idea of a varying fluid pressure and of the measure of such pressure is one of the first which presents itself as a difficulty; the student will perceive that it is a difficulty of the same kind as the idea of varying velocity and its measure. A body in motion with a changing velocity has, at any instant, a rate of motion which can be appreciated and measured; and, in a similar manner, the pressure at any point of a fluid can be conceived, and, by reference to proper units, can be made the subject of calculation. In problems relating to the equilibrium of fluids, an artificial mode of thought enables us to reduce such problems to the form of statical problems, and we are thus enabled to employ the laws of equilibrium, which have been proved for rigid bodies. Some of the most important results of the science will be found in the construction of Hydrostatic instruments; a consideration of these instruments, many of which we shall describe, will shew how universal are the practical applications of fluids, and that, while doing the hardest work of levers and pullies, they at the same time assist in the most delicate manipulations for determining weights and measures. The Hydraulic Press and the Stereometer illustrate these extreme applications of the properties of fluids. The articles printed in smaller characters in the following chapters may if necessary be omitted during a first reading of the subject, and the Examination papers which follow the first eight chapters are intended as a first course of questions upon the chapters. The examples which follow the Examination papers are somewhat more difficult, and should be dealt with after the former have been studied and discussed. |