« PreviousContinue »
A COLLECTION OF PROBLEMS
IN ILLUSTRATION OF THE PRINCIPLES OF
BY WILLIAM WALTON, M.A.
TRINITY COLLEGE, CAMBRIDGE.
Δια τί εν τη θαλάττη μάλλον νείν δύνανται ή εν τοίς ποταμούς και
SIMPKIN, MARSHALL, & CO.; AND GEORGE BELL, LONDON.
Recat, 5-17-23-0. B
The success which has within the last few years attended the publication of systematic collections of Examples in several departments of Natural Philosophy and Mathematics, has led me to entertain a belief that a like treatise on the mathematical doctrine of Fluids, would, if composed with a due reference to the necessities of students, be not without its utility. Having been accordingly induced to enter upon this work, I have proposed to myself to furnish the beginner with classes of Problems methodically arranged in elucidation of the various hydrostatical and hydrodynamical theorems ordinarily falling within the province of Academic study. In the fulfilment of this design I have endeavoured, as much as possible, to give to each branch of the subject a proportionate amount of illustration, in order that students, whether of higher or lower mathematical attainment, may be able to meet with a sufficient body of matter applicable to the condition of their knowledge. In carrying out this, my primary object, I have omitted no opportunity of introducing incidentally to the notice of the reader, by historical references, those remarkable memoirs and works of mathematical philosophers in which the first principles of the science of fluids and their most striking consequences were originally unfolded. This secondary purpose of my treatise I have been anxious to fulfil adequately, not only from a wish to enable the higher order of students to acquire more thorough information on particular questions than could have been communicated in accordance with my general design, but also from a conviction that an
acquaintance with the researches of inventive writers in their original form tends greatly to invigorate our conceptions of the fundamental principles of science, and that our interest in its discoveries is ordinarily much augmented by an historical knowledge of their progressive development.
The obligations to various authors under which I have been placed in preparing this volume for the press have been specially acknowledged in the course of the work, whenever I have had any reason to suppose that the source of my information was original. I may add also generally that I have derived great assistance in my undertaking from various examination papers which have been published from time to time in the University of Cambridge. The solutions of those problems which have been extracted from the works of the earlier mathematicians, as well as many for which I am indebted to more modern writers, are almost all presented in this treatise under an entirely new form.
CAMBRIDGE, September 24, 1847.
N.B.—A table of Errata, should one be found requisite, is intended to be published in November 1848.
TABLE OF CONTENTS.
Sect. I.—Normal pressure of homogeneous incompressible fluids on
the surfaces of immersed solids
II.- Normal pressure of heterogeneous fluids on the surfaces of
III.—Normal pressure of aeriform fluids of uniform temperature
Equilibrium of Solid Bodies flonting freely.
Sect. I.-Bodies floating in incompressible homogeneous fluids
II.-Bodies floating in incompressible heterogeneous fluids.
III.-Bodies floating under the action of elastic fluids