HYDROSTATICS AND ELEMENTARY HYDROKINETICS GEORGE M. MINCHIN, M. A. i PROFESSOB OF APPLIED MATHEMATICS IN THE ROYAL INDIAN ENGINEERING COLLEGE, COOPERS HILL AT THE CLAEENDON PRESS 1892 Ojcfori P-RTNTED AT THE CLARENDON PRESS BY HORACE HART, PRINTER TO THE UNIVEKS. UY PREFACE TN this work no previous acquaintance with the nat and properties of a fluid is assumed. As in my treatise Statics, I have begun with the very elements, and, sum ing that the students reading in pure mathemai is advancing simultaneously with his study of Hydrostat I have endeavoured to lead him into the advanced porti of the subject. It will be noticed, however, that the v in which the reader is introduced to the notion of a peri fluid is very different from that which is usually adop in similar treatises. A definition of a perfect fluid foun upon the elementary facts and principles of the the of strain and stress is not calculated to produce the imp sion of simplicity, more especially when the symbols the Differential Calculus are employed in the process. I maintain, however, that in such a presentation of basis of the subject there is really nothing which a begin who is familiar with the elements of Geometry, Algel and Trigonometry cannot readily understand. The pre lent view that the fundamental notions of the Differen Calculus are a mystery which the beginner should not d to approach, and which cannot be unveiled until gi experience in mathematics has been attained, has 1 vl Preface. seemed to me to be a most unfortunate fallacy. Indeed, 1 think that, with the aid of a few simple illustrations borrowed from ordinary experience, the process of lifferenilaium and the notion of a limiting value towards which a ratio tends will be found much more easy of attainment and compre hension than are the initial simple processes of Algebra themselves namely, those of subtraction, multiplication., and transformation. Hence I have not hesitated to define the particular kind of body which forms the ideal basis of - Hydrodynamics-viz., a perfect fluid with reference to the nature of its stress and strain and such a definition is, I think, tho only one that is really direct and scientific. The critical reader will probably notice th complete absence of reference anywhere in this work to a certain term which is very familiar to students of Hydrostatics namely, the whole pressure of a fluid on a curved surface. This term is one of the unfortunate misconceptions of Physics not, indeed, so fatally charged with mischief as that other venerable illusion, centrifugal force., by the balancing 1 of which with centripetal force, in the science of previous generations, the planets are enabled to revolve round the Sun. This notion of whole pressure on a curved surface has served as a peg from which to hang very many visionary problems of pure mathematics but it has don more than this for, the author of one of our elementary text-boots of Hydrostatics tells his readers that, when, a cylindrical vessel is filled with water, the e whole pressure of the liquid on its curved surface is the measure of the total strain to which the vessel is subjected 1 So far Preface. vii as I am aware, there is no reality in Physics corresponding to this notion of whole pressure on a curved surface, and certainly none is indicated by those writers who use the term. There is 3 indeed, in the theory of Electrostatics, and in that of Newtonian gravitation in general, the result that the surface-integral of the normal component of force intensity taken over any closed curved surface is pro portional to the quantity of attracting matter contained within the surface but, apart from this, the arithmetical non-vectorial addition of a number of forces which are not parallel is a process devoid of physical meaning...