FELLOW AND LADY SADLEIR'S LECTURER OF S. JOHN'S COLLEGE. CAMBRIDGE: LONDON: BELL AND DALDY. 1859. MY object in the following pages has been to put forth the principles of the Science of Motion in their true geometrical form, postponing the consideration of force (the properties of which are presumed to have been fully investigated in Statics) until the reader may be able to separate in his mind the geometrical ideas from the mechanical. To the fact that these ideas are not kept separate at the outset I apprehend that the want of clearness in the student's mind about the real investigation that does take place in any case may be attributed. Until a comparatively recent period all works on this subject have been concerned with answering the question, Given the force acting on any body, how will it move? But how a motion is to be estimated, which of course is a preliminary question that should be fully investigated, on this point very little has been said. The first book, I think, in which the geometry of Motion was formally treated of, separate from the cause, was Griffin's Dynamics of a Rigid Body; this of course could not be referred to till the elements of the subject had been mastered. The same method of treatment was adopted in Sandeman's excellent treatise of the Motion of a Single Particle; a work to which I am greatly indebted, as the reader will easily see, the 6th chapter being very little else than a transcript 416390 of his second chapter on the Laws of Motion. There is one defect in that work, but for which the present treatise would never have appeared: it is, that a certain amount of previous knowledge of the subject is almost necessary, and the work itself is inadmissible in the case of those who are unacquainted with the Differential Calculus. This introductory position I propose to take up. I have written this book so that a knowledge of the Differential Calculus is not necessary; the student, by simply omitting the articles marked A, will become acquainted with the Science of Motion as far as he can by the application of the lower analysis only: such an one I presume to proceed to the first three sections of Newton's Principia, which will take the place of my 4th chapter; and I may remark in passing, that in them Newton always uses the word "force" as synonymous with "acceleration;" and I think that if any editor of Newton should in future replace the words "force" and "body" by "acceleration" and "point," he will do good service to the cause of philosophy. But I have also considered the case of those, who, knowing the Differential Calculus, still confine themselves to the elementary portions of the Science of Motion: to such readers it is scarcely sufficient merely to indicate the method to be pursued, as is done in Sandeman's first chapter, but actually to deal with the most ordinary cases of Motion in a geometrical manner before applying ourselves to cases of nature. Those who purpose to follow the subject throughout, may perhaps find this treatise useful, and for the higher portions of it may be referred to Sandeman's work. For the benefit of these last two classes of readers the articles marked A are intended. In the first four chapters I have confined myself entirely to the phænomena of Motion, that is, I have treated of what has hitherto been called (though not universally) Kinematics this name would have been given to the present treatise, had it not been that it was thought open to objection; other names were suggested, which were in their turn objected to: I did not therefore adopt any one, not being desirous of controversy: it is to be hoped that scholars will soon agree upon a name that will be satisfactory. I may be thought a purist in my nomenclature, but it seems at least a fault on the right side, especially in a work on first principles: for the furtherance of my purpose of keeping the reader's mind free from any idea of force in his considering motion abstractedly, I have rejected the usual symbol ƒ for an acceleration, using instead a; for the actual choice of ƒ would in my opinion naturally lead the reader to think of force. For a similar reason, in Chapter IV. I have adopted λ instead of μ: this latter having been hitherto said to represent the "absolute force." In subsequent chapters this treatise becomes Dynamical and in them I have endeavoured to shew how in any case we get rid of force, and investigate the motion geometrically; most of the cases of motion considered are brought under the formulæ in the first four chapters. I have rather avoided representing the intensity of a force by the product of the mass moved and the acceleration produced, as the beginner would not be very likely to have a clear notion of this: this is more especially true of those Articles in which the Differential Calculus is not employed in the other Articles I have not so rigidly restricted myself. * J. Hermann (1716) and Kant use the word Phoronomy. L. b |