66 A NEW TREATISE ON MECHANICS. BY THE AUTHOR OF 66 A NEW INTRODUCTION TO THE MATHEMATICS," A NEW SUPPLEMENT TO EUCLID'S ELEMENTS OF GEOMETRY," PREFACE. THE present work has originated in consequence of the extreme brevity of expression, and deficiency of explanation, in the treatises on this subject now in use. If it be very important to maintain conciseness in these works, it should, at least, be employed in stating all that is desirable to be known, and requisite to be explained, on a subject, not of itself difficult to be understood, if the whole of it were clearly laid before the reader, nor indeed difficult to communicate; although from the practice of these authors, it would appear to be impossible. But they are sparing, not only of their words, but of their matter. Nay, in order to avoid wasting language, they will sometimes use a word, not in its ordinary sense (in which they use it themselves in other parts of their works), but in a new meaning, unknown to the beginner; and in this manner they sometimes communicate the most important truths. For instance, Mr. Bridge, in treating of uniform motion in the very beginning of his work (Mechanics, p. 7.) states, that if the space described by a body moving uniformly be given, the time of its motion will be in the inverse ratio of its velocity. Now, the ordinary mathematical sense of the A 2 word "given" is "known;" and it seems to be made a condition in this proposition, that provided the space described is a known quantity, the time will be inversely as the velocity; from which the beginner would infer (what certainly is not meant), that if the space were an unknown quantity, the time would not be inversely as the velocity, and that their ratio changes, as soon as the space is known or found, from what it was before, while the space was unknown, although the space continues the same unvarying quantity, whether it be known or unknown. But this short expression saved that author the circumlocution of stating the proposition in words at length, as follows:-" If a body moving uniformly at one time with a certain velocity, and at another time with a different velocity, describes equal spaces, the time in which the space will be described with the greater velocity will be in the inverse ratio of the velocity: the greater velocity will require less time, and the less velocity will require more time." As this truth or proposition is demonstrable from the known properties of uniform motion, it would not have been an unprofitable instruction to have added the demonstration. The reader will observe how pregnant of meaning is the word "given," as used by that author, and he will judge whether a beginner would be likely to ascribe the author's meaning to it, or to take it in its ordinary sense. The present author, being convinced of the perplexity and mischief occasioned to the student by these sacrifices of important instruction to an overweening and meretricious leaning to brevity, has undertaken the present work, in which he has endeavoured to supply the explanation wanting. The work is, therefore, strictly elementary, and intended for beginners. It embraces the prime principles of Motion, Moving Force, and the Mechanical Powers, without attempting the higher branches usually treated of by authors on this subject. Indeed, the necessity for such full explanation does not exist as to the higher branches, because the student, when he has acquired not merely the technical rules, but the rationale of the elementary parts, will not require much assistance in pursuing his studies further; which, for the most part, will consist merely of the application of the principles which he has previously acquired to other investigations. Chapter i. part i. contains the Definition and Laws of Motion. The second law of motion is stated by most authors, as follows:-" Motion, or the change of motion, is proportional to the force impressed, and is produced in the right line in which that force acts." (Bridge's Mechanics, p. 12.) In the present work it is stated thus:-"Motion, or the change of motion, is produced uniformly in the line of direction in which the impulse or force acts, and is proportional to the excess of the force applied above the resistance;" which is materially different from the other. For it appeared to the author, that the reaction of the resistance destroyed an equal quantum of the action of the force originally applied. Thus, if the force impressed were equal to a weight of 2lbs., and if the resistance of the body were equal to a weight of 1lb., the remaining force, 2 1 = 1lb., would be that which moves the body. But let the force be doubled = 4lbs., the resistance being 1, the remaining force 41 3lbs. would be that which moves the body; that is, this second motion would be to the first as 3 to 1, and not as 2 to 1, which is the ratio of the forces impressed. This is demonstrated in the chapter on the lever in the second part of this work. (Part ii. chap. i. § 2. art. 8 to 13.) The third law of motion is stated in chap. i. as follows:"When a force applied to a body is resisted, the resistance re-acts upon the body in a direction opposite to that of the |