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GALILEO is accused of having adopted the conversational form in his physical treatises, in order that he might be the more free under the disguise of his interlocutors to praise his own discoveries. Without caring to undertake a complete defence, I can easily suggest a more charitable reason for his having expounded his views in the form of a dialogue. Galileo might feel, indeed must have felt, a freedom of explanation, and a facility in putting difficulties and solving them, when he adopted the dialogue, of which the greater stiffness and dignity of an ordinary treatise might not seem to allow and certainly we must admit that he has been singularly happy in bringing out and explaining the various points of his subject in an easy and entertaining manner.

It was probably the example of Galileo's dialogues, which suggested to me the possible advantage of introducing the conversational element into school-books on Mechanics. I knew, however, that a mere conversationbook could not be made to convey the subject in a form such as the student requires; I knew that the fundamental propositions must be given in that plain stern form in which they are usually presented; yet I thought that the dialogue might be introduced as subsidiary to the common method; and, finally, I determined to attempt an elementary treatise founded upon the union of the two. The following book, therefore, has been composed upon

this principle; first, there is a general introductory conversation between the tutor and his pupil upon the subject of Mechanics; then follow the various chapters of the book in order, and to each chapter (except the last, which contains problems only) is appended a conversation longer or shorter, as the case may be, containing explanations of difficulties, collateral matter, and the like, such as I deemed it inconvenient to introduce into the body of the chapter; and then follows an examination paper. It is intended that each chapter should be complete in itself, the appended conversation being merely supplementary and explanatory. And I may mention that I regard the conversations as a depôt for illustrative matter, and that I shall feel thankful for any hints which may tend in future editions to render this part of the work more useful.

There is another feature in which this treatise differs from any which have preceded it. I have divided the subject into experimental and demonstrative Mechanics; while I have felt the extreme importance of putting Mechanics upon its true basis as a demonstrative science, I have, nevertheless, considered that it may be treated experimentally, and that an experimental introduction is probably (for young minds) the simplest and the best. I have endeavoured, therefore, by means of two chapters depending upon experiment, to familiarize the student with the general notions of the subject before proceeding to its more abstract treatment.

These are the only points in the plan of the Work which I think it necessary to notice; the utility of the plan, and the manner of its execution, I must leave to the judgment and experience of those teachers and students by whom the book may be used: I will only add, that, as


I cannot expect to earn fame in such a humble walk of mathematics, I hope I shall have the credit of an honest endeavour to supply a want which I know to be very generally felt; and further, I shall feel obliged if those who use my book, and approve it on the whole, will favour me with any suggestions which may occur to them for the improvement of its details.

The treatise on Dynamics is not yet prepared; I am anxious, before it shall be published, to see what view is taken of the plan which I have adopted for the Statics.

I may also take this opportunity of mentioning, that as in the treatise on Dynamics I shall have frequent occasion to refer to the properties of the Conic Sections, I have thought it desirable to prepare a treatise on that subject, adapted as much as possible to the use of Schools. This treatise may be expected shortly.



November, 1851.

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