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PREFACE TO THE THIRD EDITION.

THIS edition of the Treatise on Statics differs so little from the last as scarcely to require a separate notice. A few Articles have been added, on the pressure which a rigid body is made to exert on a fixed point or axis of support by the action of forces when there is equilibrium. These will be found useful in those Problems of Dynamics wherein it is required to find the pressure which a rigid body in motion, under the influence of any forces, exerts on a fixed point or axis. Indeed, it is chiefly with a view to this application of them that the articles alluded to have been introduced into this edition of the Statics.

The collection of Problems for practice given at the end of the Treatise has been considerably enlarged, chiefly by the addition of Examples of an elementary character. In the selection of them care has been taken to choose such as illustrate Statical Principles under every important variation of aspect, without impeding the student's progress through them by analytical and other difficulties foreign to the proper object of this Treatise.

PREFACE TO THE SECOND EDITION.

Though the general plan and arrangement of this edition of the Treatise on Statics are the same as in the former, in the details there will be found, it is hoped; some important improvements.

The fundamental proposition of the science,—the Parallelogram of Forces,—I have proved after Duchayla's method, by reason of its simplicity ; but I think it necessary here to inform the reader that, as that method is inapplicable when the forces 'act upon a single particle of matter (as a particle of a fluid medium on the hypothesis of finite intervals), on account of its assuming the transmissibility of the forces to other points than that on which they act, I have, in an Appendix, given the proof which in the first edition was given in the text. The same objection, (and for the same reason) lies against the proof of the parallelogram of forces from the properties of the lever. This method, though allowable in the infancy of the science, can never be exclusively adopted in a treatise which professes to take a more philosophical view of the subject; for, were the transmissibility of force not true in fact, the law of the composition of forces acting on a point would still be true; it is evident, therefore, that to make the truth of the former an essential step in the proof of the latter, is erroneous in principle.

acting in

In the former edition, forces were considered as

any directions in space; a mode of treatment
of the subject which necessarily rendered the inves-
tigations useless to such readers as had not studied
Geometry of Three Dimensions. In the present edi-
tion this defect is remedied; and a chapter, in which
the forces are supposed to act in a plane, is always
made to precede the more general investigations. At
the end of Chapter IV. several propositions are proved
which have hitherto been used in Elementary Books
without proof.

The fifth Chapter contains a new (and it is hoped
a satisfactory) and complete proof of the Principle of
Virtual Velocities, and its Converse. The proof given
by Lagrange in his Mécanique Analytique, page 22,
et seq., though highly ingenious, I regard as a fallacy;
and, if not fallacious, deficient in generality.

In the last Chapter, I have endeavoured to set
before the reader such problems as, without involving
analytical difficulties, seemed best calculated to make
him acquainted with the mode of applying all the
most important principles of the science : and not un-
frequently I have added remarks upon important steps
with the view of pressing them more particularly upon
the reader's attention.

St John's COLLEGE, CAMBRIDGE,

March 12, 1842.