Abstract
THE author has already written an excellent book on geometrical statics, and it has been his present object to produce an elementary treatise which shall cover the well-trodden ground of the parallelogram of forces, moments and couples, centres of gravity, work, machines and friction, and at the same time shall develop the subject simultaneously from its geometrical and analytical aspect. It is sufficient to open the book almost anywhere to find evidence of originality in the treatment. Thus in the introduction the author does not leave his readers ignorant of the existence of non-rigid bodies (p.7). Again, in dealing with the parallelogram of forces, he wisely eschews the fallacious so-called dynamical proof and gives an ingenious modification of Duchayla's proof, together with an experimental verification in which three strings stretched by spring balances, instead of being knotted together, are attached to a triangular string which forms a funicular triangle of the forces. This plan has the advantage of also showing that three forces in equilibrium meet at a point when produced. The proof of the formula for the resultant of two parallel fin s is based on the “funicular” method—a change that will be most refreshing to examiners. Whenever a question is set in any examination, in which candidates are asked to find the resultant or centre of a number of parallel forces in such cases as that of a rod loaded at different points, where the answer comes out in a line by taking moments, pages and pages of work are usually sent up with the old familiar figure and proof for the resultant of two parallel forces: “(1) when the forces are like; (2) when the forces are unlike,” and so on, finishing up with the lame conclusion that the resultant “may be found.” The author's treatment of friction strikes us as a very sensible innovation, the laws of friction being; based on a consideration of the angle of friction, and the coefficient of friction being defined as the tangent of this angle. There are a few points we do not altogether care about; for example, a crowbar problem on p. 119, where “perfect roughness” exists between the stone and the ground and between the crowbar and ground, and “perfect smoothness” between the sharp edge of the stone and the crowbar. In connection with such a problem, too, the author might do well in Chapter v. to say something about the direction of the reaction when an edge of one body rests against, but does not dig into, the surface of another. The book is copiously supplied with examples.
A Treatise on Elementary Statics for the Use of Schools and Colleges.
By W. J. Dobbs Pp. xi + 311. (London: A. and C. Black, 1901.) Price 7s. 6d.
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A Treatise on Elementary Statics for the Use of Schools and Colleges . Nature 65, 125 (1901). https://doi.org/10.1038/065125a0
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DOI: https://doi.org/10.1038/065125a0