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science cannot be filled up with a sufficient portion of illustration and remark, without danger of forming a work too bulky and too difficult of reference for the time-pressed Senate-House student, could not the two parts be with advantage separated? the first might then appear under the rigid form of a Syllabus, and the second could be sought in books, whose style should, more nearly than it does at present, approach that in which our continental neighbours are accustomed to write upon Physics.

It is often urged that it is better to leave each student to construct his own syllabus than to present him with a printed abstract, the very conciseness of which must be repulsive to him: such may be the theory, but if so, it would seem not to work well in practice; for with rare exceptions the syllabus which an Undergraduate uses, is the production of either his public or his private Tutor. But it is rather with the view of improving the style of our mathematical writing than on account of the specific utility of a published syllabus, that I conceive the system advocated should be more widely extended than it hitherto has been.

So strongly did these opinions influence me, that in the early part of this year I offered a Syllabus of Statics for publication. My aim was to present a complete scheme of the subject to the student, wherein the most important propositions, and those which have met with some little neglect at the hands of our University writers, should be illustrated both verbally and graphically; in some instances the definitions would have been given in a new form of words, and the sequence of propositions slightly altered. But it was intended that the marked characteristic of the work should be the copiousness of examples, solved for the most part geometrically, and accompanied by explanations of the circumstances of each case and of the principles involved in it.

A few words may here be allowed me in justice to myself to explain why, with my views remaining unchanged, I ultimately gave my work a character so inconsistent with them. Upon submitting the MS. to the consideration of some friends, who were obliging enough to undertake its revisal, and certainly qualified in no ordinary degree for the task, they were pleased to express approbation of its arrangement, but urged me to change in some measure its design; they wished me to turn it into a complete treatise upon Elementary Statics and Dynamics, considering that its simple geometrical character rendered it peculiarly adapted to the wants of Schools and the junior students of the University. I was perhaps too ready to adopt their suggestions, without measuring sufficiently my own power to carry them into effect: at any rate the patchwork that was necessary in order to complete the work of transformation is the cause of, and at the same time affords the only excuse I can offer for, the unevenness of construction which obtains throughout the book.

I am well aware of how greatly I stand in need of forbearance at the hands of those who may think it worth their while to pass judgment upon the following treatise; but while I trust that the preceding explanation is sufficient to remove all misconstruction regarding the nature of its pretensions, I hope that its many deficiencies will not render it altogether inefficient and devoid of utility.

Clare Hall, Nov. 1850.

J. B. P.

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ON COUPLES AND SOME PROPOSITIONS RELATING TO FORCES NOT IN

ONE PLANE

Couples, 65, 66; equal of Couples, 67; resultant of any number of
Couples, 68; proportionality of Couples to their moments, 69;
resultant of three forces acting at a point in space, 70; Equili-
brium of a body in contact with a smooth plane, 71, 72

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