Proceedings of the Royal Society of Edinburgh, Volume 23

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Royal Society of Edinburgh., 1902
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Page 169 - The rules used by vector-analysts are : — 1-2= +1 /*=+! /,:2=+l ij= k jk= i ki= j ji=* -k kj= -i ik= -j, and they suppose an order from left to right.
Page 478 - Crown 8vo. gr. 6d. GRAVITATION: an Elementary Explanation of the Principal Perturbations in the Solar System.
Page 218 - electro-magnetic theory of light " does not cut away this foundation from the old undulatory theory of light. It adds to that primary theory an enormous province of transcendent interest and importance ; it demands of us not merely an explanation of all the phenomena of light and radiant heat by transverse vibrations of an elastic solid called ether, but also the inclusion of electric currents, of the permanent magnetism of steel and lodestone, of magnetic force, and of electrostatic force, in a...
Page 500 - After enjoying eighteen years' joint work with Tait on our book, twenty-three years without this tie have given me undiminished pleasure in all my intercourse with him. I cannot say that our meetings were never unruffled. We had keen differences (much more frequent agreements) on every conceivable subject, — quaternions, energy, the daily news, politics, quicquid agunt homines, etc., etc. We never agreed to differ, always fought it out. But it was almost as great a pleasure to fight with Tait as...
Page 182 - NX28.e = (2, where (0,0)= -(1,0) and generally (o,/3) + (/8,a) = 0. This form of his own he frankly characterises as "elegant and completely symmetrical"; but the same description would apply equally appropriately to the solution which he gives. Unfortunately, the method by which the latter was obtained is not indicated, and we can only hazard a guess in regard to it. The balance of probability would seem to be in favour of the method of devising a set of multipliers which, when applied to the given...
Page 498 - I substituted for the brass tube, was cracked, and an iron disc, tightly screwed into the bottom of it to close it, was blown in. I have since used a portion of a thicker gun-barrel, and have had the end welded in. But I feel sure that an impulsive pressure of ten or twelve tons weight would seriously damage even this. These remarks seem to be of interest on several grounds ; for they not only explain the crushing of the open copper cases of those of the 'Challenger...
Page 476 - Lectures on Phrenology; with Notes, an Essay on the Phrenological Mode of Investigation, and an Historical Sketch, by A.
Page 218 - REPULSION*. § 1. THE title of the present communication describes a pure problem of abstract mathematical dynamics, without indication of any idea of a physical application. For a merely mathematical journal it might be suitable, because the dynamical subject is certainly interesting both in itself and in its relation to waves and vibrations. My reason for occupying myself with it, and for offering it to the Royal Society of Edinburgh, is that it suggests a conceivable explanation of the greatest...
Page 480 - SYSTEM OF ANALYTIC MECHANICS. Physical and Celestial Mechanics. By BENJAMIN PEIRCE, Perkins Professor of Astronomy and Mathematics in Harvard University, and Consulting Astronomer of the American Ephemeris and Nautical Almanac. Developed in four systems of Analytic Mechanics, Celestial Mechanics, Potential Physics, and Analytic Morphology.
Page 224 - By drawing on paper (four times the scale of the annexed diagram), showing engraved squares of -5 inch and '1 inch, and counting the smallest squares and parts of squares in the two areas, I have verified that they are equal within less than 1 per cent, of either sum, which is as close as can be expected from the numerical approximations shown in the tables, and from the accuracy attained in the drawing.

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