Proceedings of the Cambridge Philosophical Society: Mathematical and physical sciences, Volumes 1-2

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Cambridge Philosophical Society., 1863 - Mathematics

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Page 5 - He cannot see the force in either case ; he supplies it out of his own Ideas. And thus, a true Theory is a Fact; a Fact is a familiar Theory. That which is a Fact under one aspect, is a Theory under another. The most recondite Theories when firmly established are Facts : the simplest Facts involve something of the nature of Theory.
Page 26 - ... its dissipation is not instantaneous. The tail leans towards that portion of space last quitted by the comet, a general fact of observation being thus accounted for. " 6. In the struggle for mastery of the two classes of rays a temporary advantage, owing to variations of density or some other cause, may be gained by the actinic rays even in parts of the cometary atmosphere which are unscreened by the nucleus. Occasional lateral streamers, and the apparent emission of feeble tails towards the...
Page 57 - being determined by allowing a given number for the interval between the freezing- and the boiling-points. Now it is found by Regnault that various thermometers, constructed with air under different pressures, or with different gases, give indications which coincide so closely, that, unless when certain gases, such as sulphurous acid, which approach the physical condition of vapours at saturation, are made use of, the variations are inappreciable!. This remarkable circumstance enhances very much...
Page 221 - ... practice which is incompatible with the avowed objects of the present work, may yet find their account in its perusal, — for this reason, that it is always of advantage to present any given body of knowledge to the mind in as great a variety of different lights as possible.
Page 73 - Hast thou seen this, O son of man? Is it a light thing to the house of Judah that they commit the abominations which they commit here? For they have filled the land with violence and have returned to provoke me to anger; and lo, they put the branch to their nose.
Page 26 - ... motions in which they have not hitherto been compared, so far as I am aware. When a box of the form of a rectangular parallelepiped, filled with fluid and closed on all sides, is made to perform small oscillations, it appears that the motion of the box will be the same as if the fluid were replaced by a solid having the same mass, centre of gravity, and principal axes as the solidified fluid, but different principal moments of inertia. These moments are given by infinite series, which converge...
Page 141 - The total electromotive force acting round a circuit at any instant is measured by the rate of decrease of the number of lines of magnetic force which pass through it.
Page 210 - Society, nominated by the Council of the Society for each occasion. 6. That, in the event of any difficulty arising in carrying out the above provisions in any particular instance, either from lack of a prize-subject of sufficient merit, or from any other cause, the Council of the Cambridge Philosophical Society be at liberty to carry over the amount of the Prize for that term towards augmenting the fund for future prizes, or to award it to some one not a member of the University. Award of the Hopkins...
Page 272 - For the equilibrium of any isolated system it is necessary and sufficient that in all possible variations of the state of the system which do not alter its entropy, the variation of its energy shall either vanish or be positive.
Page 88 - ... graduated to degrees, turns round within the annulus, and the angle through which it is turned is read by verniers engraved on the face of the annulus. The brass circle is pierced at its centre, and carries on the side turned towards the incident light a plate of selenite, of such a thickness as to produce a difference of retardation in the oppositely polarized pencils, amounting to about a quarter of an undulation for rays of mean refrangibility.

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