Memoirs Presented to the Cambridge Philosophical Society on the Occasion of the Jubilee of Sir George Gabriel Stokes, Bart., Hon. LL. D., Hon. SC. D., Lucasian Professor

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The University Press, 1900 - 447 من الصفحات

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الصفحة 296 - A circular spindle is a solid generated by the revolution of a segment of a circle about its chord, which remains fixed.
الصفحة 218 - I found the proposition that by a centrifugal force reciprocally as the square of the distance a planet must revolve in an ellipsis about the centre of the force placed in the lower umbilicus of the ellipsis and with a radius drawn to that centre describe areas proportional to the times.
الصفحة 47 - V and V possess regular integrals, which vanish with t and involve an arbitrary constant that does not appear in the differential equations. The inferences stated earlier are therefore established. It appears from the investigation that two conditions must be satisfied...
الصفحة 349 - For every free period of vibration (with a wave-length sufficiently large in comparison with the diameter of a molecule), there is a corresponding period (almost exactly, but not quite, coincident with it) of maximum dissipation for the incident waves.
الصفحة 57 - When the real part of X is positive, these integrals vanish with t ; and there is a double infinitude of them. When the real part of X is negative, then it is necessary that A and B both vanish : that is, the integrals do not exist if they are to vanish with t. When B is zero, then the integrals become of the form where p 2 is an arbitrary finite quantity and p 1 is zero, when £=0.
الصفحة 68 - ... are to vanish with t. It has been proved that there are no regular integrals of the equation vanishing with t unless a is zero: and that, if a = 0, there exists a simple infinitude of regular integrals satisfying the equations. We proceed, not in the first place to the complete theorem but only to a partial theorem, by shewing that when a is not zero, there exists a simple infinitude of non-regular integrals vanishing with t, these integrals being regular functions of t and tlogt: and when a...
الصفحة 323 - Accordingly it may be possible to make use of 50 elements and the plane may be inclined at an angle of 20° to 30°. It would be necessary in this case however to use a rather large objective. Possibly this may be avoided by cutting the surface A to a, spherical curvature, thus forming a sort of concave echelon.
الصفحة 292 - ... the angle 2-y at the summit of the cone, which is now directed outwards, being very small, n will be given...
الصفحة 37 - Konigsberger's treatise, already cited, is devoted to the corresponding discussion for n equations ; some difficulties as regards adequacy of proof of the theorems, independently of the general statement, prevent me from thinking the investigation entirely satisfactory, that is, if I understand it correctly*. Some papers by Hornf may be consulted : further references will be found in them. My intention in this paper is to take account of the different general cases that can arise owing to the various...
الصفحة 46 - ... to be regarded as determining a, and then for each value of a so determined, there is a single infinitude of regular solutions vanishing with t. These results are stated on the assumption that the power-series, as obtained with the coefficients p and q, converge : the assumption can be justified as follows. Let qj' + . . . + q^t*-1, the coefficients p and q being known; then if functions u

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