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 ProfessorThe University Press, 1900 - 447 من الصفحات |
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الصفحة 13
... respectively . The principal X theorem , that has been obtained loc . cit . , is to the effect that con- structing any X rectangle Χ . X2 X3 X. ... Xi X2 X , X X , X3 X1 X1 X6 ... ... X1 + 1 X1 + 2 X. Xo X6 X , ... X1 + 3 Im Xm + 1 X m ...
... respectively . The principal X theorem , that has been obtained loc . cit . , is to the effect that con- structing any X rectangle Χ . X2 X3 X. ... Xi X2 X , X X , X3 X1 X1 X6 ... ... X1 + 1 X1 + 2 X. Xo X6 X , ... X1 + 3 Im Xm + 1 X m ...
الصفحة 16
... respectively we write down the Ω function 1 Ω 1 - acN1 . 1 - N2 - 1 N3 bc as the expression of the sum ΣN ,, N12 N ̧ . It must be observed that the operating symbol , has reference to each of the three > auxiliaries a , b , c . These ...
... respectively we write down the Ω function 1 Ω 1 - acN1 . 1 - N2 - 1 N3 bc as the expression of the sum ΣN ,, N12 N ̧ . It must be observed that the operating symbol , has reference to each of the three > auxiliaries a , b , c . These ...
الصفحة 18
... respectively . - - - 2 — N ̧2Ñ3Ñ ̧ ‚ — N ̧2Ñ3Ñ ̧ ‚ — Ñ‚2ÑƒÑ ̧2 ‚ + Ñ ̧3Ñ¿Ñ‚3 ‚ + Ñ ̧3Ñ3N2 39 3 , 39 The generating function takes also the suggestive form : - + 1- N , N3N1 - 1- N1.1 - N1N1⁄2 . 1 — Ñ‚Ñ1⁄2Ñ ̧ . 1 — Ñ‚Ñ3Ñ ̧ - N1N2N3 - 3 1 ...
... respectively . - - - 2 — N ̧2Ñ3Ñ ̧ ‚ — N ̧2Ñ3Ñ ̧ ‚ — Ñ‚2ÑƒÑ ̧2 ‚ + Ñ ̧3Ñ¿Ñ‚3 ‚ + Ñ ̧3Ñ3N2 39 3 , 39 The generating function takes also the suggestive form : - + 1- N , N3N1 - 1- N1.1 - N1N1⁄2 . 1 — Ñ‚Ñ1⁄2Ñ ̧ . 1 — Ñ‚Ñ3Ñ ̧ - N1N2N3 - 3 1 ...
الصفحة 35
... respectively when xa ; these solutions are the only regular functions satisfying the assigned conditions ; and it may be ( but it is not necessarily ) the case that they are the only solutions of the equation ( whether regular or non ...
... respectively when xa ; these solutions are the only regular functions satisfying the assigned conditions ; and it may be ( but it is not necessarily ) the case that they are the only solutions of the equation ( whether regular or non ...
الصفحة 37
... respectively . The only way in which can be a factor of x is by having B = 0 , and then z is not a factor of y ; and similarly as regards and 211 . + Crelle , t . cxvi ( 1896 ) , pp . 265-306 , ib . , t . cxvII ( 1897 ) , pp . 104-128 ...
... respectively . The only way in which can be a factor of x is by having B = 0 , and then z is not a factor of y ; and similarly as regards and 211 . + Crelle , t . cxvi ( 1896 ) , pp . 265-306 , ib . , t . cxvII ( 1897 ) , pp . 104-128 ...
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a₁ absorption acid aether amplitude axis B₁ bands centim chaîne chloride circle coefficients coil condenser conic constant contact transformations convergence coordinates corresponding cosh critical quadratic curve deflexion denote determined deux didymium diffuse dilution disc effect electric electrons equal équations erbium expression finite formula given Hence integer integrals vanishing Kimn linéaires lines lumière magnetic field minimal surface molecule monômes N₁ nitrate non-regular obtained opérateurs P₁ parallel period peut plane plate polynôme régulier positive integer produits quantity quartic surfaces refrangible regular functions regular integrals rotation S₁ satisfied self-induction shews spark spectra spectrum subgroup substitution suppose surface t₁ t₂ tacnode tangent theorem theory thick u₁ U₂ v₁ variables velocity vibrations waves wire x₁ XVIII Zeeman effect zero α₁
مقاطع مشهورة
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