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aether amplitude arbitrary constant average axis bands c'est capacity centim chaîne fermée chloride circle CM CM CM r—i CO HO coefficients coil combinaison linéaire condenser condition conic contact transformations contain converge absolutely convergence coordinates corresponding cosh critical quadratic curve d'une deflexion degré denote Desargues determined deux didymium disc effect equal équations erbium être expression facteurs finite formula frequency given H CO CM Hence hyperbola infinitesimal transformation infinitude integer Lemma lines lumière magnetic magnetic declination minute of arc molecule monômes Newton non-regular integrals observed obtained one-parameter group opérateurs operations of order oscillations parabola parallel Periodogram peut plane plate polynôme régulier positive integer quantity rayons regular functions regular integrals vanishing relations root satisfied self-induction shews solution somme spark substitution suppose surface tangent theorem théorème theory values variables vibrations waves wire XVIII zero
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 xii - Talia propter merita non rnodo in insulis nostris doctrinae sedes septem te doctorem honoris causa nominaverunt, sed etiam exterae gentes honoribus eximiis certatim cumulaverunt. Hodie eodem doctoris titulo studiorum tuorum socios nonnullos exteris e gentibus ad nos advectos, et ipsorum et tuum in honorem, velut exempli causa, libenter ornamus. In perpetu.um denique observantiae nostrae et reverentiae testimonium, in honorem alumni diu a nobis dilecti et ab aliis nomismate honorifico non uno donati,...
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 p2 is an arbitrary finite quantity, and pl is zero when t = 0.
الصفحة 42 - ... 0, t = 0. The equations are, in form, the same as before, except that the coefficients of the first power of the dependent variables on the right-hand side have been reduced by unity ; and the relation between the two sets of dependent variables is It is manifest that the equations in...
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 68 - It has been proved that there are no rpgular 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 t log t : and when a is zero, these non-regular...
الصفحة 53 - The equations in 77, and ^ possess regular integrals vanishing with t, and their expression involves A, the arbitrary constant; and therefore the original equations in u and v possess no regular integrals vanishing with t, unless the condition represented by a = 0 be satisfied ; but if that condition be satisfied, they possess a simple infinitude of regular integrals vanishing with t. The conditions represented by a = 0 and...
الصفحة 145 - A piece of brass wire 6'6 centims. long, with a screw thread cut on it, was fixed to this stirrup at right angles to the plane of the mirror, projecting equally on either side of the mirror. Two small brass cylinders could be screwed along this brass wire, and by means of them the moment of inertia and time of swing of the needle could be adjusted as required. The stirrup and mirror weighed 6'6 grms. The galvanometer has a solid...