Coherent Identifier About this item: 20.500.12592/s89rk7

Bulletin of the Calcutta Mathematical Society 1913-14

1915

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Summary

When the bowed point divides the string in a rational ratio the form of the velocity—diagram may be derived from that of the correponding irrational type by the following process : Taking the form of the velocity—diagram at any specified epoch in the irrational case we have to analyse it into its Fourier components and then effect a summation of the series of components which have a node at t [...] the origin of co-ordinates being now the centre of the sphere B. We proceed now to determine the arbitrary solid harmonics w„ and w'„ so as to satisfy the boundary conditions on the surface of the sphere B. The boundary conditions can be expressed as follows:— (I) Since the sphere B is a perfect conductor the electric force and therefore the electric polarization are at right angles to its surf [...] are all of the same type we at once deduce the following property:— The induced current on the surface of the sphere B is of the same type as the inducing current on the surface of the :pltere A. For instance (1) The inducing current on the surface of the sphere A flows meridionally having the line joining the centres as axis and so does the induced current on the surface of the sphere B. (2) The [...] If the distribution of electricity on the surface of the sphere A instead of being symmetrical about the line joining the centres is symetrical about any other line we could effect the solution with the help of the theorems given in § 2 by transforming the zonal harmonic to harmonies referred to the line joining the centres. [...] To determine the transverse components of the vector given by the solutions of the second type we subtract from each of the components of this vector the corresponding resolved part of the radial compnent of the vector i.e.

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technology medicine science

Pages
64
SARF Document ID
sarf.120023

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