The Journal of the Indian Mathematical Society

C. Racine ¹

Affiliations
1 Loyola College, Madras, IN

Abstract

A necessary and sufficient condition for a Frullani integral to exist has been given by K. S. K. Iyengar.

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C. Racine ¹

Affiliations
1 Madras, IN

Abstract

It is well known that the relativistic problem of n bodies cannot be stated in a precise manner without assuming a certain number of more or less arbitrary hypotheses in order to obtain the abstraction of material points. Two attempts have been made recently to arrive at the schematic case of n points. The first one is due to Prof. T. Levi Civita and is based upon the method of approximations used in 1916 by Droste and de Sitter but with rather too much haste as is shown by Levi Civita. The second one is due to Prof. A. Einstein and is based upon a new method of successive approximations. It leads to results different from those arrived at by Levi Civita, in particular with regard to the secular acceleration of the centre of masses.

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C. Racine ¹

Affiliations
1 Madras, IN

Abstract

In the previous paper, I have established two "fundamental" formulae, the second of which will now be applied to the relativistic problem of n bodies. Using the same notations as in that paper, but taking units of length and time so that the velocity of light in vacuum is equal to I.

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C. Racine ¹

Affiliations
1 St. Joseph's College, Trichinopoly, IN

Abstract

The ten gravitational equations of Einstein's Relativity theory are reducible to a system of only seven equations of a more tractable type when the metric can be written in the form

(1.1)               ds²=V²(x¹, x², x³) dt²-Σgij(x¹, x², x³) dxⁱdx^j.

This case has been studied and called the static case by Prof. Levi-Civita. The space-time then admits a group of isometry defined by the transformation t' = t + constant.

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