Problems of Cosmogony And Stellar Dynamics

Cover Problems of Cosmogony And Stellar Dynamics
Problems of Cosmogony And Stellar Dynamics
James Hopwood Jeans
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In the latter case the second term on the right of equation (209) becomes very small, through the gravitational effects of successive elevations and depressions neutralising one another. No corresponding effect occurs in the first term on the right of equation (209), of which the value is represented by expression (211). Hence it is seen that the ellipsoid can only become unstable through a many-furrowed distortion when it is itself very long. It is easily seen that the more furrows there are i...n the distortion the longer the ellipsoid has to j. C. 6 82 Pear-shaped Configurations of Equilibrium [OH. V be before instability can set in through this distortion. It follows that the ellipsoid will first become unstable through a distortion in which the number of furrows is the fewest possible, namely one, and this is the third zonal har- monic distortion. -- 83. The value of P at the first point of bifurcation on every ellipsoidal series must accordingly be of the form and the corresponding value of P is *2 \ .

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