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VII. The Stability of the Pear-Shaped Figure of Equilibrium of a Rotating 
Mass of Liquid. 
By G. H. Daewtn, F.R.S., Plumian Professor and Fellow of Trinity College, 
in the University of Cambridge. 
Eeceived June 19,—Eead June 19, 1902. 
Table of Contents. 
Introduction 
Pai^’o 
2 . 5^2 
Part I.—Analytical Investigation. 
§ 1. Method of procedure.253 
§ 2. The lost energy of the system.254 
§ 3. Expression for the element of volume.256 
§ 4. Determination of h ; definition of symbols for integrals.260 
§ 5. The energies \ JJ and Jll .262 
§ 6. Surface density of concentration C'; energy Cli .264 
§ 7. The energy \CC result for ^.7/ - JR + CR - |C'C'.267 
§ 8. The term - 268 
§ 9. Double layers.268 
§ 10. Determination of e and A.274 
§11. The energy |7rp2 JfS _ Xe) r/fr.275 
' 7 
§12. The energy If) R . 
§ 13. Terms in the energy depending on the moment of inertia.279 
§ 14. The lost energy of the system; solution of the problem.282 
Part II.—Numerical Calculation. 
§ 15. Determination of certain integrals.284 
§ 16. The integrals a-^, o-^, 290 
§17. The integrals wi®, 291 
§ 18. The integrals 294 
§19. Synthesis of numerical results; stability of the pear.296 
§ 20. Second approximation to the form of the pear.301 
Part III. 
Summary.306 
(327.) 
2 K 2 
9.1.03 
