AND THE NEBULAR HYPOTHESIS. p; , 



surface. This law has the merit that the case of an incompressible fluid is covered 

 by the special value c = oo or K = 0, the density now having the value a throughout. 



There is the d priori objection to the kw that its form precludes first harmonic 

 displacements (rf. below, 11). This objection would be fatal were it not that we 

 have seen that first harmonic displacements are in any case of no importance. This 

 being so, the objection falls to the ground, and I have thought it worth working out 

 this-law as far as possible. 



9. Using the relation (12), we have in place of the more general equations (3), (4), 

 and (5), the particular equations 



(13) 



VV = -4*7>, 



On putting 

 this last equation reduces to 



(17) 



No Rotation. 



* 



10. When there is no rotation w = 0, x = p and the equation becomes 



(V'nV) /> = (). 



The general solution is 



P-ZA.r-'tf.+.fcGtr)^.. 



while the particular solution giving a spherical boundary is 



the last being, of course, the well-known solution which occurs in LAPLACE'S theory 

 of the figure of the earth. It will now be shown that this configurat, 



8 a be the free surface corresponding to the simple solution (19). 

 Consider an adjacent solution 



and let the corresponding free surface be 



