330 APPENDIX. 



. ^f 



dw 



And by the properties of the ellipse 



cos Sp H i 

 2 



. f[E. 



which agrees with the result in the text. 



Note to p. 246. 



To prove that the equilibrium of the medium will be un 



A 4 

 stable, unless -^ > -. We have 



fff 



pdxdydefy. 



And (f>j as shewn by Green, = </> + < 2 . 



Now, in order that equilibrium may be stable, it is necessary 

 that < be a maximum value of $, or that be a maximum 

 value of $ a . In other words, that fa should never be positive. 

 But 



du dv dw\* dv dw dw du du dv 



dy 



Now 



dv dw dw du du dv 



4-7--j- + 4-y- -7-+4^ =- 



ay dz dz dx dx dy 



dv dw\* 

 dy 



