ON THE ENERGY OF STORMS MARGULES 581 



then analogous to equation (I) see §25, or (I*) see §31, we have 



1 1 I 



P01 



Po 



(B) Following the initial condition assumed in the third analysis 

 we now assume that a parallelopipedon having the height h, length 

 / and breadth unity, is filled with liquid whose density is a func- 

 tion of the length x only. We also assume that the density dimin- 

 ishes continuously from x = c up to x = I. 

 We thus have for the initial stage 



C l C h gh 2 C l 



*« = h dX Jo gZtidz= 2 Jo'" (/v 



In the final stage the liquid that was initially in a vertical column at 

 x above the elementary strip dx with density /« becomes a horizontal 

 layer at the altitude £ with the thickness dr. 



Since hdx = ld£ and hx = lr therefore for the final stage we 

 have 



rh gh 2 ri 



If now we put 



there results 



M = lhfi (1 -i a) 



Pa = g^lfi (l~ \ ) P 6 =gh'lv o (± - | 



M V 2 



-dp =P a - P e = gh 2 I /x Q — 



and when a is a small fraction then, and in agreement with (II) 

 (§27) we have 



(C) Let us now arrange the liquid in the trough in parallel inclined 

 layers of equal density and assume for the initial stage 



/ x z \ 



V- = M 1 - a x -j - a z -r) = /t (1 - <p). 



