RESIDUO-CAPILLARY ATTRACTION. 215 



13. For this purpose let 



^-=... and ^=..; 



therefore by No. (10). 



making these substitutions in the equations of No. 11., we have 



K = s,{H) + il-s,){K). 



L =s,.{l-s,){L) + s,.{l-s,){L) + s,s,{M) + {l-s,){l-s,){N'). 



M= 2s, (1 -*0 {L) + s,' {M) + (1 -*,)' (^)- 



N = 2s, (1 - s,) {L) + si (M) + (1 - s,y (N). 



Hence 2H-2K-M+ N=A (H) + BiK) + C {L) + D{M) + E{N-), 



where A = 2. {s, — S2). 



B = 2.{l-s,)-2.{l-s,) 



= -2{si-s,). 

 C=-2s,.{l-s,) + 2s, (1 - s,) 



= -2{s,-s,) + 2{8{'-si). 

 D=-{s,'~si). 

 E=-{l-s,Y + {l-s,Y 



= 2{s,-s,)-{s,'-'Si). 



EE2 



