SURFACES OF DISCONTINUITY 603 



p' - p" = a(ci + C2) + ^r cos 6. [613] 



Also 



gT (ai Soji + 02 5co2) = t 5coi + ~ 5w2. 



ocoi aw2 



This means that for any arbitrary displacement of a point in 

 the surface in a direction tangential to the surface the variation 

 8a in o- is equal to ^r multiplied by the vertical component of 

 this displacement; for a reference to the expression for 8z^ 

 above reveals that this is the meaning of ai5wi + a28u2. Hence 

 we have 



'i = sr. [6141 



To summarize the matter we see that the potential of any 

 component does not remain constant throughout a given phase; 

 it decreases with altitude. What remains constant throughout 

 the phase is /i + gz, and the constant value of this for a given 

 component is the same in each homogeneous phase and on the 

 surface of discontinuity. The pressures p' and p" and the 

 surface tension a are functions of t and the constants Mi, M2, and 

 are therefore functions of z, and their rates of change with 

 respect to z are given in [612] and [614]. They are independent 

 of X and y. We have omitted the last result 



faSTDl = 0. 



This has been written so far in too simple a form, in order to 

 avoid causing trouble at the moment by an awkward digres- 

 sion. We have been considering, it will be recalled, two homo- 

 geneous phases and one surface of discontinuity. This would of 

 course be realized if one phase were surrounded entirely by the 

 other, but as in that case the dividing surface would have no 

 perimeter at all the condition written would be meaningless. 

 However, we are not necessarily confined to this case, but if we 

 treat two phases in a fixed enclosure, then we must include the 

 wall of the enclosure as a "surface of discontinuity" as well as the 

 dividing film between the two phases. It is true that we assume 



