212 M. A. Bitter's Contributions to the Study 



parallel edges lying infinitely near each other*. The two 

 parallel edges may be considered as separated by a crevasse 

 that reaches a maximum depth at K, gradually shallowing to 

 zero towards J and. L — the term depth not being taken in its 

 actual sense ; but figuratively [since there is no real variation 

 ofT]. 



§ 7. Adiabatic passage over the principal edge. 



When a mixture of water and steam expands adiabatically, 

 the temperature and pressure continuously diminish till the 

 temperature falls to i = Q o, G0744. At this instant the water 

 begins to freeze, and the heat that is thus set free prevents 

 any further fall of temperature while any part of the mass 

 remains liquid. The adiabatic will thus form an angular point 

 at M where it reaches the principal edge, and its next piece 

 will be a straight horizontal length coinciding with the prin- 

 cipal edge (fig. 13). After the mixture of water and steam 

 has been changed into a mixture of ice and steam, the tempe- 

 rature and pressure begin anew to fall. The extremity K of 

 the horizontal length M N is therefore a second angular point 

 on the adiabatic. 



The motion of the point along the horizontal length M N 

 represents a change of state during which part of the water 

 freezes while another part vaporizes. The heat set free during 

 the freezing of the first part goes to vaporize the second. If 

 x x denotes the mass of steam in the condition M, and x 2 de- 

 notes the mass of steam at the end of the change M N, then 

 1 — x 2 is the mass of water frozen and x 2 — %\ the mass of water 

 vaporized. The vaporization of the latter requires the heat 



Q=H>2-^i); (i) 



and the heat set free during the freezing of the first part has 

 the same value, 



Q=/(l-* 2 ). ....... (2) 



On equating these two values and solving the resulting 

 equation for x 2 , we obtain 



**t+t (3) 



The change of x 2 — #i kilograms of water into steam increases 

 the volume by 



*>s— V!-u(x 2 — ^); ..... (4) 



and the work thus done by the steam-pressure is 



»fej**(a*~*i) (5) 



* C. Neumann, Vorks'angen ilber die mcchantsche Wiirmetheoric, p. 159. 



