260 



SMITHSONIAN MISCELLANEOUS COLLECTIONS 



VOL. 51 



In fig. 32 again 



eventually come to a complete equilibrium, still I hold it to be advan- 

 tageous to supplement the investigation in this direction also. 



We thus obtain a correct idea as to how large the error would be 

 if the assumption as to the sudden freezing of the whole mass and the 

 subsequent gradual evaporation should prove not to be appro- 

 priate. 



I have therefore in the example to be communicated later deter- 

 mined the value /? 3 of the final pressure as it would result from the 

 assumption that the necessary evaporation goes on directly hand in 

 hand with the sudden freezing. 



In this determination we again advantageously make use of the 

 graphic method. 



as before in fig. 30 let F t T t = y v and 

 F t ' T x = y t ': then we find T 2 by draw- 

 ing tli rough F t a straight line that makes 

 the angle /? = arc tg 0.47 = 25 11' with 

 the axis of ordinates and find the point 

 of intersection F 2 of this line with a hori- 

 zontal line tli rough F x . Then T 2 is the 

 end of the abscissa representing t 2 and 

 consequently 7\ T 2 = /. 



We now draw through F 2 a straight 

 line making an angle 10 «*„ = arc tg \ 

 with the horizontal axis of abscissas 

 (owing to want of room, this angle is 

 only marked with a in fig. 32). 

 The abscissa of the intersection F 3 of 

 this line with the curve F'F' of the quantity of vapor needed for 

 saturation corresponds to the temperature t 3 while the ordinate it- 

 self F 3 T 3 is equal to y 3 . 



In the preceding it is assumed that t 2 < o and that the whole 

 process goes on so rapidly that the volume can be regarded as con- 

 stant. 



If the graphic construction or the numerical computation should 

 give a value t 2 > o, then this argument loses its significance. 



But in this case the temperature t 2 simply rises to o° C. Hence 

 only a part of the subcooled water is converted into ice, while another 

 part remains fluid and a third part becomes vapor. 



Since it is not now of importance to determine the magnitudes of 

 these three parts we may abstain from their evaluation, as well as 

 from the investigation of the special cases where the subsequent 



FIG. 32 



See p. 252 of this translation. 



