of States of Aggregation. 213 



This work, which is represented in fig. 13 by the shaded rect- 

 angle, is equivalent to the heat 



g = Apu(x 2 —x 1 ) (6) 



Here p = 62-58, w = 210, Z=80, ^ = 606'5; and on substi- 

 tuting these values in tho above equations we get them in the 

 forms 



# 3 = 0-1165 + 0-8835 #!, .... (7) 



r 2 -^ = 24-5(l-^), ...... (8) 



2= 3-61(1-^) (9) 



If, for instance, tho whole mass were at first liquid, so that 

 t r i = 0, we have in this case 



^ 2 = 0-1165, r 2 -vi = 24-5, ^ = 3-61. 



In the adiabatic change of a kilogram of water into a mixture 

 of ice and steam, therefore, 0*1165 kilogram will vaporize and 

 0-8835 kilogram freeze ; 3'61 calories of the intrinsic energy 

 will be turned into external work; and the increment of volume 

 represented in fig. 13 by the length MN will be 24*5 cubic 

 metres. 



§ 8. Conclusion. 



As a result of the above discussion, there follows the theo- 

 retical possibility of representing the behaviour of water in its 

 three different states of aggregation by a solid geometrical 

 figure, even though considerable difficulties would be encoun- 

 tered in the exact practical execution of such a model by reason 

 of the insufficiency of the experimental results already in 

 hand*. 



The same procedure as this we have followed for water may 

 also be adopted for representing the behaviour of any other 

 body by a model of its temperature-surface. As the ground 

 of such a model we may take a hyperbolic paraboloid, which 

 represents the behaviour of the so-called perfect gases, and 

 pieces may be stuck on it to represent the differing behaviour 

 of other bodies. 



On the model for such bodies as expand in melting (e. g. 

 sulphur, phosphorus, &c.) the frost- edge will appear as a rece- 

 ding edge, and the melting-edge as a prominent one. Instead 

 of the prominent cornice that represents the freezing-region 

 on the water model, we shall find on the models for these 

 bodies a terrace-shaped prominence to represent the same 

 region. 



* A plaster model of the temperature-surface of water, made by the 

 sculptor Blum, of Aachen, is in the museum of the Aachen Polytechnicum. 



