1871.] Abrupt Change at Boiling or Condensing fyc. 5 



presented before the explosive or bumping change to gas occurs, is very 

 variable under different circumstances, being much affected by the presence 

 of other fluids, even in small quantities, as impurities in the fluid experi- 

 mented on, and by the nature of the surface of the containing vessel, &c. 



The consideration of the subject may be facilitated, and aid towards the 

 attainment of clear views of the mutual relations of temperature, pressure, 

 and volume in a given mass of a fluid may be gained, by actually making, or 

 by conceiving there to be made, for carbonic acid, from the data supplied 

 in Dr. Andrews's experimental results, a solid model consisting of a curved 

 surface referred to three axes of rectangular coordinates, and formed so 

 that the three coordinates of each point in the curved surface shall repre- 

 sent, for any given mass of carbonic acid, a temperature, a pressure, and a 

 volume which can coexist in that mass. It is to be noticed here that in his 

 diagram of curves the results for each of the several temperatures experi- 

 mented on are combined in the form of a plane curved line referred to two 

 axes of rectangular coordinates, one of each pair of ordinates representing 

 a pressure, and the other representing the volume corresponding to that 

 pressure at the temperature to which the curve belongs. Now to form a 

 model such as I am here recommending, and have myself made, Dr. An- 

 drews's curved lines are to be placed with their planes parallel to one an- 

 other, and separated by intervals proportional to the differences of the tem- 

 peratures to which the curves severally belong, and with the origins of co- 

 ordinates of the curves situated in a straight line perpendicular to their 

 planes, and with the axes of coordinates of all of them parallel in pairs to 

 one another, and then the curved surface is to be formed so as to pass 

 through those curved lines smoothly or evenly*. The curved surface so ob- 

 tained exhibits in a very obvious way the remarkable phenomena of the vo- 

 luminal conditions at and near the critical point of temperature and pressure, 

 in comparison with the voluminal conditions throughout other parts of 

 the range of gradually varying temperatures and pressures to which it ex- 

 tends, and even throughout a far wider range into which it can in imagi- 

 nation be conceived to be extended. It helps to afford a clear view of the 

 nature and meaning of the continuity of the liquid and gaseous states of 

 matter. It does so by its own obvious continuity throughout its expanse 

 round the end of the range of points of pressure and temperature where 

 an abrupt change of volume can occur by boiling or condensing. On the 

 curved surface in the model Dr. Andrews's curves for the temperatures 13 0, 1, 

 21°-5, 31°1, 32°-5, 35°-5, and 48°-l Centigrade, which afford the data for 

 its construction, may with advantage be all shown drawn in their proper 



* For the practical execution of this, it is well to commence with a rectangular block 

 of wood, and then carefully to pare it down, applying, from time to time, the various 

 curves as templets to it, and proceeding according to the general methods followed in 

 a shipbuilder's modelling-room in cutting out small models of ships according to 

 curves laid down on paper as cross sections of the required model at various places 

 in its length. 



