Dec. 7, 1 871] 



NATURE 



107 



will be a question suggested at the close of this paper in connec- 

 tion mth some allied considerations. 



It is first to be observed that the ordinaiy liquid state does not 

 necessarily cease abruptly at the line of boiling-points, as it is 

 well known that liquids may with due precautions be heated 

 considerably beyond the boiling temperature for the pressure to 

 which they are exposed. This condition is commonly manifested 

 in the boiling of water in a glass vessel by a lamp placed below, 

 when the temperature of the internal parts of the water, or, in 

 otlier words, of the parts not exposed to contact with gaseous 

 matter, rises consideral)Iy above the boiling-point for the pressure, 

 and the water boils with bumping. * At this stage it becomes 

 desirable to refer to Dr. Andrews's diagram of curves, showing 

 Ills principal results for carbonic acid, and to consider carefully 

 some of the remarkable features presented by those curves. In 

 doing so, we have first, in the case of the two curves for I3°'i 

 and2i°'5 which pass through the boiling interruption of con- 

 tinuity, to guard against being led by the gradually bending 

 transition from the curve representing obviously the liquid state 

 into the line seen rapi^lly ascending towards the curve repre- 



senting obviously the gaseous state, to suppose that this curved 

 transition is in any way indicative of a gradual transition from 

 the liquid towards the gaseous state. Dr. Andrews has clearly 

 pointed out, in describing those experimental curves, that the 

 slight bend at about the commencement of the rapid ascent from 

 the liquid state is to be ascribed to a trace of air unavoidably 

 present in the carbonic acid ; an 1 that if the carbonic acid had 

 been absolutely pure, the ascent from the liquid to the gaseous 

 state would doubtless have been quite abrupt, and would have 

 shown itself in his diagram by a vertical straight line, wlien we 

 regard the co-ordinate axes for pressures and volumes as being 

 horizontal and vertical respectively. Now in the diagram here 

 submitted, the continuous curves (that is to say, those which are 

 not dotted) are obtained from Dr. Andrews's diagram with the 

 slight alteration of substituting, in accordance with the explana- 

 tions just given, an abrupt meeting instead of the curved transi- 

 tion between the curve for the liquid state and the upright line 

 which shows the boiling stage. Looking to eitlier of the given 

 curves which pass through boiling, and, for instance, selecting 

 the curve for I3°'I, we perceive, from what h.as been said as to 



the conditions to which boiling by bumping is due, that for the 

 temperature pertaining to this curve the liquid state does not 

 necessarily end at the boiling pressure for this temperature ; and 

 that thus in the diagram the curve showing voKimes for the 

 liquid state must not cease at the foot of the upright line which 

 marks the boiling stage of pressure, but must extend continuously, 

 for some distance at least, into lower pressures in some such way 

 as is sho%vn by the dotted continuation from a to /'. But now the 

 question arises. Does this curve necessarily end at any particular 

 point h ? We know that the extent of this curve in the direction 

 from a towards or past /', along which the liquid volume will 

 continue to be represented 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 



* It his even been found by Dufour (Bibliothcque Universelle, Archives, 

 year 1861, vol. xii. " Recherchcs sur I'Ebullition des Liquides") that globules 

 of wntcr floating immersed in oil, so as neither to be in contact ivith any solid 

 nor with any gaseous body, may, under atmospheric pressure, be raised to 

 various temperatures far above the ordinary boiling-point, and occasionally 

 to so high a temperature as 178° C. without boiling. On this subject refer- 

 ence may a'so be made to the impottant researches of Donny, "Sur la 

 Cohesion des Liquides et sur leur .adherence aux Corps solides," Ann. de 

 Chimie, year 1846, 3rd ser. vol .\vi. p. 167,— July 28. 1S71. 



quantities, as impurities in the fluid experimented on, and by the 

 nature of the surface of the containing vessels, &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 conceiving there to be made, 

 for carbonic acid, from the data supplied in Dr. Andrews' ex- 

 perimental results, a solid model consisting of a curved surface 

 referred to three axes of rectangular co-ordinates, and formed so 

 that tlie three co-ordinates of each point in the curved surface 

 shall represent, for any given mass of carbonic acid, a tempera- 

 ture, a pressure, and a volume wliich can co-exist in that mass. 

 It is to be noticed here that in his diagram of curves the results 

 for each of the several temperatures experimented on are com- 

 bined in the form of a plane-curved line referred to two axes of 

 rectangular co-ordinates, one of eacli pair of co-ordinates repre- 

 senting a pressure, and the other representing the volume corre- 

 sponding to that pressure at the temperature to which the curve 

 belongs. Now to form a model such as I am here recommend- 

 ing, and have myself made. Dr. Andrews' curved lines are to 

 be placed with their planes parallel to one another, and separated 

 by intervals proportional to the differences of the temperatures to 



