I( 



NATURE 



[£>ec. 7, 1871 



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 co-oidinates 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 obtained exhibits in a very 

 obvious way the remarkable phenomena of the voluminal condi- 

 tions 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 extends, and even throughout a far wider range into 

 which it can in imagination be conceived to be extended. It 

 helps to afford a clear view of the nature and meaning of the con- 

 tinuity 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 whire an 

 abrupt change of volume can occur by boiling or condensing. 

 On the curved surface in the model Dr. Andrews' curves for the 

 temperatures I3'''I, 2i°'5, 31' i, 32°'5, 35°-5 and 48°! Centi- 

 grade, which afford the data for its construction, may with advan- 

 tage be all shown draA\n in their proper places. The model 

 admits of easily exhibiting in due relation to one another a second 

 set of curves, in which each would be for a constant pressure, 

 and in each of which the co-ordinates would represent tempera- 

 tures and corresponding vo'umes. It may be used in various 

 ways for affording quandtative relations interpolated among those 

 more immediately given by the experiments. 



We may now, aided by the conception of this model, return 

 to the consideration of continuity or discontinuity in the curves 

 in crossing the boiling stage. Let us suppose an indefinite 

 number ol curves, each for one constant temperature, to be 

 drawn on the model, the several temperatures differing in suc- 

 cession by very small intervals, and the curves consequently bemg 

 sections of the curved surface by numerous planes closely spaced 

 parallel to one another and to the plane containing the pair of 

 co-ordinate axes for pressure and volume. Now we citn see that, 

 as we pass from curve to curve in approaching towards the 

 critical ponit from the higher temperatures, the tangent to the 

 curve at the steepest point or point of inflection is rotatin'4, so 

 that its inclination to the plane of the co-ordinate axes for 

 pressure and temperature, which we may regard as horizont;;!, 

 increases till, at the critical point, it becomes a right angle. Then 

 it appears very natural to suppose that in proceeding onwards 

 past the critical point, to curves successively for lower and lower 

 temperatures, the tangent at the point of inflection would con- 

 tinue its rotation, and the angle of its inclination, which before 

 was acute, would now become obtuse. It seems much more 

 natural to make such a .supposition as this than to suppose that 

 in passing the ciitical point from higher into lower temperatures 

 the curved line, or the curved surface to which it belongs, should 

 break itself asunder, and should come to have a part of its con- 

 ceivable continuous course absolutely deficient. It thus seems 

 natural to suppose that in some sense tlieie is continuity in each 

 of the successive curves by courses such as those drawn in the 

 accompanying diagram as dotted curves uniting continuously 

 the curves for the ordinary gaseous state with those for the ordi- 

 nary liquid state. 



The physical conditions corre.^ionding to the extension of the 

 curve from a to some point /' we have seen are perfectly attain- 

 able in practice. Some extension of the gaseous curve inio 

 points of temperature and pressure below what I h.ive called the 

 boiling, or condensing line, as for instance some extension such 

 as from c to d in the figure, I think we need not despair of prac- 

 tically realising in physical operations. As a likely mode in 

 which to bring steam continuing gase us to points of pressure 

 and temperamre at which it would collapse to liquid water if it 

 had any particle of liquid water present along with it, or if other 

 circumstances were present capable of affording some appa- 

 rently rejuisile conditions for inabling it to make a begin- 

 ning of the change of state,^ I would suggest the ad- 



* For the practicaf execution of tliis, it is well to commence with a rectan- 

 gular block of wood, and then carefully to pare it down, applying, from time 

 to time, the various curves as templets to it ; and proceedit.g 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 th^ required model at various p'aces in its length. 



t Tne priociple tha' "the particles of a substance, when e.visting all in one 

 state onl", and in continuons contact with one another, or in contact only 

 under special circumstances with other substances, experience a dijftCJtlty 

 of making a begiitning 0/ tliciy cimiige of state, whether from liquid to 

 solid, or from liquid to gaseous, or probably also from solid to liquid," was 

 proposed by me, and, so far as I am aware, was first announced in a paper by 



miffing speedily of dry steam nearly at its condensing tempera- 

 ture for its pressure (or, to use a common expression, nearly 

 saturated) into a vessel with a piston or plunger, all kept hotter 

 than the steam, and then allowing the steam to expand till by 

 its expansion it Avould be cooled below its condensing point for 

 its pressure ; and yet I would suppose that if this were done 

 with very careful precautions the steam might not condense, on 

 account of the cooled steam being surrounded entirely with a 

 thin film of superheated steam close to the superheated con- 

 taining vessel. The fact of its not condensing miglit perhaps 

 best be ascertained by observations on its volume and pressure. 

 Such an experiment as that sketched out here would not be 

 easily made, and unless it were conducted -with very great pre- 

 cautions, there could be no reasonable expectation of success in 

 its attempt ; and perhaps it might not be possible so completely 

 to avoid the presence of dust or other dense particles in the 

 steam as to make it prove successful. I mention it, however, 

 as appearing to be founded on correct principles, and as tending 

 to suggest desirable courses for experimental researches. The 

 overhanging part of the curve from e tof seems to represent a 

 state in which there would be some kind of unstable equilibrium ; 

 and so, although the curve there appears to have some important 

 theoretical significance, yet the states represented by its various 

 points would be unattainable throughout any ordinary mass of 

 the fluid. It seems to represent conditions of co-existent tempera- 

 ture, pressure, and volume, in which, if all parts of a mass of 

 fluid were placed, it would be in equilibrium, but out of which 

 it would be led to rush, partly into the rarer state of gas, and 

 partly into the denser state of liquid, by the slightest inequality 

 of temperature or of density in any part relatively to other parts. 

 1 might proceed to state, in support of these views, several con- 

 siderations founded on the ordinary statical theory of capillary 

 or superficial phenomena of liquids, which is dependent on the 

 supposition of an attraction acting very intensely for very small 

 distances, and causing intense pressure in liquids over and above 

 the pressure applied by the containing vessel and measureable 

 by any pressure-gauge. That statical theory has fitted remarkably 

 well to many observed phenomena, and has sometimes even led 

 to the forecasting of new results in advance of experiment. 

 Hence, although dynamic or kinetic theories of the constitution 

 and pressure of fluids now seem likely to supersede any statical 

 theory, y^t phenomena may still be discussed according to the 

 principles of statical theory ; and there may be considerable 

 likelihood that conditions explained or rendered probable under 

 the statical theory would have some corrcsporiding explanation 

 or confirmation under any true theory by which the statical 

 might come to be superseded. With a view to brevity, how- 

 ever, and to the avoidance of putting forward speculations per- 

 haps partly rash, though, I think, not devoid of real significance, 

 I shall not at present enter on details of these considerations, 

 but shall leave them with merely the slight suggestion now offered, 

 and with the suggestion mentioned in an earlier part of the 

 present paper, of the question wheiher in an extremely thin 

 lamina of gradual transition from a liquid to its own gas, at their 

 visible face of demarcation, conditions may not exist in a stable 

 state having a correspondence with the unstable conditions here 

 theoretically conceived. 



ALTERNATION OF GENERATIONS IN 

 FUNGI 



TT has long since been shown that certain fungi pass 

 ■*■ through an alternation of generations on thesame plant. 

 The Rev. M. J. Berkeley demonstrated that in the case of 

 the common '• bunt " at least four consecutive forms of re- 

 productive cellules were produced. In the majority of Ure- 

 dines there are two forms of fruit, but these can scarcely 

 be regarded as an alternation of generations, since there 

 is no evidence that the spores of TricJiobasis by germi- 

 nation, or otherwise, produce the bilocular spores of Piic- 

 ciiiia. In Podisoma and GymnosporangiiDn (if the two 

 genera are really distinct) the bilocular spores germinate 

 freely and produce unilocular secondary spores. Prof. 



me in the Proceedings of the Royal Society for November 24, 1850, and in a 

 paper submitted to the British Assciciation in the same year. In the present 

 paper, at tne place to which this note is annexed, I adduce ihe like further 

 supposition that a difficulty 0/ making a beginning 0/ ciiangc of state from 

 gaseous to liquid may also probably exist. 



