Phase (matter)

“ Since a phase cannot vary continuously without variations of the temperature or the potentials, it follows from these conditions that the phase at any point in a fluid system which has the same independently variable components throughout, and is in equilibrium under the influence of gravity, must be one of a certain number of phases which are completely determined by the phase at any given point and the difference of level of the two points considered. ”

“ If the temperature is changed, the system will undergo alteration in such a way that one of the phases will disappear, and a univariant system will result; if heat be added, ice will melt, and we shall have left water and vapour; if heat be abstracted, water will freeze, and we shall have left ice and vapour; if, when the temperature is altered, the pressure is kept constant, then we shall ultimately obtain only one phase (see Chap. IV.) .
The triple point is not only the point of intersection of the vaporization and sublimation curves, but it is also the end-point of the fusion curve. ”

“ The Phase Rule.—When the material system contains only a single phase, the number of independent variations, in addition to change of temperature and pressure, that can spontaneously occur in its constitution is thus one less than the number of its independent constituents. But where several phases coexist in contact in the same system, the number of possible independent variations may be much smaller. The present independent variables μ1, ..., μn are specially appropriate in this problem, because each of them has the same value in all the phases. ”

“ At temperatures and pressures represented by any point in the field I., solid only can exist as a stable phase. Since we have here one component in only one phase, the system is bivariant, and at any given temperature, therefore, ice can exist under a series of pressures ”

“ While an ethereal particle is performing a complete oscillation, a series of others, to which it has communicated its motion, are also performing oscillations in various phases—the adjacent particle being a little behind the first, the next a little behind the second, and so on, until, in the file of particles, we come to one which is in the same phase of its oscillation as the first one. ”

“ Although it is not always possible to observe the formation of the least stable form, it should be remembered that that may quite conceivably be due to the great velocity of transformation of the less stable into the more stable form. From what we have learned about the velocity of transformation of metastable phases, we can understand that rapid cooling to a low temperature will tend to preserve the less stable form ”

“ Examples of such a triple point have already been given in sulphur and tin, and a list of other substances capable of yielding two solid phases is given below. The triple point S-S-V is not precisely the same as the transition point, but is very nearly so. The transition point is the temperature at which the relative stability of the two solid phases undergoes change, when the vapour phase is absent and the pressure is 1 atm.; whereas at the triple point the pressure is that of the system itself. ”

“ These theories have proved of incalculable value in elucidating electrical and radiation phenomena.
Another discovery of Gibbs, made in 1876, has also had brilliant results. It is known as the Phase Law. The homogeneous substances into which a material system is divided is called a phase. Carbonate of lime, lime, and carbonic acid gas are the three phases of a system which comprises Iceland spar partially dissociated into lime and carbonic acid gas. ”

“ It is important to powder the salt, since otherwise the dehydration of the hydrate and the production of equilibrium occurs with comparatively great tardiness.
[164] A chemical individual is a substance which persists as a phase of constant composition when the conditions of temperature, pressure, and composition of the other phases present, undergo continuous alteration within certain limits—the limits of existence of the substance (Wald, Zeitschr. physikal. Chem., 1897, 24. 648) .
[165] Van't Hoff, Zeitschr. physikal. ”

“ From the mutual attraction of the atoms of a diffused mass whose form is unsymmetrical, there results not only condensation but rotation: gravitation simultaneously generates both the centripetal and the centrifugal forces. While the condensation and the rate of rotation are progressively increasing, the approach of the atoms necessarily generates a progressively increasing temperature. As this temperature rises, light begins to be evolved; and ultimately there results a revolving sphere of fluid matter radiating intense heat and light—a sun. ”

“ In the accompanying cut, when the earth is at A the moon is between it and the sun, in the phase called new moon. At this point the earth's orbit about the sun is more curved than the moon's, and the earth is moving relatively faster than the moon, so that when it arrives at B it is ahead of the moon, and we see the latter to the right of the earth, in the phase called first quarter. ”

“ Long eras of crumpling, elevation and mountain-formation follow, to be in turn succeeded by other ages of denudation. "The energy which determines the place of yielding and upheaval, and ordains that the mountains shall stand around the continental border," passes through a rhythmic interchange or cycle. The cosmogonical process which I have described embodies an analogous cycle, embracing the formation of matter from the ether, and most abundantly in the vicinity of stellar aggregates, by the fixation of the radiant energy, outpouring from the disintegrating stellar substance. ”

“ In this respect a critical phase resembles any phase which has a coexistent phase, but differs from such phases in that the two parts into which the mass divides when it ceases to be homogeneous differ infinitely little from each other and from the original phase, and that neither of these parts is in general infinitely small. If we consider a change in the mass to be determined by the values of it is evident that the change in question will cause the mass to cease to be homogeneous whenever the expression has a negative value. ”

“ The phase rule asserts that a homogeneous substance having n components is capable of only n + 1 independent phases, while a heterogeneous system of r coexistent phases, each of which has n independently variable components, is capable of degrees of freedom or variations in phase, of which not more than can coexist at the same pressure and temperature. ”

“ When the number of phases exceeds the number of components by unity, the system is capable of a single variation of phase. The pressure and all the potentials may be regarded as functions of the temperature. The determination of these functions depends upon the elimination of the proper quantities from the fundamental equations in , etc. ”

“ It is usual to call each part of the system of uniform composition through- out a phase; in the example given, water substance, the only component is present in two phases—a liquid phase and a vapour phase, and when the potentials of the component are the same in each phase equilibrium exists.
If in unit mass of any phase we have n components instead of one we must know the amount of n−1 components present in that unit mass before we know the exact composition of it. ”

“ Taking the results for the whole year in Table XXVIII., this advance of phase in the S min. years represents in time 15.6 minutes for the 24-hour term, 9.4 minutes for the 12-hour term, and 14.7 minutes for the 8-hour term. The difference in the phase angles, as in the amplitudes, is greatest in winter. Similar phenomena are shown by the horizontal force, and at Falmouth24 as well as Kew.
Table XXVIII.—Fourier Coefficients in Years of many and few Sun-spots. ”

“ A system consisting of n components can exist in n + 2 phases only when the temperature, pressure, and concentration have fixed and definite values; if there are n components in n + 1 phases, equilibrium can exist while one of the factors varies, and if there are only n phases, two of the varying factors may be arbitrarily fixed. ”

“ The presence of the solid phase will prevent the supercooling of the liquid; and the presence of the vapour phase will prevent the superheating of the liquid. However, even in the presence of the more stable phase, transformation of the metastable phase occurs with very varying velocity; in some cases so quickly as to appear almost instantaneous; while in other cases, the change takes place so slowly as to require hundreds of years for its achievement. It is this slow rate of transformation that renders the existence of metastable forms possible, when in contact with the more stable phase. ”

“ At a certain stage in that condensation or compressed — a stage when the radius of His globe still extent far beyond the orbit of the outermost planet of our system as it is to-day — He sets up within it a whirling motion accompanied by intense electrical action, thus making a kind of colossal vortex in many dimensions. The compression of the whirling mass is continued through what to us would be untold ages, in the course of which He breathes the seven breaths of which we have previously spoken, and thereby groups the bubbles into the atomic matter of the various planes. ”

“ The resulting values, therefore, had nothing to do with the phase correction as such, but they did, nevertheless, have to do with the phase itself.
To see exactly how this is possible, let us consider the effect an illuminated atmosphere would have upon the measurements in question. To make matters more obvious we will introduce a diagram. The inner circle represents a section of the planet in the plane of the ecliptic; the arrows, the directions in the same plane of the Sun and Earth from the centre of the planet, in the different positions to be considered ”

“ The power of attraction which, according to the theory of gravity, each body possesses, is in proportion to the quantity of matter contained in that body. But the periodic time in which one body, at a given distance, revolves round another that attracts it, is shorter in proportion as this power is greater, and consequently as the quantity of matter in the attracting body. If the densities of Jupiter and Saturn were the same with that of the Earth, the periodic times of their several Satellites would be shorter than by observation they are found to be. ”

“ The number of specific phases contained in a generic phase would then be , where denote the numbers of equivalent positions belonging to the several kinds of particles. The case in which a is infinite would then require especial attention. ”

“ Since the seasons are regulated by the phases of the stars, the months can also be named after these phases and regulated by them, and a very accurate and practical means of regulation is thus afforded. When a phase of a star does not appear in the month to which it gives its name, the month is ‘forgotten’, the next month brings round the phase in question, and takes its name. ”

“ Further, it is evident that account must be taken of the variation of phase in estimating the magnitude of the effect at P of the first zone. The middle element alone contributes without deduction; the effect of every other must be found by introduction of a resolving factor, equal to cos θ, if θ represent the difference of phase between this element and the resultant. Accordingly, the amplitude of the resultant will be less than if all its components had the same phase, in the ratio
or 2: π. Now 2 area /π = 2λr ”

“ That these processions of energy particles appear as wave phenomena when subjected to certain observations is due to the resistance of the undifferentiated force blanket of all space, the hypothetical ether, and to the intergravity tension of the associated aggregations of matter. The spacing of the particle-intervals of matter, together with the initial velocity of the energy beams, establishes the undulatory appearance of many forms of energy-matter. ”

“ The analogy between the motion of an ensemble of systems in an extension-in-phase and a steady current in an incompressible liquid, and the diagrammatic representation of the case of one degree of freedom, which appeals to our geometrical intuitions, may be sufficient to show how the conservation of density in phase, which involves the conservation of the average value of the index of probability of phase, is consistent with an approach to a limiting condition in which that average value is less. ”

“ We may then conveniently discard the idea of phase, and regard the amplitudes as at random positive or negative. If all the signs are the same, the intensity is n2; if, on the other hand, there are as many positive as negative, the result is zero. But, although the intensity may range from 0 to n2, the smaller values are much more probable than the greater. ”

“ The systems which we now proceed to study are characterized by the fact that the different phases have no longer all the same chemical composition, and cannot, therefore, according to definition, be considered as one-component systems. ”

“ A Cycle is a perpetual round, or circulation of the same parts of time of any sort. The Cycle of the Sun is a revolution of 28 years, in which time, the days of the months return again to the same days of the week; the Sun’s Place to the same Signs and Degrees of the Ecliptic on the same months and days, so as not to differ one degree in 100 years; and the leap-years begin the same course over again with respect to the days of the week on which the days of the months fall. The Cycle of the Moon, commonly called the Golden Number, is a revolution of 19 years ”