Chapter XXII: Act 1899: are other codes of law designed for incorporation in special (8)

/ T \
[rho]l + [rho]v = 2[rho]c {1 + a(1 - -- ) },
\ Tc/

and that, accordingly, the curve which represents the densities at different temperatures possesses a rectilinear diameter. According to the law of corresponding states, a would be the same for all substances. Many substances, indeed, actually appear to have a rectilinear diameter, and the value of a appears approximatively to be the same. In a _Memoire presente a la societe royale a Liege_, 15th June 1899, E. Mathias gives a list of some twenty substances for which a has a value lying between 0.95 and 1.05. It had been already observed by Sydney Young that a is not perfectly constant even for normal substances. For associating substances the diameter is not rectilinear. Whether the value of a, near 1, may serve as a characteristic for normal substances is rendered doubtful by the fact that for nitrogen a is found equal to 0.6813 and for oxygen to 0.8. At T = Tc/2, the formula of E. Mathias, if [rho]v be neglected with respect to [rho]l, gives the value 2 + a for [rho]l/[rho]c.

Latent heat.

The heat required to convert a molecular quantity of liquid coexisting with vapour into saturated vapour at the same temperature is called _molecular latent heat_. It decreases with the rise of the temperature, because at a higher temperature the liquid has already expanded, and because the vapour into which it has to be converted is denser. At the critical temperature it is equal to zero on account of the identity of the liquid and the gaseous states. If we call the molecular weight m and the latent heat per unit of weight r, then, according to the law of corresponding states, mr/T is the same for all normal substances, provided the temperatures are corresponding. According to F. T. Trouton, the value of mr/T is the same for all substances if we take for T the boiling-point. As the boiling-points under the pressure of one atmosphere are generally not equal fractions of Tc, the two theorems are not identical; but as the values of p_c for many substances do not differ so much as to make the ratios of the boiling-points under the pressure of one atmosphere differ greatly from the ratios of Tc, an approximate confirmation of the law of Trouton may be compatible with an approximate confirmation of the consequence of the law of corresponding states. If we take the term boiling-point in a more general sense, and put T in the law of Trouton to represent the boiling-point under an arbitrary equal pressure, we may take the pressure equal to pc for a certain substance. For this substance mr/T would be equal to zero, and the values of mr/T would no longer show a trace of equality. At present direct trustworthy investigations about the value of r for different substances are wanting; hence the question whether as to the quantity mr/T the substances are to be divided into normal and associating ones cannot be answered. Let us divide the latent heat into heat necessary for internal work and heat necessary for external work. Let r' represent the former of these two quantities, then:--

r = r' + p(v_v - v_l).

Then the same remark holds good for mr'/T as has been made for mr/T. The ratio between r and that part that is necessary for external work is given in the formula,

r T dp
------------ = ----.
p(v_v - v_l) p dT

By making use of the approximate formula for the vapour tension:--

p /Tc - T\
log_[epsilon] --- = [int]' (--------), we find--
p_c \ T /

r Tc
------------ = [int]' --.
p(v_v - v_l) T

At T = Tc we find for this ratio [int]', a value which, for normal substances is equal to 3/0.4343 = 7. At the critical temperature the quantities r and vv-vl are both equal to 0, but they have a finite ratio. As we may equate p(v_v - v_l) with pv_v = RT at very low temperatures, we get, if we take into consideration that R expressed in calories is nearly equal to 2/m, the value 2[int]'Tc = 14Tc as limiting value for mr for normal substances. This value for mr has, however, merely the character of a rough approximation--especially since the factor f' is not perfectly constant.

Nature of a liquid.

All the phenomena which accompany the condensation of gases into liquids may be explained by the supposition, that the condition of aggregation which we call liquid differs only in quantity, and not in quality, from that which we call gas. We imagine a gas to consist of separate molecules of a certain mass [mu], having a certain velocity depending on the temperature. This velocity is distributed according to the law of probabilities, and furnishes a quantity of _vis viva_ proportional to the temperatures. We must attribute extension to the molecules, and they will attract one another with a force which quickly decreases with the distance. Even those suppositions which reduce molecules to centra of forces, like that of Maxwell, lead us to the result that the molecules behave in mutual collisions as if they had extension--an extension which in this case is not constant, but determined by the law of repulsion in the collision, the law of the distribution, and the value of the velocities. In order to explain capillary phenomena it was assumed so early as Laplace, that between the molecules of the same substance an attraction exists which quickly decreases with the distance. That this attraction is found in gases too is proved by the fall which occurs in the temperature of a gas that is expanded without performing external work. We are still perfectly in the dark as to the cause of this attraction, and opinion differs greatly as to its dependence on the distance. Nor is this knowledge necessary in order to find the influence of the attraction, for a homogeneous state, on the value of the external pressure which is required to keep the moving molecules at a certain volume (T being given). We may, viz., assume either in the strict sense, or as a first approximation, that the influence of the attraction is quite equal to a pressure which is proportional to the square of the density. Though this molecular pressure is small for gases, yet it will be considerable for the great densities of liquids, and calculation shows that we may estimate it at more than 1000 atmos., possibly increasing up to 10,000. We may now make the same supposition for a liquid as for a gas, and imagine it to consist of molecules, which for non-associating substances are the same as those of the rarefied vapour; these, if T is the same, have the same mean _vis viva_ as the vapour molecules, but are more closely massed together. Starting from this supposition and all its consequences, van der Waals derived the following formula which would hold both for the liquid state and for the gaseous state:--

/ a \
(p + --- )(v - b) = RT.
\ v^2/

It follows from this deduction that for the rarefied gaseous state b would be four times the volume of the molecules, but that for greater densities the factor 4 would decrease. If we represent the volume of the molecules by [beta], the quantity b will be found to have the following form:--

{ /4[beta]\ /4[beta]\^2 }
b = 4[beta]{ 1 - [gamma]1( ------- ) + [gamma]2( ------- ) &c.}
{ \ v / \ v / }

Only two of the successive coefficients [gamma]1, [gamma]2, &c., have been worked out, for the determination requires very lengthy calculations, and has not even led to definitive results (L. Boltzmann, _Proc. Royal Acad. Amsterdam_, March 1899). The latter formula supposes the molecules to be rigid spheres of invariable size. If the molecules are things which are compressible, another formula for b is found, which is different according to the number of atoms in the molecule (_Proc. Royal Acad. Amsterdam_, 1900-1901). If we keep the value of a and b constant, the given equation will not completely represent the net of isothermals of a substance. Yet even in this form it is sufficient as to the principal features. From it we may argue to the existence of a critical temperature, to a minimum value of the product pv, to the law of corresponding states, &c. Some of the numerical results to which it leads, however, have not been confirmed by experience. Thus it would follow from the given equation that p_c.v_c/Tc = 3/8.pv/T, if the value of v is taken so great that the gaseous laws may be applied, whereas Sydney Young has found 1/3.77 for a number of substances instead of the factor 3/8. Again it follows from the given equation, that if a is thought to be independent of the temperature, Tc/p_c.(dp/dT)_c = 4 whereas for a number of substances a value is found for it which is near 7. If we assume with Clausius that a depends on the temperature, and has a value a'.273/T, we find Tc/p_c.(dp/dT)_c = 7 That the accurate knowledge of the equation of state is of the highest importance is universally acknowledged, because, in connexion with the results of thermodynamics, it will enable us to explain all phenomena relating to ponderable matter. This general conviction is shown by the numerous efforts made to complete or modify the given equation, or to replace it by another, for instance, by R. Clausius, P. G. Tait, E. H. Amagat, L. Boltzmann, T. G. Jager, C. Dieterici, B. Galitzine, T. Rose Innes and M. Reinganum.

If we hold to the supposition that the molecules in the gaseous and the liquid state are the same--which we may call the supposition of the identity of the two conditions of aggregation--then the heat which is given out by the condensation at constant T is due to the potential energy lost in consequence of the coming closer of the molecules which attract each other, and then it is equal to a(1/v_l - 1/v_v). If a should be a function of the temperature, it follows from thermodynamics that it would be equal to (a - T.da/dT)(1/v_l - 1/v_v). Not only in the case of liquid and gas, but always when the volume is diminished, a quantity of heat is given out equal to a(1/v1 - 1/v2) or (a -T.da/dT)(1/v1 - 1/v2).

Associating substances.

If, however, when the volume is diminished at a given temperature, and also during the transition from the gaseous to the liquid state, combination into larger molecule-complexes takes place, the total internal heat may be considered as the sum of that which is caused by the combination of the molecules into greater molecule-complexes and by their approach towards each other. We have the simplest case of possible greater complexity when two molecules combine to one. From the course of the changes in the density of the vapour we assume that this occurs, e.g. with nitrogen peroxide, NO2, and acetic acid, and the somewhat close agreement of the observed density of the vapour with that which is calculated from the hypothesis of such an association to double-molecules, makes this supposition almost a certainty. In such cases the molecules in the much denser liquid state must therefore be considered as double-molecules, either completely so or in a variable degree depending on the temperature. The given equation of state cannot hold for such substances. Even though we assume that a and b are not modified by the formation of double-molecules, yet RT is modified, and, since it is proportional to the number of the molecules, is diminished by the combination. The laws found for normal substances will, therefore, not hold for such associating substances. Accordingly for substances for which we have already found an anormal density of the vapour, we cannot expect the general laws for the liquid state, which have been treated above, to hold good without modification, and in many respects such substances will therefore not follow the law of corresponding states. There are, however, also substances of which the anormal density of vapour has not been stated, and which yet cannot be ranged under this law, e.g. water and alcohols. The most natural thing, of course, is to ascribe the deviation of these substances, as of the others, to the fact that the molecules of the liquid are polymerized. In this case we have to account for the following circumstance, that whereas for NO2 and acetic acid in the state of saturated vapour the degree of association increases if the temperature falls, the reverse must take place for water and alcohols. Such a difference may be accounted for by the difference in the quantity of heat released by the polymerization to double-molecules or larger molecule-complexes. The quantity of heat given out when two molecules fall together may be calculated for NO2 and acetic acid from the formula of Gibbs for the density of vapour, and it proves to be very considerable. With this the following fact is closely connected. If in the pv diagram, starting from a point indicating the state of saturated vapour, a geometrical locus is drawn of the points which have the same degree of association, this curve, which passes towards isothermals of higher T if the volume diminishes, requires for the same change in T a greater diminution of volume than is indicated by the border-curve. For water and alcohols this geometrical locus will be found on the other side of the border-curve, and the polymerization heat will be small, i.e. smaller than the latent heat. For substances with a small polymerization heat the degree of association will continually decrease if we move along the border-curve on the side of the saturated vapour in the direction towards lower T. With this, it is perfectly compatible that for such substances the saturated vapour, e.g. under the pressure of one atmosphere, should show an almost normal density. Saturated vapour of water at 100 deg. has a density which seems nearly 4% greater than the theoretical one, an amount which is greater than can be ascribed to the deviation from the gas-laws. For the relation between v, T, and x, if x represents the fraction of the number of double-molecules, the following formula has been found ("Moleculartheorie," _Zeits. Phys. Chem._, 1890, vol. v):

x(v - b) 2(E1 - E2)
log --------- = ---------- + C,
(1 - x)^2 R1T

from which

T /dv\ E1 - E2
------( -- ) = -2-------,
(v - b) \dT/_x R1T

which may elucidate what precedes.

Condensation of substances with low Tc.

By far the majority of substances have a value of Tc above the ordinary temperature, and diminution of volume (increase of pressure) is sufficient to condense such gaseous substances into liquids. If Tc is but little above the ordinary temperature, a great increase of pressure is in general required to effect condensation. Substances for which Tc is much higher than the ordinary temperature T0, e.g. Tc > 5/3 T0, occur as liquids, even without increase of pressure; that is, at the pressure of one atmosphere. The value 5/3 is to be considered as only a mean value, because of the inequality of p_c. The substances for which Tc is smaller than the ordinary temperature are but few in number. Taking the temperature of melting ice as a limit, these gases are in successive order: CH4, NO, O2, CO, N2 and H2 (the recently discovered gases argon, helium, &c., are left out of account). If these gases are compressed at 0 deg. centigrade they do not show a trace of liquefaction, and therefore they were long known under the name of "permanent gases." The discovery, however, of the critical temperature carried the conviction that these substances would not be "permanent gases" if they were compressed at much lower T. Hence the problem arose how "low temperatures" were to be brought about. Considered from a general point of view the means to attain this end may be described as follows: we must make use of the above-mentioned circumstance that heat disappears when a substance expands, either with or without performing external work. According as this heat is derived from the substance itself which is to be condensed, or from the substance which is used as a means of cooling, we may divide the methods for condensing the so-called permanent gases into two principal groups.

Liquids as means of cooling.

In order to use a liquid as a cooling bath it must be placed in a vacuum, and it must be possible to keep the pressure of the vapour in that space at a small value. According to the boiling-law, the temperature of the liquid must descend to that at which the maximum tension of the vapour is equal to the pressure which reigns on the surface of the liquid. If the vapour, either by means of absorption or by an air-pump, is exhausted from the space, the temperature of the liquid and that of the space itself depend upon the value of the pressure which finally prevails in the space. From a practical point of view the value of T3 may be regarded as the limit to which the temperature falls. It is true that if the air is exhausted to the utmost possible extent, the temperature may fall still lower, but when the substance has become solid, a further diminution of the pressure in the space is of little advantage. At any rate, as a solid body evaporates only on the surface, and solid gases are bad conductors of heat, further cooling will only take place very slowly, and will scarcely neutralize the influx of heat. If the pressure p3 is very small, it is perhaps practically impossible to reach T3; if so, T3 in the following lines will represent the temperature practically attainable. There is thus for every gas a limit below which it is not to be cooled further, at least not in this way. If, however, we can find another gas for which the critical temperature is sufficiently above T3 of the first chosen gas, and if it is converted into a liquid by cooling with the first gas, and then treated in the same way as the first gas, it may in its turn be cooled down to (T3)2. Going on in this way, continually lower temperatures may be attained, and it would be possible to condense all gases, provided the difference of the successive critical temperatures of two gases fulfils certain conditions. If the ratio of the absolute critical temperatures for two gases, which succeed one another in the series, should be sensibly greater than 2, the value of T3 for the first gas is not, or not sufficiently, below the Tc of the second gas. This is the case when one of the gases is nitrogen, on which hydrogen would follow as second gas. Generally, however, we shall take atmospheric air instead of nitrogen. Though this mixture of N2 and O2 will show other critical phenomena than a simple substance, yet we shall continue to speak of a Tc for air, which is given at -140 deg. C., and for which, therefore, Tc amounts to 133 deg. absolute. The lowest T which may be expected for air in a highly rarefied space may be evaluated at 60 deg. absolute--a value which is higher than the Tc for hydrogen. Without new contrivances it would, accordingly, not be possible to reach the critical temperature of H2. The method by which we try to obtain successively lower temperatures by making use of successive gases is called the "cascade method." It is not self-evident that by sufficiently diminishing the pressure on a liquid it may be cooled to such a degree that the temperature will be lowered to T3, if the initial temperature was equal to Tc, or but little below it, and we can even predict with certainty that this will not be the case for all substances. It is possible, too, that long before the triple point is reached the whole liquid will have evaporated. The most favourable conditions will, of course, be attained when the influx of heat is reduced to a minimum. As a limiting case we imagine the process to be isentropic. Now the question has become, Will an isentropic line, which starts from a point of the border-curve on the side of the liquid not far from the critical-point, remain throughout its descending course in the heterogeneous region, or will it leave the region on the side of the vapour? As early as 1878 van der Waals (_Verslagen Kon. Akad. Amsterdam_) pointed out that the former may be expected to be the case only for substances for which c_p/c_v is large, and the latter for those for which it is small; in other words, the former will take place for substances the molecules of which contain few atoms, and the latter for substances the molecules of which contain many atoms. Ether is an example of the latter class, and if we say that the quantity h (specific heat of the saturated vapour) for ether is found to be positive, we state the same thing in other words. It is not necessary to prove this theorem further here, as the molecules of the gases under consideration contain only two atoms and the total evaporation of the liquid is not to be feared.

In the practical application of this cascade-method some variation is found in the gases chosen for the successive stages. Thus methyl chloride, ethylene and oxygen are used in the cryogenic laboratory of Leiden, while Sir James Dewar has used air as the last term. Carbonic acid is not to be recommended on account of the comparatively high value of T3. In order to prevent loss of gas a system of "circulation" is employed. This method of obtaining low temperatures is decidedly laborious, and requires very intricate apparatus, but it has the great advantage that very _constant_ low temperatures may be obtained, and can be regulated arbitrarily within pretty wide limits.

Cooling by expansion.

In order to lower the temperature of a substance down to T3, it is not always necessary to convert it first into the liquid state by means of another substance, as was assumed in the last method for obtaining low temperatures. Its own expansion is sufficient, provided the initial condition be properly chosen, and provided we take care, even more than in the former method, that there is no influx of heat. Those conditions being fulfilled, we may, simply by adiabatic expansion, not only lower the temperature of some substances down to T3, but also convert them into the liquid state. This is especially the case with substances the molecules of which contain few atoms.

Let us imagine the whole net of isothermals for homogeneous phases drawn in a pv diagram, and in it the border-curve. Within this border-curve, as in the heterogeneous region, the theoretical part of every isothermal must be replaced by a straight line. The isothermals may therefore be divided into two groups, viz. those which keep outside the heterogeneous region, and those which cross this region. Hence an isothermal, belonging to the latter group, enters the heterogeneous region on the liquid side, and leaves it at the same level on the vapour side. Let us imagine in the same way all the isentropic curves drawn for homogeneous states. Their form resembles that of isothermals in so far as they show a maximum and a minimum, if the entropy-constant is below a certain value, while if it is above this value, both the maximum and the minimum disappear, the isentropic line in a certain point having at the same time dp/dv and d^2p/dv^2 = 0 for this particular value of the constant. This point, which we might call the critical point of the isentropic lines, lies in the heterogeneous region, and therefore cannot be realized, since as soon as an isentropic curve enters this region its theoretical part will be replaced by an empiric part. If an isentropic curve crosses the heterogeneous region, the point where it enters this region must, just as for the isothermals, be connected with the point where it leaves the region by another curve. When c_p/c_v = k (the limiting value of c_p/c_v for infinite rarefaction is meant) approaches unity, the isentropic curves approach the isothermals and vice versa. In the same way the critical point of the isentropic curves comes nearer to that of the isothermals. And if k is not much greater than 1, e.g. k < 1.08, the following property of the isothermals is also preserved, viz. that an isentropic curve, which enters the heterogeneous region on the side of the liquid, leaves it again on the side of the vapour, not of course at the same level, but at a lower point. If, however, k is greater, and particularly if it is so great as it is with molecules of one or two atoms, an isentropic curve, which enters on the side of the liquid, however far prolonged, always remains within the heterogeneous region. But in this case all isentropic curves, if sufficiently prolonged, will enter the heterogeneous region. Every isentropic curve has one point of intersection with the border-curve, but only a small group intersect the border-curve in three points, two of which are to be found not far from the top of the border-curve and on the side of the vapour. Whether the sign of h (specific heat of the saturated vapour) is negative or positive, is closely connected with the preceding facts. For substances having k great, h will be negative if T is low, positive if T rises, while it will change its sign again before Tc is reached. The values of T, at which change of sign takes place, depend on k. The law of corresponding states holds good for this value of T for all substances which have the same value of k.

Now the gases which were considered as permanent are exactly those for which k has a high value. From this it would follow that every adiabatic expansion, provided it be sufficiently continued, will bring such substances into the heterogeneous region, i.e. they can be condensed by adiabatic expansion. But since the final pressure must not fall below a certain limit, determined by experimental convenience, and since the quantity which passes into the liquid state must remain a fraction as large as possible, and since the expansion never can take place in such a manner that no heat is given out by the walls or the surroundings, it is best to choose the initial condition in such a way that the isentropic curve of this point cuts the border-curve in a point on the side of the liquid, lying as low as possible. The border-curve being rather broad at the top, there are many isentropic curves which penetrate the heterogeneous region under a pressure which differs but little from p_c. Availing himself of this property, K. Olszewski has determined p_c for hydrogen at 15 atmospheres. Isentropic curves, which lie on the right and on the left of this group, will show a point of condensation at a lower pressure. Olszewski has investigated this for those lying on the right, but not for those on the left.

From the equation of state (p + a/v^2)(v-b) = RT, the equation of the isentropic curve follows as (p + a/v^2)(v-b)^k = C, and from this we may deduce T(v - b)^(k-1) = C'. This latter relation shows in how high a degree the cooling depends on the amount by which k surpasses unity, the change in v - b being the same.

What has been said concerning the relative position of the border-curve and the isentropic curve may be easily tested for points of the border-curve which represent rarefied gaseous states, in the following way. Following the border-curve we found before [int]' Tc/T for the value of T/p.dp/dT. Following the isentropic curve the value of T/p dp/dT is equal to k/(k - 1). If k/(k - 1) < [int]'Tc/T, the isentropic curve rises more steeply than the border-curve. If we take f' = 7 and choose the value of Tc/2 for T--a temperature at which the saturated vapour may be considered to follow the gas-laws--then k/(k - 1) = 14, or k = 1.07 would be the limiting value for the two cases. At any rate k = 1.41 is great enough to fulfil the condition, even for other values of T. Cailletet and Pictet have availed themselves of this adiabatic expansion for condensing some permanent gases, and it must also be used when, in the cascade method, T3 of one of the gases lies above Tc of the next.

Linde's apparatus.

A third method of condensing the permanent gases is applied in C. P. G. Linde's apparatus for liquefying air. Under a high pressure p1 a current of gas is conducted through a narrow spiral, returning through another spiral which surrounds the first. Between the end of the first spiral and the beginning of the second the current of gas is reduced to a much lower pressure p2 by passing through a tap with a fine orifice. On account of the expansion resulting from this sudden decrease of pressure, the temperature of the gas, and consequently of the two spirals, falls sensibly. If this process is repeated with another current of gas, this current, having been cooled in the inner spiral, will be cooled still further, and the temperature of the two spirals will become still lower. If the pressures p1 and p2 remain constant the cooling will increase with the lowering of the temperature. In Linde's apparatus this cycle is repeated over and over again, and after some time (about two or three hours) it becomes possible to draw off liquid air.

The cooling which is the consequence of such a decrease of pressure was experimentally determined in 1854 by Lord Kelvin (then Professor W. Thomson) and Joule, who represent the result of their experiments in the formula

p1 - p2
T1 - T2 = [gamma]-------.
T^2

In their experiments p2 was always 1 atmosphere, and the amount of p1 was not large. It would, therefore, be certainly wrong, even though for a small difference in pressure the empiric formula might be approximately correct, without closer investigation to make use of it for the differences of pressure used in Linde's apparatus, where p1 = 200 and p2 = 18 atmospheres. For the existence of a most favourable value of p1 is in contradiction with the formula, since it would follow from it that T1 - T2 would always increase with the increase of p1. Nor would it be right to regard as the cause for the existence of this most favourable value of p1 the fact that the heat produced in the compression of the expanded gas, and therefore p1/p2, must be kept as small as possible, for the simple reason that the heat is produced in quite another part of the apparatus, and might be neutralized in different ways.

Closer examination of the process shows that if p2 is given, a most favourable value of p1 must exist for the cooling itself. If p1 is taken still higher, the cooling decreases again; and we might take a value for p1 for which the cooling would be zero, or even negative.

If we call the energy per unit of weight [epsilon] and the specific
volume v, the following equation holds:--

[epsilon]1 + p1v1 - p2v2 = [epsilon]2,

or [epsilon]1 + p1v1 = [epsilon]2 + p2v2.

According to the symbols chosen by Gibbs, [chi]1 = [chi]2.

As [chi]1 is determined by T1 and p1, and [chi]2 by T2 and p2, we
obtain, if we take T1 and p2 as being constant,

/[delta][chi]1\ /[delta][chi]2\
(---------------) dp1 = ( ------------- ) dT2.
\ [delta]p1 /_T1 \ [delta]T2 /_p2

If T_2 is to have a minimum value, we have

/[delta][chi]1\ /[delta][chi]1)\
(---------------) = 0, or ( -------------- ) = 0.
\ [delta]p1 /_T1 \ [delta]v1 /_T1

From this follows

/[delta][epsilon]1\ /[delta](p1v1)\
( ----------------- ) + ( ------------- ) = 0.
\ [delta]v1 /_T1 \ [delta]v1 /_T1

As ([delta][epsilon]1/[delta]v1)T is positive, we shall have to take
for the maximum cooling such a pressure that the product p_v decreases
with v, viz. a pressure larger than that at which p_v has the minimum
value. By means of the equation of state mentioned already, we find
for the value of the specific volume that gives the greatest cooling
the formula

RT1b 2a
---------- = ----,
(v1 - b)^2 v1^2

and for the value of the pressure
_ _____ _ _ _____ _
| / 4 T1 | | / 4 T1 |
p1 = 27p_c | 1 - / -- -- | | 3 / -- -- - 1 |.
|_ \/ 27 Tc _| |_ \/ 27 Tc _|

If we take the value 2Tc for T1, as we may approximately for air when
we begin to work with the apparatus, we find for p1 about 8p_c, or
more than 300 atmospheres. If we take T1 = Tc, as we may at the end of
the process, we find p1 = 2.5p_c, or 100 atmospheres. The constant
pressure which has been found the most favourable in Linde's apparatus
is a mean of the two calculated pressures. In a theoretically perfect
apparatus we ought, therefore, to be able to regulate p1 according to
the temperature in the inner spiral.

The critical temperatures and pressures of the permanent gases are given in the following table, the former being expressed on the absolute scale and the latter in atmospheres:--

Tc p_c Tc p_c

CH4 191.2 deg. 55 CO 133.5 deg. 35.5
NO 179.5 deg. 71.2 N2 127 deg. 35
O2 155 deg. 50 Air 133 deg. 39
Argon 152 deg. 50.6 H2 32 deg. 15

The values of Tc and p_c for hydrogen are those of Dewar. They are in approximate accordance with those given by K. Olszewski. Liquid hydrogen was first collected by J. Dewar in 1898. Apparatus for obtaining moderate and small quantities have been described by M. W. Travers and K. Olszewski. H. Kamerlingh Onnes at Leiden has brought about a circulation yielding more than 3 litres per hour, and has made use of it to keep baths of 1.5 litre capacity at all temperatures between 20.2 deg. and 13.7 deg. absolute, the temperatures remaining constant within 0.01 deg. (See also LIQUID GASES.) (J. D. v. d. W.)

CONDENSER, the name given to many forms of apparatus which have for their object the concentration of matter, or bringing it into a smaller volume, or the intensification of energy. In chemistry the word is applied to an apparatus which cools down, or condenses, a vapour to a liquid; reference should be made to the article DISTILLATION for the various types in use, and also to GAS (_Gas Manufacture_) and COAL TAR; the device for the condensation of the exhaust steam of a steam-engine is treated in the article STEAM-ENGINE. In woollen manufactures, "condensation" of the wool is an important operation and is accomplished by means of a "condenser." The term is also given--generally as a qualification, e.g. condensing-syringe, condensing-pump,--to apparatus by which air or a vapour may be compressed. In optics a "condenser" is a lens, or system of lenses, which serves to concentrate or bring the luminous rays to a focus; it is specially an adjunct to the optical lantern and microscope. In electrostatics a condenser is a device for concentrating an electrostatic charge (see ELECTROSTATICS; LEYDEN JAR; ELECTROPHORUS).

CONDER, CHARLES (1868-1909), English artist, son of a civil engineer, was born in London, and spent his early years in India. After an English education he went into the government service in Australia, but in 1890 determined to devote himself to art, and studied for several years in Paris, where in 1893 he became an associate of the Societe Nationale des Beaux-Arts. About 1895 his reputation as an original painter, particularly of Watteau-like designs for fans, spread among a limited circle of artists in London, mainly connected first with the New English Art Club, and later the International Society; and his unique and charming decorative style, in dainty pastoral scenes, gradually gave him a peculiar vogue among connoisseurs. Examples of his work were bought for the Luxembourg and other art galleries. Conder suffered much in later years from ill-health, and died on the 9th of February 1909.

CONDILLAC, ETIENNE BONNOT DE (1715-1780), French philosopher, was born at Grenoble of a legal family on the 30th of September 1715, and, like his elder brother, the well-known political writer, abbe de Mably, took holy orders and became abbe de Mureau.[1] In both cases the profession was hardly more than nominal, and Condillac's whole life, with the exception of an interval as tutor at the court of Parma, was devoted to speculation. His works are _Essai sur l'origine des connaissances humaines_ (1746), _Traite des systemes_ (1749), _Traite des sensations_ (1754), _Traite des animaux_ (1755), a comprehensive _Cours d'etudes_ (1767-1773) in 13 vols., written for the young Duke Ferdinand of Parma, a grandson of Louis XV., _Le Commerce et le gouvernement, consideres relativement l'un a l'autre_ (1776), and two posthumous works, _Logique_ (1781) and the unfinished _Langue des calculs_ (1798). In his earlier days in Paris he came much into contact with the circle of Diderot. A friendship with Rousseau, which lasted in some measure to the end, may have been due in the first instance to the fact that Rousseau had been domestic tutor in the family of Condillac's uncle, M. de Mably, at Lyons. Thanks to his natural caution and reserve, Condillac's relations with unorthodox philosophers did not injure his career; and he justified abundantly the choice of the French court in sending him to Parma to educate the orphan duke, then a child of seven years. In 1768, on his return from Italy, he was elected to the French Academy, but attended no meeting after his reception. He spent his later years in retirement at Flux, a small property which he had purchased near Beaugency, and died there on the 3rd of August 1780.

Though Condillac's genius was not of the highest order, he is important both as a psychologist and as having established systematically in France the principles of Locke, whom Voltaire had lately made fashionable. In setting forth his empirical sensationism, Condillac shows many of the best qualities of his age and nation, lucidity, brevity, moderation and an earnest striving after logical method. Unfortunately it must be said of him as of so many of his contemporaries, "er hat die Theile in seiner Hand, fehlt leider nur der geistiger Band"; in the analysis of the human mind on which his fame chiefly rests, he has missed out the active and spiritual side of human experience. His first book, the _Essai sur l'origine des connaissances humaines_, keeps close to his English master. He accepts with some indecision Locke's deduction of our knowledge from two sources, sensation and reflection, and uses as his main principle of explanation the association of ideas. His next book, the _Traite des systemes_, is a vigorous criticism of those modern systems which are based upon abstract principles or upon unsound hypotheses. His polemic, which is inspired throughout with the spirit of Locke, is directed against the innate ideas of the Cartesians, Malebranche's faculty--psychology, Leibnitz's monadism and preestablished harmony, and, above all, against the conception of substance set forth in the first part of the _Ethics_ of Spinoza. By far the most important of his works is the _Traite des sensations_, in which he emancipates himself from the tutelage of Locke and treats psychology in his own characteristic way. He had been led, he tells us, partly by the criticism of a talented lady, Mademoiselle Ferrand, to question Locke's doctrine that the senses give us intuitive knowledge of objects, that the eye, for example, judges naturally of shapes, sizes, positions and distances. His discussions with the lady had convinced him that to clear up such questions it was necessary to study our senses separately, to distinguish precisely what ideas we owe to each sense, to observe how the senses are trained, and how one sense aids another. The result, he was confident, would show that all human faculty and knowledge are transformed sensation only, to the exclusion of any other principle, such as reflection. The plan of the book is that the author imagines a statue organized inwardly like a man, animated by a soul which has never received an idea, into which no sense-impression has ever penetrated. He then unlocks its senses one by one, beginning with smell, as the sense that contributes least to human knowledge. At its first experience of smell, the consciousness of the statue is entirely occupied by it; and this occupancy of consciousness is attention. The statue's smell-experience will produce pleasure or pain; and pleasure and pain will thenceforward be the master-principle which, determining all the operations of its mind, will raise it by degrees to all the knowledge of which it is capable. The next stage is memory, which is the lingering impression of the smell-experience upon the attention: "memory is nothing more than a mode of feeling." From memory springs comparison: the statue experiences the smell, say, of a rose, while remembering that of a carnation; and "comparison is nothing more than giving one's attention to two things simultaneously." And "as soon as the statue has comparison it has judgment." Comparisons and judgments become habitual, are stored in the mind and formed into series, and thus arises the powerful principle of the association of ideas. From comparison of past and present experiences in respect of their pleasure-giving quality arises desire; it is desire that determines the operation of our faculties, stimulates the memory and imagination, and gives rise to the passions. The passions, also, are nothing but sensation transformed. These indications will suffice to show the general course of the argument in the first section of the _Traite des sensations_. To show the thoroughness of the treatment it will be enough to quote the headings of the chief remaining chapters: "Of the Ideas of a Man limited to the Sense of Smell," "Of a Man limited to the Sense of Hearing," "Of Smell and Hearing combined," "Of Taste by itself, and of Taste combined with Smell and Hearing," "Of a Man limited to the Sense of Sight." In the second section of the treatise Condillac invests his statue with the sense of touch, which first informs it of the existence of external objects. In a very careful and elaborate analysis, he distinguishes the various elements in our tactile experiences--the touching of one's own body, the touching of objects other than one's own body, the experience of movement, the exploration of surfaces by the hands: he traces the growth of the statue's perceptions of extension, distance and shape. The third section deals with the combination of touch with the other senses. The fourth section deals with the desires, activities and ideas of an isolated man who enjoys possession of all the senses; and ends with observations on a "wild boy" who was found living among bears in the forests of Lithuania. The conclusion of the whole work is that in the natural order of things everything has its source in sensation, and yet that this source is not equally abundant in all men; men differ greatly in the degree of vividness with which they feel; and, finally, that man is nothing but what he has acquired; all innate faculties and ideas are to be swept away. The last dictum suggests the difference that has been made to this manner of psychologizing by modern theories of evolution and heredity.

Condillac's work on politics and history, contained, for the most part, in his _Cours d'etudes_, offers few features of interest, except so far as it illustrates his close affinity to English thought: he had not the warmth and imagination to make a good historian. In logic, on which he wrote extensively, he is far less successful than in psychology. He enlarges with much iteration, but with few concrete examples, upon the supremacy of the analytic method; argues that reasoning consists in the substitution of one proposition for another which is identical with it; and lays it down that science is the same thing as a well-constructed language, a proposition which in his _Langue des calculs_ he tries to prove by the example of arithmetic. His logic has in fact the good and bad points that we might expect to find in a sensationist who knows no science but mathematics. He rejects the medieval apparatus of the syllogism; but is precluded by his standpoint from understanding the active, spiritual character of thought; nor had he that interest in natural science and appreciation of inductive reasoning which form the chief merit of J. S. Mill. It is obvious enough that Condillac's anti-spiritual psychology, with its explanation of personality as an aggregate of sensations, leads straight to atheism and determinism. There is, however, no reason to question the sincerity with which he repudiates both these consequences. What he says upon religion is always in harmony with his profession; and he vindicated the freedom of the will in a dissertation that has very little in common with the _Traite des sensations_ to which it is appended. The common reproach of materialism should certainly not be made against him. He always asserts the substantive reality of the soul; and in the opening words of his _Essai_, "Whether we rise to heaven, or descend to the abyss, we never get outside ourselves--it is always our own thoughts that we perceive," we have the subjectivist principle that forms the starting-point of Berkeley.

As was fitting to a disciple of Locke, Condillac's ideas have had most importance in their effect upon English thought. In matters connected with the association of ideas, the supremacy of pleasure and pain, and the general explanation of all mental contents as sensations or transformed sensations, his influence can be traced upon the Mills and upon Bain and Herbert Spencer. And, apart from any definite propositions, Condillac did a notable work in the direction of making psychology a science; it is a great step from the desultory, genial observation of Locke to the rigorous analysis of Condillac, short-sighted and defective as that analysis may seem to us in the light of fuller knowledge. His method, however, of imaginative reconstruction was by no means suited to English ways of thinking. In spite of his protests against abstraction, hypothesis and synthesis, his allegory of the statue is in the highest degree abstract, hypothetical and synthetic. James Mill, who stood more by the study of concrete realities, put Condillac into the hands of his youthful son with the warning that here was an example of what to avoid in the method of psychology. In France Condillac's doctrine, so congenial to the tone of 18th century philosophism, reigned in the schools for over fifty years, challenged only by a few who, like Maine de Biran, saw that it gave no sufficient account of volitional experience. Early in the 19th century, the romantic awakening of Germany had spread to France, and sensationism was displaced by the eclectic spiritualism of Victor Cousin.

Condillac's collected works were published in 1798 (23 vols.) and two
or three times subsequently; the last edition (1822) has an
introductory dissertation by A. F. Thery. The _Encyclopedie
methodique_ has a very long article on Condillac (Naigeon).
Biographical details and criticism of the _Traite des systemes_ in J.
P. Damiron's _Memoires pour servir a l'histoire de la philosophie au
dixhuitieme siecle_, tome iii.; a full criticism in V. Cousin's _Cours
de l'histoire de la philosophie moderne_, ser. i. tome iii. Consult
also F. Rethore, _Condillac ou l'empirisme et le rationalisme_ (1864);
L. Dewaule, _Condillac et la psychologie anglaise contemporaine_
(1891); histories of philosophy. (H. St.)

FOOTNOTE:

[1] i.e. abbot _in commendam_ of the Premonstratensian abbey of Mureau in the Vosges. (Ed.)

CONDITION (Lat. _condicio_, from _condicere_, to agree upon, arrange; not connected with _conditio_, from _condere, conditum_, to put together), a stipulation, agreement. The term is applied technically to any circumstance, action or event which is regarded as the indispensable prerequisite of some other circumstance, action or event. It is also applied generally to the sum of the circumstances in which a person is situated, and more specifically to favourable or prosperous circumstances; thus a person of wealth or birth is described as a person "of condition," or an athlete as being "in condition," i.e. physically fit, having gone through the necessary course of preliminary training. In all these senses there is implicit the idea of limitation or restraint imposed with a view to the attainment of a particular end.

(1) _In Logic_, the term "condition" is closely related to "cause" in so far as it is applied to prior events, &c., in the absence of which another event would not take place. It is, however, different from "cause" inasmuch as it has a predominantly negative or passive significance. Hence the adjective "conditional" is applied to propositions in which the truth of the main statement is made to depend on the truth of another; these propositions are distinguished from categorical propositions, which simply state a fact, as being "composed of two categorical propositions united by a conjunction," e.g. if A is B, C is D. The second statement (the "consequent") is restricted or qualified by the first (the "antecedent"). By some logicians these propositions are classified as (1) Hypothetical, and (2) Disjunctive, and their function in syllogistic reasoning gives rise to the following classification of conditional arguments:--(a) Constructive hypothetical syllogism (_modus ponens_, "affirmative mood"): If A is B, C is D; but A is B; therefore C is D. (b) Destructive hypothetical syllogism (_modus tollens_, mood which "removes," i.e. the consequent): if A is B, C is D; but C is not D; therefore A is not B. In (a) the antecedent must be affirmed, in (b) the consequent must be denied; otherwise the arguments become fallacious. A second class of conditional arguments are disjunctive syllogisms consisting of (c) the _modus ponendo tollens_: A is either B or C; but A is B; therefore C is not D; and (d) _modus tollendo ponens_: A is either B or C; A is not B; therefore A is C. A more complicated conditional argument is the dilemma (q.v.).[1]

The limiting or restrictive significance of "condition" has led to its use in metaphysical theory in contradistinction to the conception of absolute being, the _aseitas_ of the Schoolmen. Thus all finite things exist in certain relations not only to all other things but also to thought; in other words, all finite existence is "conditioned." Hence Sir Wm. Hamilton speaks of the "philosophy of the unconditioned," i.e. of thought in distinction to things which are determined by thought in relation to other things. An analogous distinction is made (cf. H. W. B. Joseph, _Introduction to Logic_, pp. 380 foll.) between the so-called universal laws of nature and conditional principles, which, though they are regarded as having the force of law, are yet dependent or derivative, i.e. cannot be treated as universal truths. Such principles hold good under present conditions, but other conditions might be imagined under which they would be invalid; they hold good only as corollaries from the laws of nature under existing conditions.

(2) _In Law_, condition in its general sense is a restraint annexed to a thing, so that by the non-performance the party to it shall receive prejudice and loss, and by the performance commodity or advantage. Conditions may be either: (1) condition in a deed or _express_ condition, i.e. the condition being expressed in actual words; or (2) condition in law or _implied_ condition, i.e. where, although no condition is actually expressed, the law implies a condition. The word is also used indifferently to mean either the event upon the happening of which some estate or obligation is to begin or end, or the provision or stipulation that the estate or obligation will depend upon the happening of the event. A condition may be of several kinds: (1) a condition _precedent_, where, for example, an estate is granted to one for life upon condition that, if the grantee pay the grantor a certain sum on such a day, he shall have the fee simple; (2) a condition _subsequent_, where, for example, an estate is granted in fee upon condition that the grantee shall pay a certain sum on a certain day, or that his estate shall cease. Thus a condition precedent gets or gains, while a condition subsequent keeps and continues. A condition may also be _affirmative_, that is, the doing of an act; _negative_, the not doing of an act; _restrictive, compulsory_, &c. The word is also used adjectivally in the sense set out above, as in the phrases "conditional legacy," "conditional limitation," "conditional promise," &c.; that is, the legacy, the limitation, the promise is to take effect only upon the happening of a certain event.

FOOTNOTE:

[1] The terminology used above has not been adopted by all logicians.
"Conditional" has been used as equivalent to "hypothetical" in the
widest sense (including "disjunctive"); or narrowed down to be
synonymous with "conjunctive" (the condition being there more
explicit), as a subdivision of "hypothetical."