Attached herewith is paper number ten in my liquid series which shows that the melting points under pressure can be accurately computed by means of a very simple equation. This paper makes a highly significant contribution to the work as a whole, as the melting point equation is not only a purely theoretical expression derived directly from the basic postulates of the work, but it is also the same equation that was used to calculate solid compressibilities in previous papers. It is difficult to visualize the possibility that such an equation could successfully reproduce the full range of experimental values in either field unless it were an essentially correct representation of the physical facts; the possibility that an incorrect expression could accomplish these results in both fields is wholly inconceivable.
It appears to me that this occasion, on which I am submitting some striking new evidence of the validity of the fundamental postulates on which my work is based, is an appropriate time to make some comments regarding those aspects of currently accepted physical theory with which my findings are in conflict. It is true; of course, that these conflicts are quite numerous, and there is a very understandable reluctance to believe that accepted theory can be wrong in so many important respects. But it is not difficult to prove this point. It is quite a task to prove that any of the current theories are wrong, because long years of effort on the part of the theorists have enabled them to adjust their theories to fit the facts in most cases and to devise means of evading most of the many contradictions that still remain, but it is quite simple to show that the particular theories in question are lacking in factual support and therefore can be wrong. As long as this is true, it is clearly in order to consider conflicting theories.
The case in favor of my new theoretical structure rests primarily on the contention that not a single one of the thousands of necessary and unavoidable consequences of my fundamental postulates is inconsistent with any positively established fact. It becomes very important, therefore, to distinguish clearly between items that are definitely known to be factual and those, which do not qualify. The enclosed memorandum is a discussion of this situation as it applies to the points of conflict. The memorandum does not attempt to discuss all of the points at issue, nor to make an exhaustive analysis of any case; nothing short of a booklength presentation could cover that much ground. However, the various categories of pseudofacts commonly encountered are described and illustrated by examples, and it should not be difficult to see that every one of the accepted ideas with which my findings are in conflict is one of these pseudo facts: a hypothesis, assumption, or extrapolation masquerading in the guise of an established fact.
Perhaps it will be regarded as presumptuous for me to suggest that the strict and critical tests which will be applied to my new theory be applied to the conflicting parts of currently accepted theory as well, but I believe that by this time the new developments which I have covered in the liquid papers add up to an impressive enough total to justify a full and comprehensive examination of the underlying theories, including a careful consideration of this question as to the true status of conflicting ideas.
D. B. Larson
Strictly speaking, the melting point is a phenomenon of the solid state rather than of the liquid state and in general its behavior follows the solid state pattern, but since this temperature constitutes the point of transition between the two physical states it has some close relations with various liquid properties which justify giving it some consideration in this survey of the liquid state,
If the melting point were actually a property of the liquid, we could expect that it would be linearly related to the pressure, just as the true liquid component of the volume and other liquid properties are so related. Solid state properties, however, are directly or inversely related to the square root of the pressure, rather than to the first power, for reasons that are explained in the author's book "The Structure of the Physical Universe", which develops the general physical theories underlying the liquid principles that form the basis for this series of papers. It has already been brought out in a paper which preceded this liquid series^{5} that the solid state equivalent of Bole's Law, PV = k, is PV^{2} = k, from which we obtain the relation V/V_{0} = P_{0}^{1/2}(P +P_{0})^{1/2}. In terms of density this becomes
d = 
(P +P_{0})^{1/2} 
d_{0} 

P_{0}^{1/2} 
The previous solid compressibility paper showed that this equation is able to reproduce the experimental values of the compression, within the existing margin of uncertainty, over the entire range of temperatures, pressures and substances for which data are available.
According to the basic theory, this is a characteristic relationship applying to solid state properties in general, rather than merely a volume relation, and we may therefore rewrite the equation, substituting T_{m}, the normal melting point, for d_{0}, and T_{p}, the melting point under an externally applied pressure P, for d. We then have
T_{p} = 
(P +P_{0})^{1/2} 
T_{m} 
(16) 
P_{0}^{1/2} 
It will be noted that this expression is identical with the wellknown Simon melting point equation, except for the substitution of a constant for one of the two variables of the Simon equation, which the originator expresses as
P 
= ( 
T 
)^{C}  1 

a 
T_{0} 
Simon's factor a corresponds to the initial pressure, as is generally recognized, His factor c (unexplained theoretically) has usually been assigned a value somewhere between 1.5 and 2 in application to organic compounds and other low melting point substances, and replacing this variable factor by the constant value 2 is not a major modification of the equation, so far as the effect on the calculated values is concerned, as these values are not very sensitive to changes in c if accompanied by corresponding changes in a. The situation with respect to the high melting point elements, which are often assigned considerably higher values of the factor c. will be discussed later.
No satisfactory theoretical explanation has thus far been discovered for the Simon equation, but this expression agrees with the experimental results over a wide range of pressures and substances, and it is generally conceded that such a theoretical explanation must exist. Strong and Bundy state the case in these words, "Simon's fusion equation has now endured a considerable amount of experimental and theoretical examination. Because it applies in so many cases... it must contain fundamentally correct concepts concerning some of the properties of matter".^{50}
In the areas previously covered by this series of papers, the new equations, which have been developed, are to a large degree filling a vacuum, as no generally applicable mathematical representations of these properties have hitherto been available. It is therefore quite significant that when we reach an area where an equation of recognized standing does already exist, the new development does not produce something totally new; the general liquid principles on which the work is based lead to a melting point expression which is essentially a modified form of the previously existing equation. Here, as in so many places outside the liquid field, genuine knowledge already in existence coincides with the products of the development of the postulates of this work, and can simply be incorporated into the new theoretical structure with nothing more than minor modifications. What the new development actually does, in essence, is to establish the exact nature of those "fundamentally correct concepts" to which Strong and Bundy refer.
But even though the required modification of the Simon equation is minor, it does not necessarily follow that it is unimportant. As brought out in paper IX of this series, the more restrictive the mathematical expression of a physical property can be made, the more likely it is to be a correct representation of the true physical facts, providing, of course, that it produces results which agree with the experimental values within the margin of uncertainty of the latter. Replacement of one of the two adjustable factors in the Simon equation by the constant value 2 as required by the new theory is an important move in this direction.
Now that this value has been fixed, the only additional requirement for a complete and unequivocal definition of the pressuremelting point relation for each substance is a means of calculating the initial pressure applicable in each case. In the solid compressibility paper previously mentioned, the following equation for the initial pressure applicable to compression of solids was developed:
P_{0} = 
16649 abc 
atm. 

s_{0}^{3} 
The initial pressure applicable to liquid compressibility is considerably lower and paper IV in this series expressed this relation as
P_{0} = 415.84 n/ V_{0} 
atm. 

Since the melting point is at the boundary between the liquid and solid states, it is to be expected that the initial pressure applicable to this property will lie somewhere between the true liquid and true solid values, and a study of this situation leads to an equation of an intermediate type:
P_{0} = 664.28 
abc 
atm. 

nV_{0}^{2/3} 
The symbols in this equation have the same significance as in the expressions for the true liquid and true solid initial pressures. The factors a, b, and c are the effective displacements in the three dimensions of space, a concept that is explained in the author's book previously mentioned. V_{0} is the initial specific volume of the liquid as defined in paper II of this series, and n is the number of independent units in the molecule at the melting temperature.
The values of n applicable to the solidliquid transition are usually less than those applicable to liquid compressibility, as would be expected since the number of effective units per molecule is normally less in the solid, particularly at low temperatures, than it is in the liquid, and an intermediate value is appropriate for the boundary state. There is also a marked tendency toward a constant value in each of the various homologous series of compounds, at least in those portions of these series for which experimental data are available. Thus the value for most of the aliphatic acids is 4, and for the normal alcohols it is 3. Most elements have n = 1, the principal exceptions being such elements as sulfur and phosphorus which have quite complex liquid structures.
In the majority of substances on which experimental results are available for comparison including most of the common organic compounds, the a and c factors take the theoretical maximum values 4 and 8 respectively. The factor b is usually 1 at low pressures, except for the elements in the middle of each periodic group, which have the same tendency toward higher values that was noted in the case of solid compressibility.
Some of the low melting point elements have acb values at or near the theoretical minimum, a point which is of particular interest; first, because it provides a definite reference point for these factors which helps to demonstrate that they have a real physical significance, and second, because the wide spread between the possible values of the factors at the lower end of the scale makes identification of the applicable factors a very simple matter. Helium, for example, takes the minimum values, 111. The next higher combination that is theoretically possible 1½11 would result in a reduction of more than 20 percent in the melting temperature at the upper end of the experimental temperature range. This is, of course, far outside the margin of experimental uncertainty, which is normally in the neighborhood of one or two percent and the 111 factors are therefore definitely the ones that are applicable.
The situation with respect to the other elements of very low melting point is similar, and the theoretical melting point pattern for these substances is therefore positively established. It does not necessarily follow, however, that the divergence between the experimental melting points and the values thus calculated is always chargeable to experimental error. The theoretical values are those which would result from the application of pressure only, without any "second order" effects such as those due to the presence of impurities, to consolidation of molecules under pressure, to polymorphic transitions, etc, and they will not necessarily coincide exactly with the results of accurate measurements made on a substance which is subject to extraneous influences of this kind.
It should also be recognized that correlation of the theoretical and experimental values is not as simple a matter in the melting point field as it is for a property such as surface tension, on which we have a large volume of reasonably accurate experimental data. Only a comparatively small amount of work has been done on the melting curves, and most of that has been confined to the range below 1000 atm. Outside of the recent work with the metallic elements and the elements of very low melting point, Bridgman's investigations are practically the only source of information at the higher pressures. This, of course, introduces some serious uncertainties into any correlations that we may attempt. If the calculated and experimental values agree, each serves to some extent as a corroboration for the other, but where there is a divergence it is not immediately apparent which of the two is in error.
The correlations of theory against experiment in the areas covered by previous papers in this series have been of the, massive type, Calculations have been carried out for hundreds of substances of many different classes and, although it has not been possible to show all of these data in the tabulations accompanying the papers, a reasonably good sample has been included in each case. Where the experimental data are scarce and to a large degree unconfirmed 2 as in the present instance) it will be necessary to use a more selective technique, and to examine the evidence of the validity of each phase of the theoretical relationship separately, rather than verifying the entire development in one operation by a massive demonstration of agreement with the results of observation.
The first point, which we will want to consider, is the validity of the square root relationship. For this purpose the most significant experimental results are those in which the percentage increase in the melting point is the greatest. Where the ratio of the melting point at the upper end of the experimental pressure range to the normal melting point is less than 2, the difference between a square root curve and some other possible exponential curve, or a linear curve, is small, and unless the experimental values are extremely accurate it is difficult to determine which relation these values actually follow. The divergence of the curves increases rapidly, however, as the ratio rises, and if this ratio is 4 or more the nature of the curve is readily ascertained.
For this particular purpose, therefore, the work at the highest pressures is of no particular value. Even where pressures in the neighborhood of 150,000 atm. have been reached in the study of the metallic elements, the corresponding melting point ratio is only about 1.2. In the range from 1.0 to 1.2 the difference due to even a fairly large change in the exponent of the melting point expression is negligible. It is not surprising, therefore, that there is much difference of opinion as to just what this exponent should be. In the case of iron, for example, Gilvarry arrives at an exponent of 1.9 for the Simon formula, Simon himself selects 4, and Strong gives us the value 8 (which corresponds to 1/8 on the basis of equation 16).^{51} On first consideration this seems to be an extreme case of disagreement, but if the value of Simon's constant a is adjusted empirically (as is always done, of course), the differences between these various exponential curves in this range are so much less than the experimental uncertainty that the curves are for all practical purposes coincident. For example, the square root of 1.1 is 1.0488 and the square root of 1.2 is 1.0954. If the curve from 1.0 to 1.2 were linear, the value at 1.1 would be 1.0477, which differs from 1.0448, the value on the square root basis, by only onetenth of one percent. A similar calculation using an exponent of 1/8 (equivalent to Strong's value 8) shows that the deviation from the linear curve is still less, only about ½0 of one percent. Where the normal melting point is in the vicinity of 20000, a change from Gilvarry's exponent 1.9 to Strong's exponent 8 changes the position of the midpoint of the curve only about one degree if the value of a is fitted to the maximum experimental value of the melting temperature. It is therefore clear that within the experimental pressure range all of the exponents selected by previous investigators are in agreement with each other and with the exponent of equation 16, But where the experimental data fit everything they prove nothing.
The definite verification of the square root relationship is furnished by the elements of very law melting point, the most conclusive demonstration coming from helium and hydrogen. Helium does not melt at all except under pressure, and its melting curve cannot be referred to the normal melting point in the usual manner, but a study of the situation indicates that the melting point of this element can be calculated from equation 16 by the use of a pseudomelting point which has been evaluated empirically as 11.1° K. We first calculate the melting point under pressure just as if 11.1° were the normal melting point, and then we subtract 11.1° from the result. At 5000 atm. for example, we find that the quantity (P +P_{0})^{1/2}/P_{0}^{1/2} amounts to 4.516. Multiplying by 11.1° we obtain 50.13°, and subtracting 11.1° we arrive at a theoretical melting point of 39.03° K. A measurement at this pressure is reported as 39° K. If the value of the expression

(P +P_{0})^{1/2} 
 1 

P_{0}^{1/2} 
is less than 1.0 (that is, if the true melting point is below the pseudomelting point), the true melting point is proportional to the 2/3 power of the foregoing expression instead of the first power. The reasons for this behavior are not clear, although it is not surprising to find that the values below the reference temperature, which correspond in some degree to negative temperatures, are abnormal, Table X1 compares the calculated and experimental melting points of helium. Here we see that although the maximum pressure of observation is only 7270 atm, the melting point ratio (designated as R in this and the following tables) at this pressure is 4.4, which is well above the minimum requirement for positive identification of the nature of the melting curve.
Also included in this table are the values for He^{3} which are computed in the same manner, except that the pseudomelting point is slightly higher, 11.5º K, and the 5/6 power is substituted for the 2/3 power below the pseudomelting point. It will be noted that for both isotopes the differences between the theoretical and experimental values are abnormally high in the vicinity of the pseudomelting point. This is a mathematical effect of the distribution of molecular velocities in the neighborhood of a transition point, similar to the effect on the fluidity values discussed in paper VIII, page 3, and rough calculations indicate that when the transition is studied in detail so that the proper corrections for this effect can be determined, the agreement at these temperatures will be found just as close in this range as it is where the transition effect is absent.
Aside from hydrogen, which will be discussed later, there is no other substance on which the melting curve has been followed farther than a ratio of about 2.5. In the range from around 2.0 to 2.5 we find such substances as nitrogen, which shows an agreement within 1º over the full experimental pressure range (if we use Bridgman's values up to his pressure limit); carbon tetrachloride, which agrees within 1º to 6000 kg/cm², with somewhat larger deviations above this pressure ethyl bromide, which agrees within 2º to 25,000 kg/cm² and shows a deviation of 5º at 30,000 kg/cm², beyond what appears to be a transition of some kind; chloroform, which agrees with the results of one set of measurements by Bridgman to within 2º but differs substantially from another set of results; and two of the normal alcohols, ethyl and butyl, for which the agreement is within 4º and 3º respectively up to 25,000 kg/cm², beyond which the values diverge. It is not clear whether this divergence is due to experimental error or to a transition to a new value of P_{0} similar to the transitions, which were found in the study of compressibility.
The calculated and experimental melting points for these substances are listed in Table X2,. Also included in this table are values for a few other substances which have been observed up to 11,000 kg/cm² or higher) but only to melting point ratios between 1.25 and 2.0, Even though the information available within the range of significant melting point ratios is quite limited, the comparisons in this table should be sufficient to add considerable weight to the conclusions reached on the basis of the helium values
The melting curves of a large number of substances have been determined with precision to pressures in the neighborhood of 1000 atm. For reasons previously discussed, these determinations are of no value from the standpoint of verifying the square root relation, but now that the validity of this relation has been confirmed by other means, the values in the lower pressure range can be utilized as a test of equation 17, and a number of comparisons of melting points in this range are given in Table X  3. Since all other factors that enter into the determination of the melting points of the common organic compounds are definitely fixed, identity of the values of n applicable to related compounds) or obvious regularities in the values for such compounds, are strong evidence of the validity of equations 16 and 17 and of the theoretical principles from which these equations were derived. For example, melting points for the first seven of the aliphatic acids computed on the basis of n = 4 agree with the experimental results within 1° in four cases, and in only one of these compounds (propionic acid) is there any deviation as large as 3°
Benzene and some of its simple derivatives contribute additional evidence of the same kind. Benzene itself has n = 5, and a large percentage of the closely related compounds for which melting curves are available take the same values of this factor. Among these are toluene, two of the xylenes, naphthalene, benzophenone, nitrobenzene, and two of the nitrobenzene. Representative examples of both the benzenes and the aliphatic acids are included in Table X3.
The data for water, Table X  4, are particularly interesting. The acb values are 481 as usual, except that there is a transition to 482 between 8000 and 9000 kg/cm² affecting ice VI only. Disregarding the abnormal forms of ice that exist below 2000 kg/cm², we find that the entire melting point pattern of water, complex as it is, can be reproduced simply on the assumption that the factor n, the number of effective units in the molecule, increases step by step as we pass from one form of ice to the next: ice III  1, ice V  2. ice VI  3, ice VII  4. (The status of ice IV is questionable; it may not even exist). Except in the range from 20,000 to 28,000 kg/cm², where the effects of a polymorphic transition that takes place at 22,400 kg/cm² are in evidence, the agreement between the calculated and experimental values is within 2º in all cases.
The increase in the factor b from 1 to 2 which was found at a pressure of approximately 9000 kg/cm² in ice VI is one of the very few instances where the existence of a transition of this kind, involving an increase in the initial pressure, appears to be definitely confirmed. The pattern of increase in this factor found in the study of solid compressibility suggests, however, that such transitions may be normal, and that their infrequent appearance in melting phenomena is merely due to the relatively narrow pressure range that has thus far been covered experimentally.
A similar transition in the opposite direction occurs in hydrogen and the inert gases above helium. Here we find that the initial acb values are 1½11, but subsequently these factors drop to the minimum level 111, What we may regard as the normal pattern for this transition is illustrated by krypton and xenon, Table X5. In these elements the 1½11 factors prevail up to 170º K (onethird of the liquid temperature unit, 510º). From 170º to 340º (twothirds of the temperature unit) there is a linear transition to 111, and above 340º the effective factors remain at this minimum level. The experimental results on argon are erratic and inconclusive, but not inconsistent with values calculated on the same basis. Neon and hydrogen follow the same general pattern, but the transition temperatures are fractional values of those normally applicable. In the case of hydrogen, the transition begins at 28.3º K, onesixth of the normal 170º, and is completed in 113.3º, twothirds of the normal interval. Table X6 compares the hydrogen melting points calculated on this basis with a set of values compiled from experimental data. As the table shows, the two sets of values agree within 1/4 degree up to the two highest pressures of observation, and even in these cases the difference is less than ½ degree.
Table X7 lists the values of the various factors entering into the calculation of initial pressures and melting points for all of the substances included in the preceding tabulations.
TABLE X  1  
Melting Points  Helium  
He^{4}  P_{0} = 266.4 kg/cm² (52)  
P  R  T_{m}  Obs. 
37.3  .068  1.85  1.91 
238.7  .377  5.79  5.70 
482.2  .676  8.55  8.75 
750.8  .954  10.76  12.54 
1018.9  1.197  13.29  13.88 
1280.3  1.409  15.64  16.01 
1539.2  1.603  17.79  18.01 
1746.8  1.749  19.41  19.52 
2032.8  1.938  21.51  21.52 
2251.5  2.074  23.02  23.01 
2480.1  2.211  24.54  24.46 
2813.3  2.400  26.64  26.48 
2986.4  2.494  27.68  27.50 
3323.9  2.671  29.65  29.47 
3496.0  2.758  30.61  30.47 
TABLE X  1  
Melting Points  Helium  
He^{4}  atm. (53)  
P  R  T_{m}  Obs. 
3280  2.704  30.01  30 
4170  3.144  34.90  35 
5140  3.576  39.69  40 
6170  3.993  44.32  45 
TABLE X  1  
Melting Points  Helium  
He^{3}  P_{0} = 294.1 kg/cm² (52)  
P  R  T_{m}  Obs. 
75.9  .173  1.99  1.94 
232.0  .405  4.66  4.68 
322.3  .512  5.89  5.86 
535.3  .724  8.33  8.42 
729.9  .887  10.20  10.45 
1010.9  1.106  12.72  13.00 
1251.2  1.292  14.86  15.03 
1505.1  1.473  16.94  17.00 
1776.0  1.653  19.01  19.00 
2054.9  1.826  21.00  21.00 
2281.2  1.959  22.53  22.51 
2518.3  2.092  24.66  24.02 
2759.6  2.222  25.55  25.51 
3008.3  2.351  27.04  27.01 
3262.3  2.478  28.50  28.50 
3253.7  2.603  29.93  30.01 
TABLE X  2  
Melting Points  
Nitrogen (54)  
P M kg/cm² 
R  T_{m}  Obs. 
0  1.000  63  63 
1  1.324  83  82 
2  1.582  100  99 
3  1.806  114  113 
4  2.003  126  126 
5  2.183  138  138 
6  2.350  148  149 
M atm.  (55)  
7  2.540  160  157.5 
8  2.689  169  169 
9  2.830  178  178.5 
TABLE X  2  
Melting Points  
Carbon Dioxide  
P M kg/cm² 
R  T_{m}  Obs. (54) 
0  1.000  217  217 
1  1.078  234  236 
2  1.151  250  253 
3  1.219  265  268 
4  1.283  278  282 
5  1.345  292  295 
6  1.404  205  306 
7  1.461  317  317 
8  1.514  329  328 
9  1.567  340  339 
10  1.618  351  349 
12  1.715  372  367 
TABLE X  2  
Melting Points  
Lead  
P M kg/cm² 
R  T_{m}  Obs. (56) 
0  1.000  600  600 
3  1.036  622  622 
6  1.071  643  643 
9  1.105  663  663 
12  1.138  683  682 
15  1.171  703  701 
18  1.202  721  719 
21  1.232  739  737 
24  1.262  757  754 
27  1.291  775  770 
30  1.320  792  785 
33  1.347  808  800 
TABLE X  2  
Melting Points  
Mercury  
P M kg/cm² 
R  T_{m}  Obs. 
0  1.000  234  234 
2  1.047  245  245 
4  1.092  256  255 
6  1.135  266  265 
8  1.176  275  275 
10  1.216  285  285 
12  1.255  294  295 
TABLE X  2  
Melting Points  
Chloroform  
P M kg/cm² 
R  T_{m}  Obs. 
0  1.000  210  212 
1  1.090  229  228 
2  1.173  246  245 
3  1.250  263  261 
4  1.323  278  277 
5  1.392  292  291 
6  1.458  306  306 
7  1.521  319  319 
8  1.581  332  332 
9  1.640  344  345 
10  1.696  356  357 
11  1.750  368  369 
12  1.803  379  381 
TABLE X  2  
Melting Points  
Ethyl Bromide  
P M kg/cm² 
R  T_{m}  Obs. 
0  1.000  154  154 
5  1.318  203  203 
10  1.572  242  244 
15  1.791  276  278 
20  1.986  306  307 
25  2.164  333  331 
30  2.327  358  353 
TABLE X  2  
Melting Points  
Aniline  
P M kg/cm² 
R  T_{m}  Obs. 
0  1.000  267  267 
1  1.070  286  286 
2  1.136  303  305 
3  1.198  320  322 
4  1.257  336  338 
5  1.313  351  352 
6  1.368  365  366 
7  1.420  379  380 
8  1.470  392  392 
9  1.518  405  405 
12  1.655  442  439 
TABLE X  2  
Melting Points  
Chlorobenzene  
P M kg/cm² 
R  T_{m}  Obs. 
0  1.000  228  228 
1  1.071  244  245 
2  1.138  259  261 
3  1.201  274  276 
4  1.261  288  290 
5  1.318  301  303 
6  1.373  313  315 
7  1.426  325  327 
8  1.476  337  337 
9  1.525  348  348 
10  1.573  359  358 
11  1.619  369  367 
12  1.664  379  377 
TABLE X  2  
Melting Points  
Nitrobenzene  
P M kg/cm² 
R  T_{m}  Obs. 
0  1.000  279  279 
1  1.080  301  300 
2  1.155  322  321 
3  1.225  342  342 
4  1.291  360  361 
5  1.354  378  379 
6  1.414  395  396 
7  1.472  411  411 
8  1.528  426  427 
9  1.581  441  443 
10  1.633  456  458 
11  1.683  470  472 
TABLE X  2  
Melting Points  
Bromobenzene  
P M kg/cm² 
R  T_{m}  Obs. 
0  1.000  242  242 
1  1.071  259  261 
2  1.139  276  279 
3  1.202  291  295 
4  1.262  305  309 
5  1.320  319  323 
6  1.375  333  335 
7  1.428  346  347 
8  1.479  358  359 
9  1.528  370  370 
10  1.576  381  381 
11  1.623  393  391 
12  1.668  404  401 
TABLE X  2  
Melting Points  
Carbon Tetrachloride  
P M kg/cm² 
R  T_{m}  Obs. 
0  1.000  250  251 
1  1.145  286  287 
2  1.274  319  319 
3  1.391  348  349 
4  1.498  375  376 
5  1.599  400  400 
6  1.694  424  423 
7  1.783  446  444 
8  1.868  467  465 
9  1.950  488  485 
TABLE X  2  
Melting Points  
Bromoform  
P M kg/cm² 
R  T_{m}  Obs. 
0  1.000  281  281 
1  1.086  305  305 
2  1.166  328  327 
3  1.241  349  348 
4  1.311  368  368 
5  1.378  387  387 
6  1.442  405  404 
7  1.502  422  421 
8  1.561  439  436 
9  1.618  455  452 
10  1.672  470  467 
11  1.725  485  482 
TABLE X  2  
Melting Points  
Ethyl Alcohol  
P M kg/cm² 
R  T_{m}  Obs. 
0  1.000  156  156 
5  1.290  201  197 
10  1.525  236  234 
15  1.729  270  268 
20  1.911  298  298 
25  2.078  324  327 
30  2.232  348  355 
35  2.375  371  382 
TABLE X  2  
Melting Points  
Butyl Alcohol  
P M kg/cm² 
R  T_{m}  Obs. 
0  1.000  188  183 
5  1.278  240  240 
10  1.505  283  285 
15  1.703  320  322 
20  1.880  353  353 
25  2.041  384  381 
30  2.191  412  405 
35  2.331  438  428 
TABLE X  3  
Melting Points  
Benzene  
P M kg/cm² 
R  T_{m}  Obs. (57) 
0  1.000  279  279 
166  1.015  283  283 
349  1.033  288  288 
538  1.050  293  293 
728  1.066  297  298 
993  1.090  304  305 
TABLE X  3  
Melting Points  
pNitrotoluene  
P M kg/cm² 
R  T_{m}  Obs. (57) 
0  1.000  325  325 
112  1.009  328  328 
297  1.024  333  333 
483  1.039  338  338 
671  1.054  343  343 
857  1.068  347  348 
972  1.077  350  351 
TABLE X  3  
Melting Points  
Rutures Acid  
P M kg/cm² 
R  T_{m}  Obs. (57) 
0  1.000  268  268 
290  1.021  274  213 
567  1.041  279  278 
837  1.060  284  283 
986  1.071  287  286 
TABLE X  3  
Melting Points  
oXylene  
P M kg/cm² 
R  T_{m}  Obs. (57) 
0  1.000  248  248 
220  1.021  253  253 
437  1.042  258  258 
654  1.063  264  263 
865  1.082  268  268 
1080  1.101  273  273 
TABLE X  3  
Melting Points  
mNitrotoluene  
P M kg/cm² 
R  T_{m}  Obs. (57) 
0  1.000  289  289 
164  1.013  293  293 
372  1.031  298  298 
578  1.047  303  303 
781  1.063  307  308 
982  1.079  312  313 
TABLE X  3  
Melting Points  
Caproic Acid  
P M kg/cm² 
R  T_{m}  Obs. (57) 
0  1.000  269  269 
218  1.016  273  273 
487  1.036  279  278 
760  1.056  284  283 
890  1.065  286  286 
996  1.073  289  288 
TABLE X  3  
Melting Points  
pXylene  
P M kg/cm² 
R  T_{m}  Obs. (57) 
0  1.000  286  286 
49  1.006  288  288 
197  1.024  293  293 
343  1.041  298  298 
495  1.058  303  303 
647  1.075  307  308 
803  1.093  313  313 
957  1.110  317  318 
TABLE X  3  
Melting Points  
Acetic Acid  
P M kg/cm² 
R  T_{m}  Obs. (57) 
0  1.000  290  290 
168  1.011  293  293 
415  1.029  298  298 
663  1.045  303  303 
957  1.064  309  309 
TABLE X  3  
Melting Points  
Caprylic Acid  
P M kg/cm² 
R  T_{m}  Obs. (57) 
0  1.000  289  289 
190  1.014  293  293 
434  1.033  299  298 
669  1.050  303  303 
922  1.068  309  308 
TABLE X  5  
Melting Points  
Krypton  
P M kg/cm² 
R_{1}  R_{2}  2%  T_{m}  Obs. (58) 
0  1.000  1.000  0.0  116  116 
2  1.414  1.581  2.4  164  165 
4  1.732  2.000  27.1  209  209 
6  2.000  2.345  48.2  251  252 
8  2.236  2.646  66.5  291  293 
10  2.449  2.915  82.9  329  332 
12  2.646  3.162  100.0  367  370 
TABLE X  5  
Melting Points  
Xenon  
P M kg/cm² 
R_{1}  R_{2}  2%  T_{m}  Obs. (58) 
0  1.000  1.000  0.0  166  161 
1  1.183  1.265  19.4  199  198 
2  1.342  1.484  37.6  232  231 
3  1.483  1.674  54.1  263  262 
4  1.612  1.844  68.8  294  292 
5  1.732  2.000  82.3  324  322 
6  1.844  2.146  94.7  353  351 
7  1.949  2.281  100.0  379  379 
8  2.049  2.409  100.0  400  406 
TABLE X  4  
Melting Points  
Water (54) Ice III  
P M kg/cm² 
R  T_{m}  Obs. (57) 
0  1.000  241  
2  1.038  250  251 
2.5  1.048  253  253 
3  1.057  255  255 
3.5  1.066  257  256 
TABLE X  4  
Melting Points  
Water (54) Ice VI (481)  
P M kg/cm² 
R  T_{m}  Obs. (57) 
0  1.000  206  
4.5  1.237  255  255 
5  1.261  260  260 
5.5  1.283  264  266 
6  1.306  269  270 
6.5  1.329  274  274 
7  1.351  278  278 
8  1.394  287  286 
TABLE X  4  
Melting Points  
Water (54) Ice V  
P M kg/cm² 
R  T_{m}  Obs. (57) 
0  1.000  226  
3.5  1.129  255  256 
4  1.146  259  260 
4.5  1.163  263  263 
5  1.180  267  266 
5.5  1.197  271  269 
6  1.213  274  272 
TABLE X  4  
Melting Points  
Water (54) Ice VI (482)  
P M kg/cm² 
R  T_{m}  Obs. (57) 
0  1.000  237  
9  l.237  293  293 
10  1.261  299  299 
15  1.372  325  326 
16  1.394  330  330 
18  1.435  340  339 
20  1.476  350  347 
22  1.515  359  354 
TABLE X  4  
Melting Points  
Water (54) Ice VII  
P M kg/cm² 
R  T_{m}  Obs. (57) 
0  1.000  172.5  
22.4  2.125  367  355 
24  2.183  377  369 
26  2.254  389  384 
28  2.323  401  397 
30  2.389  412  410 
32  2.454  423  423 
34  2.517  434  434 
36  2.579  445  445 
38  2.639  455  456 
40  2.690  465  466 
TABLE X  6  
Melting Points  
Hdrogen (59)  
P M kg/cm² 
R  T_{m}  Obs. (57) 
0  l.000  14.00  14 
33.2  1.077  15.08  15 
67.3  1 150  16.10  16 
103.5  1:223  17.12  17 
142.3  1.297  18.16  18 
183.6  1.371  19.19  19 
227.1  1.445  20.23  20 
272.3  1.518  21.25  21 
318.6  1.589  22.25  22 
366.0  1.659  23.23  23 
415.0  1.729  24.20  24 
465.6  1.797  25.16  25 
518  1.866  26.12  26 
TABLE X  6  
Melting Points  
Xenon  
P M kg/cm² 
R_{1}  R_{2}  2%  T_{m}  Obs. (58) 
572  1.934  2.261  0.7  27.11  27 
628  2.002  2.348  1.5  28.10  28 
685  2.069  2.434  2.2  29.08  29 
744  2.136  2.519  3.0  30.06  30 
867  2.270  2.689  4.5  32.04  32 
996  2.402  2.856  6.0  34.01  34 
1131  2.534  3.021  7.4  35.97  36 
1274  2.605  3.186  8.9  37.96  38 
1422  2.795  3.350  10.4  39.94  40 
1821  3.118  3.753  14.0  44.89  45 
2258  3.438  4.150  17.5  49.87  50 
2735  3.755  4.544  21.0  54.89  55 
3249  4.070  4.935  24.5  59.95  60 
3801  4.382  5.321  27.9  65.02  65 
4389  4.693  5.704  31.4  70.14  70 
5014  5.002  6.085  34.8  75.30  75 
5674  5.308  6.463  38.2  80.48  s0 
TABLE X  7  
Initial Pressures  
acb  n  V_{0}  P_{0}  
Hydrogen  1½11  1  9.318  208.8 
111  1  9.318  139.2  
Helium (He4)  111  1  3.519  266.4 
(He3)  1½11  1  6.256  294.1 
Nitrogen  211  1  1.0048  1327 
Krypton  1½11  1  .3359  2066 
111  1  .3359  1378  
Xenon  1½11  1  .2407  2581 
111  1  .2407  1720  
Mercury  241  1½  .0702  20859 
Lead  461  2  .0876  40510 
C02  481  5  .5722  6180 
C014  441  6  .4108  3212 
Ice III  481  1  .7640  25486 
Ice V  481  2  .7640  12743 
Ice VI  481  3  .7640  8495 
482  3  .7640  16990  
Ice III  481  4  .7640  6371 
Ethyl alcohol  481  3  .9145  7537 
Butyl alcohol  481  3  .8526  7897 
Acetic acid  481  4  .6346  7211 
Butyric acid  481  4  .7043  6727 
Caproic acid  481  4  .7254  6596 
Caprylic acid  481  4  .7304  6566 
Benzene  481  5  .7208  5299 
oXylene  481  5  .7721  5061 
pXylene  481  6  .7937  4141 
Nitrobenzene  481  5  .5989  5996 
mNitrotoluene  481  5  .5977  6004 
pNitrotoluerie  481  5  .5893  6061 
Aniline  481  4  .6786  6895 
Chlorobenzene  481  4½  .5827  6784 
Bromobenzene  481  5½  .4360  6735 
Chloroform  481  7  .4315  5328 
Bromoform  481  10  .2364  5567 
Ethyl bromide  481  5½  .4305  6792 
REFERENCES
5. Larson, D. B., Compressibility of Solids, privately circulated paper available from the author on request.
50. Strong, H. M., and Bundy, F. P., Phys. Rev., 115278.
51. See discussion by Strong in Nature, 1831381.
52. MiIls, R. L., and Frilly, E. R., Phys. Rev., 99480. Numerical values supplied by Dr, Mills in private communication.
53. Holland, Huggill and Jones, Proc. Roy, Soc. (London), A 207268.
54. Bridgman, P. W., various, For a bibliography of Bridgman's reports see his book "The Physics of High Pressure". 0. Bell & Sons., London, 1958. All values in Table X2 are from Bridgman unless otherwise specified.
55. Robinson., D. W., Proc. Roy. Soc. (London), A 225393. Butuzov, V. P., Doklady Akad. Nauk, S.S.S.R., 911083
57. Deffet, Ll, Bull, Soc. Chim. Belg., 4441.
58. Lahr, P. H. and Eversolet W. 0., J. Chem. Engr. Data, 742.
59. Compiled from original sources by Wooley, Scott and Brickwedde, J. Res. N.B.S., 413790