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monosymmetric form which melts at 120°, but if heated rapidly point of greatest constancy of temperature in the case of homo the rhombic form melts at 114.5. The two forms, rhombic and geneous crystalline solids. monosymmetric, can exist in equilibrium at 95-6°, the transition

Fusing Points of Common Metcls. point at which they have the same vapour pressure. Similarly Mercury


630 a solid solution of carbon in iron, when cooled slowly, passes




Sodium at about 700° C., with considerable evolution of heat, into the


962 Tin.

231.90 Gold form of “pearlite," which is soft when cold, but if rapidly chiled

1064 Bismuth


1082" the carbon remains in solution and the steel is very hard (see Cadmium


1427 also Alloys).



· 1535 In the case of crystalline fusion it is necessary to distinguish



1710° two cases, the homogeneous and the heterogeneous. In the first The above table contains some of the most recent values of case the composition of the solid and liquid phases are the same, fusing points of metals determined (except the first three and and the temperature remains constant during the whole process the last three) with platinum thermometers. The last three of fusion. In the second case the solid and liquid phases differ values are those obtained by extrapolation with platinum. in composition; that of the liquid phase changes continuously, rhodium and platinum-iridium couples. (Sce Harker, Proc. and the temperature does not remain constant during the fusion. Roy. Soc. A 76, p. 235, 1905.) Some doubt has recently been The first case comprises the fusion of pure substances, and raised with regard to the value for platinum, which is much that of eutectics, or cryohydrates; the second is the general lower than that previously accepted, namely 1775o. case of an alloy or a solution. These, have been very fully 3. Superfusion, Supersaturation.-It is generally possible to studied and their phenomena greatly elucidated in recent cool a liquid several degrees below its normal freezing point years.

without a separation of crystals, especially if it is protected There is also a sub-variety of amorphous fusion, which may from agitation, which would assist the molecules to rearrange be styled colloid or gelatinous, and may be illustrated by the themselves. A liquid in this state is said to be “undercooled " behaviour of solutions of water in gelatin. Many of these jellies or "superfused.” The phenomenon is even more familiar in melt at a fairly definite temperature on heating, and coagulate or the case of solutions (e.g. sodium sulphate or acetate) which may set at a definite temperature on cooling. But in some cases the remain in the "metastable." condition for an indefinite time process is not reversible, and there is generally marked hysteresis, if protected from dust, &c. The introduction into the liquid the temperature of setting and other phenomena depending on under this condition of the smallest fragment of the crystal, the rate of cooling. This case has not yet been fully worked out; with respect to which the solution is supersaturated, will probut it appears probable that in many cases the jelly possesses duce immediate crystallization, which will continue until the a spongy framework of solid, holding liquid in its meshes or temperature is raised to the saturation point by the liberation interstices. It might be regarded as a case of “ heterogeneous" of the latent heat of fusion. The constancy of temperature at amorphous fusion, in which the liquid separates into two phases the normal freezing point is due to the equilibrium of exchange of different composition, one of which solidifies before the other. existing between the liquid and solid. Unless both solid and The two phases cannot, as a rule, be distinguished optically, liquid are present, there is no condition of equilibrium, and the but it is generally possible to squeeze out some of the liquid temperature is indeterminate. phase when the jelly has set, which proves that the substance It has been shown by H. A. Miers (Jour. Chem. Soc., 1906, 89, is not really homogeneous. In very complicated mixtures, such p. 413) that for a supersaturated solution in metastable equilias acid lavas or slags containing a large proportion of silica, brium there is an inferior limit of temperature, at which it passes amorphous and crystalline solidification may occur together. into the “ labile" state, i.e. spontaneous crystallization occurs In this case the crystals separate first during the process of throughout the mass in a fine shower. This seems to be analogous cooling, the mother liquor increases gradually in viscosity, and to the fine misty condensation which occurs in a supersaturated finally sets as an amorphous ground-mass or matrix, in which vapour in the absence of nuclei (see VAPORIZATION) when the crystals of different kinds and sizes, formed at different stages supersaturation exceeds a certain limit. of the cooling, remain embedded. The formation of crystals in an amorphous solid after it has set is also of frequent fusing-point depends on the change of volume during fusion. Sub

4. Effect of Pressure on the F.P.- The effect of pressure on the It is termed devitrification, but is a very slow stances which expand on freezing, like ice, have their freezing points process unless the solid is in a plastic state.

lowered by increase of pressure; substances which expand on 2. Homogeneous Crystalline Fusion.—The fusion of a solid of fusing, like wax, have their melting points raised by pressure.

In each case the effect of pressure is to retard increase of volume. this type is characterized most clearly by the perfect constancy This effect was first predicted by James Thomson on the analogy of temperature during the process. In fact, the law of constant of the effect of pressure on the boiling point, and was numerically temperature, which is generally stated as the first of the so-called verified by Lord Kelvin in the case of ice, and later by Bunsen in " laws of fusion," does not strictly apply except to this case. I change of the F.P. is calculated may be proved by a simple applica.

the case of paraffin and spermaceti. The equation by which the The constancy of the F.P. of a pure substance is so characteristiction of the Carnot cycle, exactly as in the case of vapour and liquid. that change of the F.P. is often one of the most convenient tests (See THERMODYNAMICS.) If I be the latent heat of fusion in of the presence of foreign material. In the case of substances mechanical units, o' the volume of unit mass of the solid, and a like ice, which melt at a low temperature and are easily

obtained that of the liquid, the work done in an elementary Carnot cycle of in large quantities in a state of purity, the point of fusion may to produce a change do in the F.P. Since the ratio

of the work be very accurately determined by observing the temperature difference or cycle-area to the heat-transferred L must be equal to of an intimate mixture of the solid and liquid while slowly 2010, we have the relation melting as it absorbs heat from surrounding bodies. But in the

do/dp =0(v' - ')/L.

(1) majority of cases it is more convenient to observe the freezing The sign of do, the change of the F.P., is the same as that of the point as the liquid is cooled. By this method it is possible to

change of volume (v - O'). Since the change of volume seldom

exceeds 0:1 c.c. per gramme, the change of the F.P. per atmosphere ensure perfect uniformity of temperature throughout the mass is so small that it is not as a rule necessary to take account of variaby stirring the liquid continuously during the process of freczing, tions of atmospheric pressure in observing a freezing point. A whereas it is difficult to ensure uniformity of temperature in

variation of 1 cm. in the height of the barometer would correspond melting a solid, however gradually the heat is supplied, unless limits of accuracy of most observations. Although the effect of

to a change of .0001°C. only in the F.P. of ice. This is far beyond the the solid can be mixed with the liquid. It is also possible to pressure is so small, it produces, as is well known. remarkable observe the F.P. in other ways, as by noting the temperature results in the motion of glaciers, the moulding and regelation of at the moment of the breaking of a wire, of the stoppage of a explain the apparent inversion of the order of crystallization in stirrer, or of the maximum rate of change of volume, but these rocks like granite, in which the arrangement of the crystals indicates methods are generally less certain in their indications than the I that the quartz matrix solidified subsequently to the crystals of


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felspar, mica or hornblende embedded in it, although the quartz | vertical line ND, a point D is generally reached at which the has a higher melting point. It is contended that under enormous solution becomes“ saturated." The dissolved substance or pressure the freezing points of the more fusible constituents might be raised above that of the quartz, if the latter is less affected by

“solute" then separates out as the solution is further cooled, pressure bias Toh us Bunsen i faunad noso Feitice of paraffin waxoo in me and the concentration diminishes with fall of temperature in spheres the two melted at the same temperature. At higher pressures the solubility curve. Though often called by different names, silicates, however, is much smaller, and it is not so easy to explain the two curves AC and CB are a change of several hundred degrees in the F.P. It seems more essentially of a similar nature. likely in this particular case that the order of crystallization depends To take the case of an aqueous on the action of superheated water or steam at high temperatures solution of salt as an example, and pressures, which is well known to exert a highly solvent and

along CB the solution is saturmetamorphic action on silicates.

5. Variation of Lalent Heat.-C. C. Person in 1847 endeavoured to ated with respect to salt, along show by the application of the first law of thermodynamics that | AC the solution is saturated with the increase of the latent heat per degree should be equal to the respect to ice. When the point difference (s'-s') between the specific heats of the liquid and solid.

C is reached along either curve, If, for instance, water at o° C. were first frozen and then cooled to -1°C., the heat abstracted per gramme would be (L' +s't) calories. the solution is saturated with But if the water were first cooled to -1°C., and then frozen at -1°C., respect to both salt and ice. by abstracting heat L', the heat abstracted would be L'+s". The concentration cannot vary Assuming that the heat abstracted should be the same in the two


and the temperature cases, we evidently obtain L'-L' = (s' --s')l. This theory has been approximately verihed by Petterson, by observing the freezing of a

remains constant, while the salt

Fig. 1.-F.P. or Solubility liquid cooled below its normal F.P. (Jour. Chem. Soc. 24, p. 151). and ice crystallize out together, Curve: simple case. But his method does not represent the true variation of the latent maintaining the exact proportions heat with temperature, since the freezing, in the case of a superfused in which they exist in the solution. The resulting solid was liquid, really takes place at the normal freezing point. A quantity termed a cryohydrate by F. Guthrie, but it is really an intimate and freezing at oo, and s' in cooling the ice to -1. The latent heat mixture of two kinds of crystals, and not a chemical compound L'at -t does not really enter into the experiment. In order to or hydrate containing the constituents in chemically equivalent make the liquid freeze at a different temperature, it is necessary to subject it to pressure, and the effect of the pressure on the latent proportions. The lowest temperature attainable by means of a heat cannot be neglected. The entropy of a liquid at its F.P. freezing mixture is the temperature of the F.P. of the correreckoned from any convenient zero to in the solid state may be sponding cryohydrate. In a mixture of salt and ice with the least represented by the expression

trace of water a saturated brine is quickly formed, which dissolves O'-do = ss'd0/0+L/0.


the ice and falls rapidly in temperature, owing to the absorption Since odd"/d6 = s', we obtain by differentiation the relation

of the latent heat of fusion. So long as both ice and salt are dLido =s'-s'+110,

(3) present, if the mixture is well stirred, the solution must necessarily which is exactly similar to the equation for the specific heat of a become saturated with respect to both ice and salt, and this can va pour

maintained in the saturated condition., !! we suppose that only occur at the cryohydric temperature, at which the two the specific heats s' and s' of the solid and liquid at equilibrium pressure are nearly the same as those ordinarily observed at con.

curves of solubility intersect. stant pressure, the relation (3) differs from that of Person only by The curves in fig. I also illustrate the simplest type of freezing the addition of the term L/0. Since s' is greater than s' in all cases point curve in the case of alloys of two metals A and B which hitherto investigated, and L/is necessarily positive, it is clear that do not form mixed crystals or chemical compounds. The alloy the latent heat of fusion must increase with rise of temperature, or diminish with fall of temperature. It is possible to imagine the E. P. corresponding to the cryohydrate, possessing the lowest melting so lowered by pressure (positive or negative) that the latent heat point, is called the eutectic alloy, as it is most easily cast and should vanish, in which case we should probably obtain a continuous worked. It generally possesses a very fine-grained structure, passage from the liquid to the solid state similar to that which and is not a chemical compound. (See Alloys.) occurs in the case of amorphous substances. According to equation (3), the rate of change of the latent heat of water is approximately

To obtain a complete F.P. curve even for a binary alloy is a 0.80 calorie per degree at o° C. (as compared with 0.50, Person). laborious and complicated process, but the information contained if we assume s' =1, and s' =0.5. Putting (s'-s') = 0.5 in equation in such a curve is often very valuable. It is necessary to operate (2). we find L=o at -160° C. approximately. but no stress can be with a number of different alloys of suitably chosen composition, laid on this estimate, as the variation of (s" -s') is so uncertain.

and to observe the freezing points of cach separately. Each alloy 6. Freezing of Solutions and Alloys. -The phenomena of should also be analysed after the process is there is any risk of freezing of heterogencous crystalline mixtures may be illustrated its composition having been altered by oxidation or otherwise. by the case of aqueous solutions and of metallic solutions or The freezing points are generally best alloys, which have been most widely studied. The usual effect determined by observing the gradual of an impurity, such as salt or sugar in solution in water, is to cooling of a considerable mass, which took lower the freezing point, so that no crystallization occurs until is well stirred so long as it remains the temperature has fallen below the normal F.P. of the pure liquid. The curve of cooling may most solvent, the depression of F.P. being nearly proportional to the conveniently be recorded, either photoconcentration of the solution. When freezing begins, the solvent graphically, using a thermocouple and generally separates out from the solution in the pure state. This galvanometer, as in the method of Sir separation of the solvent involves an increase in the strength W. Roberts-Austen, or with pen and coook of the remaining solution, so that the temperature does not ink, a platinum thermometer is availremain constant during the freezing, but continues to fall as able, according to the method put in many more of the solvent is separated. There is a perfectly definite practice by C. T. Heycock and F. H. relation between temperature and concentration at each stage Neville. A typical set of curves obtained of the process, which may be represented in the form of a curve in this manner is shown in fig. 2. When Fig. 2.-Cooling Curves as AC in fig. 1, called the freezing point curve. The equilibrium the pure metal A in cooling reaches its of Alloys: typical case. temperature, at the surface of contact between the solid and F.P. the temperature suddenly becomes liquid, depends only on the composition of the liquid phase and stationary, and remains accurately constant for a considerable not at all on the quantity of solid present. The abscissa of the period. Often it falls slightly below the F.P. owing to superF.P. curve represents the composition of that portion of the fusion, but rises to the F.P. and remains constant as soon as original solution which remains liquid at any temperature. If freezing begins. The second curve shows the cooling of A with instead of starting with a dilute solution we start with a strong 10% of another metal B added. The freezing begins at a lower solution represented by a point N, and cool it as shown by the temperature with the separation of pure A. Tbe temperature

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no longer remains constant during freezing, but falls more and solution or the molecular dissociation changes. The most un. more rapidly as the proportion of B in the liquid increases. certain factor in the formula is the molecular weight M, since the

molecule in solution may be quite different from that denoted by When the eutectic temperature is reached there is a second the chemical formula of the solid. In many cases the molecule of F.P. or arrest at which the whole of the remaining liquid solidifies. a metal in dilute solution in another metal is either monatomic, or With 20% of B the first F.P. is further lowered, and the tempera- forms a compound molecule with the solvent containing one atom ture falls faster. The eutectic F.P. is of longer duration, but given by putting the atornic weight for M. In other cases, as still at the same temperature. For an alloy of the composition | Eu, Hg. Zn, in solution in cadmium, the depression of the F.P. of the eutectic itself there is no arrest until the eutectic tempera- per atom, according to Heycock and Neville, is only half as great, ture is reached, at which the whole solidifies without change of which would imply a diatomic molecule. Similarly As and Au in

Cd appear to be triatomic, and Sn in Pb tetratomic. Intermediate temperature. There is a great advantage in recording these

cases may occur in which different molecules exist together in curves automatically, as the primary arrest is often very slight, equilibrium in proportions which vary according to the temperature and difficult to observe in any other way.

and concentration. The most familiar case is that of an electrolyte, 7. Change of. Solubility with Temperature. The lowering of the in which the molecule of the dissolved substance is partly dissociated F.P. of a solution with increase of concentration, as shown by the into ions. In such cases the degree of dissociation may be estimated F.P. or solubility curves, may be explained and calculated by by observing the depression of the F.P., but the results obtained equation (1) in terms of the osmotic pressure of the dissolved sub.

cannot always be reconciled with those deduced by other methods, stance by analogy, with the effect of mechanical pressure.

It is such as measurement of electrical conductivity, and there are many possible in salt solutions to strain out the salt mechanically by a

difficulties which await satisfactory interpretation. suitable filter or "semi-permeable membrane," which permits the

Exactly similar relations to (8) and (9) apply to changes of boiling water to pass, but retains the salt. To separate i gramme of point or vapour pressure produced by substances in solution (see salt requires the performance of work pv against the osmotic | VAPORIZATION), the laws of which are very closely connected with pressure P, where V is the corresponding diminution in the volume

the corresponding phenomena of fusion; but the consideration of of the solution. In dilute solutions, to which alone the following the vapour phase may generally be omitted in dealing with the fusion calculation can be applied, the volume V is the reciprocal of the

of mixtures where the vapour pressure of either constituent is small. concentration C of the solution in grammes per unit volume, and the osmotic pressure P is equal to that of an equal number of mole.

8. Hydrales. The simple case of a freezing point curve, cules of gas in the same space, and may be deduced from the usual illustrated in fig. 1, is generally modified by the occurrence equation of a gas,

of compounds of a character analogous to hydrates of soluble P=RO/VM = ROC/M,


salts, in which the dissolved substance combines with one or where M is the molecular weight of the salt in solution, 0 the absolute

more molecules of the solvent. These hydrates may exist as temperature, and R a constant which has the value 8:32 joules, or nearly 2 calories, per degree c. It is necessary to consider compound molecules in the solution, but their composition two cases, corresponding to the curves CB and AB in fig. 1, in cannot be demonstrated unless they can be separated in the solid which the solution is saturated with respect to salt and water state. Corresponding to each crystalline hydrate there is generrespectively. To facilitate description we take the case of a salt ally a separate branch of the solubility curve along which the dissolved in water, but similar results apply to solutions in other crystals of the hydrate are in equilibrium with the saturated liquids and alloys of metals.

(a) If unit mass of salt is separated in the solid state from a satur. solution. At any given temperature the hydrate possessing the ated solution of salt (curve CB) by forcing out through a semi- least solubility is the most stable. If two are present in contact permeable membrane against the osmotic pressure P the corre. sponding volume of water V in which it is dissolved, the heat evolved less soluble will be formed at its expense until the conversion

with the same solution, the more soluble will dissolve, and the the work done PV. Writing (Q+PV) for L, and for (o" --J") in is complete. The two hydrates cannot be in equilibrium with the equation (1), and substituting P for p, we obtain

same solution except at the temperature at which their solu(+PV = VodP/d9,

(5) bilities are equal, i.e. at the point where the corresponding curves which is equivalent to equation (1), and may be established by of solubility intersect. This temperature is called the “ Transisimilar reasoning. Substituting for P and Vin terms of C from tion Point.' In the case of ZnSO,, as shown in fig. 3, the heptaequation (4), ir is measured in calories, R=2, and we obtain

hydrate, with seven molecules of water, is the least soluble QC=200C/do,

hydrate at ordinary temwhich may be integrated, assuming O constant, with the result 2 log.C"/C' =Q/0'-Qo',

peratures, and is generally (7)

deposited from saturated where C', C' are the concentrations of the saturated solution corresponding to the temperatures o' and ". This equation may be

solutions. Above 39° C., employed to calculate the latent heat of solution from two ob- however, the hexahydrate, servations of the solubility. It follows from these equations that with six molecules, is less Qis of the same sign as dC do, that is to say, the solubility increases soluble, and a rapid conversaturated solution, which is the usual case. "If, on the other hand, sion of the hepta. into the heat is liberated on solution, as in the case of caustic potash or hexahydrate occurs if the sulphate of calcium, the solubility diminishes with rise of temperature. former is heated above the (b) In the case of a solution saturated with respect to ice (curve transition point. The solu

FIG. 3.-Solubility Curves of

Hydrates. we obtain a precisely similar equation to (5), but with L the latest bility of the hexahydrate is heat of fusion of water instead of Q, and y instead of V. If the greater than that of the heptahydrate below 39°, but increases solution is dilute, we may neglect the external work Pv in comparison more slowly with rise of temperature. At about 80° C. with L, and also the heat of dilution, and may write Pll for dP/do. the hexahydrate gives place to the monohydrate, which where i is the depression of the F.P. below that of the pure solvent. Substituting for P in terms of V from equation (4), we obtain

dissolves in water with evolution of heåt, and diminishes in 1 = 28-v/LVM = 20w/LWM,


solubility with rise of temperature. Intermediate hydrates where W is the weight of water and w that of salt in a given volume exist, but they are more soluble, and cannot be readily isolated. of solution. If M grammes of salt are dissolved in 100 of water,

Both the mono- and hexahydrates are capable of existing in w = M and W = 100. The depression of the F.P. in this case is equilibrium with saturated solutions at temperatures far below called by van t' Hoff the “ Molecular Depression of the F.P." and their transition points, provided that the less soluble hydrate is given by the simple formula 1= .020/L.

is not present in the crystalline form. The solubility curves can

(9) Equation (8) may be used to calculate L or M, if cither is known,

therefore be traced, as in fig. 3, over an extended range of temfrom observations of I, O and w/W. The results obtained are perature. The cquilibrium of each hydrate with the solvent, sufficiently approximate to be of use in many cases in spite of the considered separately, would present a diagram of two branches rather liberal assumptions and approximations effected in the similar to fig. 1, but as a rule only a small portion of each curve course of the reasoning. In any case the equations give a simple can be realized, and the complete solubility curve, as experi. theoretical basis with which to compare experimental data in order to estimate the order of crror involved in the assumptions. We mentally determined, is composed of a number of separate may thus estimate the variation of the osmotic pressure from the pieces corresponding to the ranges of minimum solubility of value given by the gaseous equation, as the concentration of the different hydrates. Failure to recognize this coupled with the


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fact that in strong and viscous solutions the state of equilibrium FÜSSEN, a town of Germany, in the kingdom of Bavaria, at is but slowly attained, is the probable explanation of the remark the foot of the Alps (Tirol), on the Lech, 2500 ft. above the sea, able discrepancies existing in many recorded data of solubility with a branch line to Oberdorf on the railway to Augsburg. Pop. Transition Points of Hydrates.

4000. It has six Roman Catholic churches, a Franciscan monasNa,Cro 10H,0. 19.90 NaBr-2H,0

. .50.70

tery and a castle. Rope-making is an important industry, Na,SO 10H,0 32.4 MnCl2.4.0

The castle, lying on a rocky eminence, is remarkable for the Na.Co,.10H,0


• 734 peace signed here on the 22nd of April 1745 between the elector Na S,Oz:5H30

Ba(OH):8H,0 77.9°

Maximilian III., Joseph of Bavaria and Maria Theresa. Two The transition points of the hydrates given in the above list miles to the S.E., immediately on the Austrian frontier, romantiRichards, Proc. Amer. Acad., 1899, 34, p. 377) afford well.cally situated on rock overlooking the Schwanensee, is the marked constant temperatures which can be utilized as fixed magnificent castle of Hohenschwangau, and a little to the north, points for experimental parposes.

on the site of an old castle, that of Neuschwanstein, built by 9. Formation of Mixed Crystals.--An important exception Louis II. of Bavaria. to the general type already described, in which the addition of a See H. Feistle, Füssen und Umgebung (1898). dissolved substance lowers the F.P. of the solvent, is presented PUST, JOHANN ?-1466), early German printer, belonged by the formation of mixed crystals, or "soiid solutions,” in to a rich and respectable burgher family of Mainz, which is known which the solvent and solute occur mixed in varying proportions to have flourished from 1423, and to have held many civil and This isomorphous replacement of one substance by another, in religious offices. The name was always written Fust, but in the same crystal with little or no change of form, has long been 1500 Johann Schöffer, in dedicating the German translation of known and studied in the case of minerals and salts, but the Livy to the emperor Maximilian, called his grandfather Faust, relations between composition and melting point have seldom and thenceforward the family assumed this name, and the Fausts been investigated, and much still remains obscure. In this case

of Aschaffenburg, an old and quite distinct family, placed the process of freezing does not necessitate the performance of Johann Fust in their pedigree.' Johann's brother Jacob, a work of separation of the constituents of the solution, the F.P: goldsmith, was one of the burgomasters in 1462, when Mainz is not necessarily depressed, and the effect cannot be calculated

was stormed and sacked by the troops of Count Adolf of Nassau, by the usual formula for dilute solutions. One of the simplest on which occasion he seems to have perished (see a document, types of F.P. curve which may result from the occurrence of dated May 8, 1463, published by Wyss in Quartalbl. des hisi. mixed crystals is illustrated by the case of alloys of gold and Vereins für Hessen, 1879, p. 24). There is no evidence that, as silver, or gold and platinum, in which the F.P. curve is nearly is commonly asserted, Johann Fust was a goldsmith, but he a straight line joining the freezing-points of the constituents. appears to have been a money-lender or banker. On account of The equilibrium between the solid and liquid, in both of which his connexion with Gutenberg (9.v.), he has been represented the two metals are capable of mixing in all proportions, bears in by some as the inventor of printing, and the instructor as well as this case an obvious and close analogy to the equilibrium between the partner of Gutenberg, by others as his patron and benefactor, a mixed liquid (e.g. alcohol and water) and its vapour. In the who saw the value of his discovery and supplied him with means latter case, as is well known, the vapour will contain a larger to carry it out, whereas others paint him as a greedy and proportion of the more volatile constituent. Similarly in the case crafty speculator, who took advantage of Gutenberg's necessity of the formation of mixed crystals, the liquid should contain and robbed him of the fruits of his invention. However this may a larger proportion of the more fusible constituent than the solid be, the Helmasperger document of November 6, 1455, shows with which it is in equilibrium. The composition of the crystals that Fust advanced money to Gutenberg (apparently 800 which are being deposited at any moment will, therefore, guilders in 1450, and another 800 in 1452) for carrying on his necessarily change as solidification proceeds, following the work, and that Fust, in 1455, brought a suit against Gutenberg change in the composition of the liquid, and the temperature to recover the money he had lent, claiming 2020 (more correctly will fall until the last portions of the liquid to solidify will consist 2026) guilders for principal and interest. It appears that he had chiefly of the more fusible constituent, at the F.P. of which the

not paid in the 300 guilders a year which he had undertaken to solidification will be complete. If, however, as seems to be furnish for expenses, wages, &c., and, according to Gutenberg, frequently the case, the composition of the solid and liquid phases had said that he had no intention of claiming interest. The suit do not greatly differ from each other, the greater part of the

was apparently decided in Fust's favour, November 6, 1455, solidification will occur within a comparatively small range of in the refectory of the Barefooted Friars of Mainz, when Fust temperature, and the initial F.P. of the alloy will be well marked. made oath that he himself had borrowed 1550 guilders and It is possible in this case to draw a second curve representing given them to Gutenberg. There is no evidence that Fust, as the composition of the solid phase which is in equilibrium with is usually supposed, removed the portion of the printing materials the liquid at any temperature. This curve will not represent the covered by his mortgage to his own house, and carried on printing average composition of the crystals, but that of the outer coating there with the aid of Peter Schöffer, of Gernsheim (who is known only which is in equilibrium with the liquid at the moment. to have been a scriptor at Paris in 1449), to whom, probably H. W. B. Roozeboom (Zeil. Phys. Chem. xxx. p. 385) has about 1455, he gave his only daughter Dyna or Christina in attempted to classify some of the possible cases which may marriage. Their first publication was the Psalter, August 14, occur in the formation of mixed crystals on the basis of J. W.

1457, a folio of 350 pages, the first printed book with a complete Gibbs's thermodynamic potential, the general properties of which date, and remarkable for the beauty of the large initials printed may be qualitatively deduced from a consideration of observed each in two colours, red and blue, from types made in two phenomena. But although this method may enable us to classify pieces. The Psalter was reprinted with the same types, 1459 different types, and even to predict results in a qualitative | (August 29), 1490, 1502 (Schöffer's last publication) and 1516. manner, it does not admit of numerical calculation similar to Fust and Schöffer's other works are given below. In 1464 Adolf equation (8), as the Gibbs's function itself is of a purely abstract

'This date is uncertain; some place the marriage in 1453 or soon nature and its form is unknown. There is no doubt that the after, others about 1464. It is probable that Fust alluded to this formation of mixed crystals may explain many apparent relationship when he spoke of Schöffer as pueri mei in the colophons anomalies in the study of F.P. curves.

The whole subject has

of Cicero's De officiis of 1465 and 1466.

* This method was patented in England by Solomon Henry in been most fruitful of results in recent years, and appears full of 1789, and by Sir William Congreve in 1819. promise for the future.

• (3) Durandus, Rationale divinorum officiorum (1459), folio, 160 For further details in this particular branch the reader may consult leaves; (4) the Clemenline Constitutions, with the gloss of Johannes a report by Neville (Bril. Assoc. Rep., 1900), which contains numerous Andreae (1460). 51 leaves; (5) Biblia Sacra Latina (1462), folio, references to original papers by Roberts-Austen, Le Chatelier, 2 vols., 242 and 239 leaves, 48 lines to a full page; (6) the Sixth Roozeboom and others. For the properties of solutions see SOLU. Book of Decretals, with Andreae's gloss, 17th December 1465, folio,

(H. L. C.) 141 Icaves; (7) Cicero, De officiis (1465), 410, 88 leaves, the first


of Nassau appointed for the parish of St Quintin three Baumeisters theories. When he revised the book in 1875, his modifications (master-builders) who were to choose twelve chief parishioners were very slight, and it is conceivable that, had he recast it, as assistants for life. One of the first of these “ Vervaren," as he often expressed the desire to do in the last years of his life, who were named on May-day 1464, was Johannes Fust, and in he would not have abandoned any part of his fundamental 1467 Adam von Hochheim was chosen instead of “the late thesis. The work is now largely superseded. (selig) Johannes Fust. Fust is said to have gone to Paris in 1466 Fustel de Coulanges was the most conscientious of men, the and to have died of the plague, which raged there in August and most systematic and uncompromising of historians. Appointed September. He certainly was in Paris on the 4th of July, when to a lectureship at the Ecole Normale Supérieure in February he gave Louis de Lavernade of the province of Forez, then 1870, to a professorship at the Paris faculty of letters in 1875, chancellor of the duke of Bourbon and first president of the and to the chair of medieval history created for him at the parliament of Toulouse, a copy of his second edition of Cicero, Sorbonne in 1878, he applied himself to the study of the political as appears from a note in Lavernade's own hand at the end of institutions of ancient France. The invasion of France by the book, which is now in the library of Geneva. But nothing the German armies during the war of 1870-71 attracted his further is known than that on the 30th of October, probably attention to the Germanic invasions under the Roman Empire. in 1471, an annual mass was instituted for him by Peter Schöffer, Pursuing the theory of J. B. Dubos, but singularly transforming Conrad Henlif (for Henckes, or Henckis, Schöffer's partner ? it, he maintained that those invasions were not marked by the who married Fust's widow about 1468') and Johann Fust (the violent and destructive character usually attributed to them; son), in the abbey-church of St Victor of Paris, where he was that the penetration of the German barbarians into Gaul was a buried; and that Peter Schöffer founded a similar memorial slow process; that the Germans submitted to the imperial service for Fust in 1473 in the church of the Dominicans at administration; that the political institutions of the Merovingians Mainz (Bockenheimer, Gesch. der Stadt Mainz, iv. 15).

had their origins in the Roman laws at least as much as, if not Fust was formerly often confused with the famous magician more than, in German usages; and, consequently, that there was Dr Johann Faust, who, though an historical figure. had nothing no conquest of Gaul by the Germans. This thesis he sustained, to do with him (see Faust).

brilliantly in his Histoire des institutions politiques de l'ancienne See further the articles GUTENBERG and TYPOGRAPHY. (J. H. H.) France, the first volume of which appeared in 1874. It was the

FUSTEL DE COULANGES, NUMA DENIS (1830-1889), French author's original intention to complete this work in four volumes, historian, was born in Paris on the 18th of March 1830, of Breton but as the first volume was keenly attacked in Germany as well descent. After studying at the Ecole Normale Supérieure he as in France, Fustel was forced in self-defence to recast the book was sent to the French school at Athens in 1853, directed some entirely. With admirable conscientiousness he re-examined excavations in Chios, and wrote an historical account of the all the texts and wrote a number of dissertations, of which, island. After his return he filled various educational offices, though several (e.g. those on the Germanic mark and on the and took his doctor's degree with two theses, Quid Vestae cultus allodium and beneficium) were models of learning and sagacity, in institulis velcrum privatis publicisque valuerit and Polybe, all were dominated by his general idea and characterized by a ou la Grèce conquise par les Romains (1858). In these works total disregard for the results of such historical disciplines as his distinctive qualities were already revealed. His minute diplomatic. From this crucible issued an entirely new work, knowledge of the language of the Greek and Roman institutions, less well arranged than the original, but richer in facts and coupled with his low estimate of the conclusions of contemporary critical comments. The first volume was expanded into three scholars, led him to go direct to the original texts, which he read volumes, La Gaule romaine (1891), L'Invasion germanique et without political or religious bias. When, however, he had la fin de l'empire(1891)and La Monarchie franque(1888), followed succeeded in extracting from the sources a general idea that by three other volumes, L'Alleu et le domaine rural pendant seemed to him clear and simple, he attached himself to it as if 10 l'Epoque mérovingienne (1889), Les Origines du système féodal: the truth itself, employing dialectic of the most penetrating, le bénéfice et le patronal ...(1890and Les Transformations de subtle and even paradoxical character in his deduction of the le royauté pendant l'époque carolingienne (1892). Thus, in six logical consequences. From 1860 to 1870 he was professor of volumes, he had carried the work no farther than the Carolingian history at the faculty of letters at Strassburg, where he had a period. The result of this enormous labour, albeit worthy of a brilliant career as a teacher, but never yielded to the influence great historian, clearly showed that the author lacked all sense exercised by the German universities in the field of classical and of historical proportion. He was a diligent secker after the truth, Germanic antiquities.

and was perfectly sincere when he informed a critic of the exact It was at Strassburg that he published his remarkable volume number of "truths ” he had discovered, and when he remarked La Cité antique (1864), in which he showed forcibly the part to one of his pupils a few days before his death, " Rest assured played by religion in the political and social evolution of Greece that what I have written in my book is the truth.” Such superb and Rome. Although his making religion the sole factor of this self-confidence can accomplish much, and it undoubtedly helped evolution was a perversion of the historical facts, the book was to form Fustel's talent and to give to his style that admirable so consistent throughout, so full of ingenious ideas, and written concision which subjugates even when it fails to convince; in so striking a style, that it ranks as one of the masterpieces of but a student instinctively distrusts an historian who settles the the French language in the 19th century. By this literary most controverted problems with such impassioned assurance. merit Fustel set little store, but he clung tenaciously to his The dissertations not embodied in his great work were collected edition of a Latin classic and the first book containing Greek char. by himself and (after his death) by his pupil, Camille Jullian, acters, while in the colophon Fust for the first time calls Schöffer and published as volumes of miscellanies: Recherches sur

pucrum suum "; (8) the same, 4th February 1466: (9) Grammatica quelques problèmes d'histoire (1885), dealing with the Roman rhytmica (1466), folio, !I leaves. They also printed in 1461-4462colonate, the land system in Normandy, the Germanic mark, and several papal bulls, proclamations of Adolf of Nassau, &c. Nothing the judiciary organization in the kingdom of the Franks; is known to have appeared for three years after the storming and capture of Mainz in 1462.

Nouvelles recherches sur quelques problèmes d'histoire (1891); Some confusion in the history of the Fust family has arisen and Questions historiques (1893), which contains his paper on since the publication of Bernard's Orig. de l'imprimerie (1853). Chios and his thesis on Polybius. On p. 262, vol. i. he gave an extract from the correspondence between Oberlin and Bodmann (now preserved in the Paris Nat. Library).

His life was devoted almost entirely to his teaching and his from which it would appear that Peter Schoffer was the son-in-law, books. In 1875 he was elected member of the Académie des not of Johann Fust, but of a brother of his, Conrad Fust. Of the Sciences Morales, and in 1880 reluctantly accepted the post latter, however, no other trace has been found, and he is no doubt of director of the Ecole Normale. Without intervening personally a fiction of F. J. Bodmann, who, partly basing himself on the Conrad" (Henlil, or Henckis) mentioned above, added the rest

in French politics, he took a keen interest in the questions of to gratify Oberlin (sce Wyss in Quartalbläller des kish. Vereins Jür administration and social reorganization arising from the fall Hessen, 1879, p. 17).

of the imperialist régime and the disasters of the war. He wished

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