pure and hence the results are only approximate, and the percentages obtained do not represent the true composition of the mineral. The composition in many cases, especially when silica, alumina and water are present together, is extremely complicated, part of the alumina performing basic and part acid functions.

Frequently also a metal is replaced by a similar metal not in atomic proportions, thus ferrous iron may replace calcium and ferric iron aluminium in any proportion; this is expressed in formulæ by [FeCa] [Fe̱A1].

Silicates are classified by mineralogists according to their "oxygen-ratio," that is by the ratio between the number of atoms of oxygen supposed to be in combination with the metals, and the number of atoms of oxygen supposed to be in combination with silicon.

Thus calcium metasilicate CaSiO, is found native as Wollastonite, and its formula is written CaO.SiO,, the oxygenratio being 1 2. In Diopside more or less of the calcium is replaced, by magnesium and the formula is written

[CaMg] O. SiO,.

Recently however it has been proposed to bring mineralogical formulæ more into accordance with modern chemical theories, by discarding the term 'oxygen-ratio' and replacing it by 'Quantivalent ratio,' which is intended to mean the ratio of the metallic bodies present to the non-metallic bodies present in respect of valency.

Thus Wollastonite would now be regarded as a dyad metal, calcium, united by two atoms of oxygen to an atom of tetrad silicon, two atomicities of which are also satisfied by oxygen. This is expressed by the formula Ca"O,SiO. And members of the garnet family are expressed by

([Ca]0), ([A1,]O2) (SiO,), or [Ca], [A1,ˇ] 0, Si̟ ̧1.

From the use of the oxygen-ratio it became customary to calculate the results of analysis not into percentages of elements, but into percentages of oxides, and in all subsequent calculations to treat the oxides just as if they were elements (SiO, = 60. A1,0,–102. CaO = 56 &c.). The formulæ then were obtained by processes similar to those given in the last section.

3

Thus to find the formula of chrysocolla which contains:

Hence the formula of chrysocolla is CuO. SiO,. 2H2O.

If one or more similar oxides are present in small proportion, they have probably replaced one another, and must all be reduced to terms of one of them, by adding the numbers representing the ratio of their molecules present, before the calculation can be proceeded with.

Thus a brown deposit of sinter was found to contain

In the case of silicates containing alumina it is often impossible to determine except from theory what proportion of the alumina is basic and what proportion is acid in its functions.

A sample of Andalusite was found to contain:

Hence, neglecting the small proportions of Lime and Magnesia, which are probably present as silicates and hence raise the ratio of the silica, the formula of the mineral is

In Andalusite a portion of the alumina is probably basic and a portion acid, the rational formula being:—

(Al)(SiO)"
(A10,),'*

*(29) THE SOLUBILITY OF SOLIDS.

Though many experiments on the solubility of solids in liquids have been made, no general law connecting chemical composition and solubility has yet been discovered. Water

is by far the most general solvent, and with it alone sufficient experiments have been made to justify any attempt. at a general law.

When solids dissolve in water heat is generally absorbed by the solid in passing to the liquid condition. But if the substance previously combines with water to form a hydrate which subsequently dissolves, the heat evolved in the formation of the hydrate may supply or more than supply the quantity required for the solution of the solid.

The volume of the solution is generally less than the volumes of the solid and liquid together, and its boilingpoint is usually above 100° C.

The solubility of a solid is usually measured at any temperature C., by the number of grams (x) of the solid which 100 grams of water will dissolve.

If the mass of any saturated solution be M

m grams of the salt are dissolved in it

grams, and

And if y be the number of grams of water required to dissolve 1 gram of the substance,

If 100 grams of the solution contain n grams of the salt,

Generally speaking the solubility of the substance increases with and more rapidly than the temperature of the water, so that,

x = a + bt + ct2 + dt3,

where a, b, c and d are constants depending upon the nature of the substance under consideration.

In the great majority of cases b, c, and d have not been accurately determined; in a few cases e. g. calcium hydrate and strontium sulphate the solubility decreases as the temperature rises or b, c, and d are affected with minus signs.

In a few other cases, e. g. sodium and calcium sulphates, the solubility increases up to a certain temperature and then decreases. This is due to the formation of different hydrates at different temperatures, each hydrate following its own law of solubility.

Thus below about 18° C. the sodium sulphate is in the condition of the sept-hydrated salt Na,SO. 7H,O, between 18° C. and 33° C. in that of the ordinary Glauber's salts Na,SO. 10H,0, while at temperatures above 34° C. the salt is in the anhydrous condition as Na,SO.

Gay Lussac found for the solubility of potassium nitrate

x = 13·82 + 0·574t + 0·0172ť2 + 0·0000036ť3.

How much potassium nitrate will dissolve in a kilogram of water at 100° C. ?

x=13·82+57·4+172 +3.6 = 246.82 grams in 100 grams of water, hence a kilogram of water will dissolve

246.82 × 10 2468.2 grams of the salt.

=