Between the magnesium tourmalines and the iron tourmalines the closest analogy exists, and the identity of type is absolute. Taking, except when otherwise specified, the analyses by Riggs, all the iron tourmalines reduce to mixtures of the following isomorphous molecules: A. Al(SiO4)6(BO2)2. BO3(AlOH). F ̧‚H..., B. Al(SiO4)(BO2)2. BO3Ca. FеH,

C. Al5(SiO4)6(BO2)2 . BO3NaH. AlзNaH2,
D. Al(SiO4)6(BO2)1⁄2 . BO3NaH . AlзNаH,
E. Al(SiO4)6(BO2)2. BOзNaH. Al Naз.

Molecules C, D, and E are evidently identical, except in the varying replacements of sodium by hydrogen. A and B are similarly alike, so that actually only two fundamental compounds are assumed. From the commoner iron tourmalines lime is practically if not quite absent; and these may be interpreted very nearly as mixtures of A and C, such as AC5, A,С5, etc. If we take the minute quantities of lime into account, the black tourmalines from Brazil and from Stony Point, North Carolina, correspond to A13B2C9; that from Auburn, Maine, to A35B2C27, and that from Paris, Maine, to A10B,C,. It will be noticed that the molecule A is in excess of the other two, a condition which fits the analyses, but which is incompatible with the formula proposed by Penfield and Foote. To satisfy the latter the number of A molecules should be exactly equal to B+C, giving the ratio SiO2 or SiOз1. The analyses in question are as follows:

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The reduced analyses and their comparison with the calculated composition is as follows:

Here again the agreements between analysis and theory are as close as could be reasonably expected. The same thing is true of the black tourmalines from Haddam Neck, Connecticut, and Nantic Gulf. Using letters to represent the several molecules, as above, the Haddam mineral is sharply represented by A,B,D2, and that from Nantic Gulf by A,B,C3E1. Here is the comparison :

To the lithia tourmalines, as analyzed by Riggs, a similar set of formulæ apply, although the comparison between fact and theory is not quite so close as in the preceding cases. The red tourmalines from Brazil and from Rumford, Maine, are very nearly represented by the expression

Als(SiO4)6(BO2); . BO¿R'H. Al1⁄2R'H2;

with Li: Na approximately as 5: 4. The slight deficiency in the alkalies is made up by the presence of small amounts of calcium, iron, and manganese, but the ratio Al, Si, is very clear. The green tourmalines are all lower in alumina, and range downward toward the iron end of the series; and like the latter are representable as mixtures of the following molecular types:

A. Al(SiO4)6(BO2)2 · BO3(AIOH). F ̧‚Í‚.

B. Al(SiO4)6(BO2)2. BO3Cа. Fe H1.

C. Al(SiO4)6(BO2)2. BO3LiH . AlLi2H.
D. Al(SiO4)6(BO2)2. BOŽNаH. AlзNaH2.
E. Al(SiO4)6(BO2)2. BO3H2 . Al1⁄2NaH2.

Thus the dark, opaque green tourmaline from Rumford, Maine, is a molecular mixture corresponding to A,B,C,D,Es; the similar mineral from Auburn is A,B,C,D17; the light green from Auburn, A,CB310D8E129 and the nearly colorless from Auburn, A,B5C20D10E35. From Brazil the dark green is A,B,C,D, and the light green is A,B,C,D,Es. The complexity of these expressions is only apparent, not real, as a study of the original type formula will show. They compare with the reduced analyses as follows:

In these cases the low boric acid of the analyses and the uncertainties as to the significance of the water determinations account for the chief variations between observation and theory. There is another complication also, due to the fact that alternative expressions are possible between which it is very difficult to decide. In the tourmaline from Haddam Neck, Connecticut, analyzed by Penfield and Foote, a somewhat different commingling of molecules seems to be necessary, partly on account of the higher proportion of lime in the mineral and partly on account of the fluorine. This tourmaline also admits of various alternatives in formulation, but it agrees well with the molecular mixture—

3. Al(SiO4)6(BO2)2. BO3Ca. FеH,

10. Al(SiO4)(BO2)2. BO3(AIOH). Al¿Li2H1,
1. Al(SiO4)6(BO2)2. BO3Ca. AlзNaH2,

6. Al(SiO4)6(BO2)2. BOзNaH . AlзNaH ̧;

in which Ca is equivalent to a replacement of NaH. This mixture, with the group AIOH proportional to fluorine, gives a good comparison between analysis and theory, thus:

The theoretical amount of fluorine needed to replace hydroxyl in the assumed group, AIOH, is 0.97 per cent. Altogether, the comparison is fairly satisfactory.

One analysis by Riggs, that of the magnesium tourmaline from Hamburg, New Jersey, I have omitted from my discussion. In that tourmaline there are variations which I can not readily account for, unless by assuming the presence in it of a molecule

Al(SiO4)6(BO2)2. BOзR'2. R'6.

Such a molecule, written structurally, exhibits affinities to garnet rather than to the micas; and I prefer to await further evidence before

committing myself to any definite formulation in this instance. As for the analyses published by Jannasch and Kalb, they fit in well with those of Riggs, and are amenable to the same treatment.

At first glance some of the formulæ which I have proposed may seem to be complex; but they are all of the same type, and can be reduced to a few general expressions, as follows:

These formulæ cover all of the established variations in the composition of tourmaline; they render the various replacements or isomorphous admixtures intelligible, and they indicate the directions into which the species commonly alters. There is one objection to them, namely, that one of the end products contains no alkali metal, and no alkali-free tourmaline is known. The same objection applies to the Penfield-Foote formula, as will be seen by anyone who attempts to apply it in the discussion of the iron tourmalines. Under either system of formulation the existence in tourmaline of alkali-free salts must be assumed.

One further possible advantage in the proposed formulæ remains to be pointed out. All of the chemists who of late years have discussed the composition of tourmaline agree in adopting the ratio between silicon and boron of 2: 1, or 4SiO2: B2O. And yet many of the analyses vary from this ratio to an extent which may not be due to experimental errors. For example, from among Riggs's analyses the following cases show large variations, the boron being too low. I give the silica and boric oxide as determined, the boric oxide as calculated from the silica by the accepted ratio, and the amount of variation between the two.