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same relation in the liquid state, we must naturally expect that the fourth, (for which we have no data in its liquid compounds) will follow the same rule also. But this, although so extremely probable, remains to be proved. Other theoretical reasons might be adduced in support of the idea, but I prefer leaving the question for experiment to settle. In order to show more clearly the remarkable relations connecting the different atomic volumes of this group, I have arranged the values for these elements, both in the solid and liquid state, in the following tabular form. The independent numbers are those determined by theory, those in parentheses being the values actually determined. This is in order to show the extent of alteration when change has been necessary. Oxygen, 2.6 5.2 708 10.4 13.0 (12-2) Sulphur,

10:4 (10-7) 15.6 23•4 (2246) 28.6 Selenium,

10-4 (106) 15.6 (165) 234 (232) Tellurium,

20•8 (207) Of these thirteen numbers six need no alteration, and the amount of change in the other seven, varies from a minimum of 0:1 to a maximum of 0:9. Moreover, from 2:6 up to 28.6, but two multiples of the lowest are wanting, and if we place, from theoretical reasons given above, the atomic volume of liquid tellurium at 31-2, this relation becomes still more noteworthy.

It is worth while in this connection to observe the remarkable multiple relation connecting the atomic weights of this group.

Between the different allotropic conditions of sulphur and selenium I find no numerical relations whatever. The atomic volume of prismatic sulphur I find to be from 16:3 to 16:7, and that of amorphous selenium to be 18.6. These values find no place in the series above given.

The nitrogen group affords another remarkable series of relations. In the liquid state, it will be remembered, nitrogen has three values, 2 15, 8:6, and 17.2, all multiples of the lowest. Then came boron, phosphorus, vanadium, and arsenic, with a common value, three times the second number for nitrogen. In the solid state, however, we find a variation from this. For nitrogen itself we have few suitable data, and I have made no elaborate calculations concerning it; yet as far as I have examined, it seems to possess several values. One of these is easily found. Kopp determined the atomic volume of N03 in nitrates, as 28:6 : and if we subtract from

* In the numbers which required no alteration, parentheses seemed unnecessary.

this three times the most common value for oxygen, or 15:6, we have left, as the atomic volume of the nitrogen, the number 130. The specific gravity of crystalline red phosphorus, (“metallic phosphorus”) according to Hittorf is 2:34, and hence, as its atomic volume, we get 13.2. Bettendorf found the specific gravity of crystalline arsenic to be 5.727, which gives us the atomic volume 13.1. For free vanadium we have no data, but the oxyd V,0, has the specific gravity 3-64, (Schafarik) and hence the atomic volume 37:1. From this, subtracting the value of the oxygen, giving the latter element its second value, we obtain as the atomic volume of vanadium the number 13 3.

It must be borne in mind that both in this case, and with the radical NO,, it is a pure assumption to give oxygen its second value, instead of its first or third, yet the assumption seems warranted by the results. From these numbers we see that in the solid state, some at least of the atomic volumes of nitrogen, phosphorus, vanadium, and arsenic, are equal, the mean being 13:15. 12:9 (a change of 0-25) is precisely half the atomic volume of the three latter elements in the liquid state, and a multiple by 6 of the lowest value for nitrogen. In connection with the apparent equality between phosphorus and arsenic, the fact is perhaps worth recalling that the alkaline phosphates and arsenates with 12 aq. were found by Playfair and Joule to have equal atomic volumes.

Antimony was found by Dexter to have a specific gravity from 6:707 to 6:718. This gives its atomic volume as 181. If we make this 0:9 less, or 17-2, it becomes precisely half the value for this metal in its liquid compounds. Bismuth, according to Marchand and Scheerer, has a specific gravity of 9.799. Its atomic volume, then, is 21:43. 215 is exactly 10 times the lowest value of nitrogen. In the liquid state its atomic volume is a matter of uncertainty, since the specific gravity of only one volatile comipound of bismuth has been taken. In my last paper I suggested that perhaps this metal in its liquid compounds might have the same value as antimony, although farther investigations might place it higher. If now, we assume that bismuth, like phosphorus, vanadium, arsenic, and antimony has in the solid state an atomic volume half that which it possesses in liquid compounds, we shall get as the atomic volume of liquid bismuth, the number 42-86, or more probably, 43.0, which is a multiple of the second value of liquid nitrogen. This seems highly probable, yet cannot be regarded as settled. Nevertheless, it will be seen that the values actually found for the metals arsenic, antimony, and bismuth, are to each other very nearly as 3:4:5.

The atomic volume of ordinary phosphorus is from 16:9 to 17.0, and that of the amorphous red variety from 13.9 to 145. That of amorphous arsenic is 15.9. These numbers seem to bear no distinct relations to the others.

In its liquid compounds the atomic volume of boron is equal to that of phosphorus and arsenic, but this relation does not hold true for the solid element. The specific gravity of the diamond modification is given in Graham-Otto's “Lehrbuch” as 2:68, whence we get 4:1 as the atomic volume. If we place this element in the nitrogen group, as its atomic volume in the liquid state would induce iis, it is worth while to notice that its value here is very nearly twice the lowest number for nitrogen, and one-sixth (if the alteration be made) of its value in liquid compounds.

Passing now to the carbon group, we still find close multiple relations existing. The sp. gr. of the purest graphite is 2-25 (Brodie) and hence its atomic volume is found to be 5:3. If we alter this to 5'5, we have just half the value of carbon in its liquid compounds. In the “Handwörterbuch” the specific gravity of graphitoidal silicon is given as 2:49, and from this we get 11.2 as its atomic volume. This is 0-2 greater than a multiple by two of the altered value for graphite.

For titanium in the free state I have been able to find no data, but in its compounds it approximates closely to silicon. Rock crystal has the sp. gr. 2.663 (Deville), and an atomic volume of 22.5.* Octahedrite, Tio,, has a sp. gr. of 3-82—3.95, corresponding to an atomic volume of 21.5. If we assume that the atomic volumes of silicon and titanium are equal, and double the altered value for graphite, we shall find as the calculated atomic volume of rock crystal and of octahedrite, the number 21:4, (giving oxygen its second value.) Again, the native mineral enstatite, MgSiOg, has a sp. gr. of 3.13, and an atomic volume of 31.9. The artificial titanate, MgTi0,, obtained by Hautefeuille, has a sp. gr. of 391, and hence the atomic volume 31.2. If we also take into account the seeming equality between the atomic volumes of these elements in their liquid compounds, the conclusion concerning their values in the solid condition seems almost inevitable.

The specific gravity of tin, according to Miller, is 7.177. Hence its atomic volume is 16:4, which is only 0:1 less than three times the changed value for graphite. If now we take into review these four tetrad elements we see that with very trifling variations, their atomic volumes for the solid state are

* For specific gravities of minerals quoted in this paper, see the last edition of "Dana's Mineralogy." AN. JOUR. SCI.-SECOND SERIES, VOL. XLVII, No. 141.-MAY, 1869.

to each other as 1:2:2:3. In the liquid state these elements have values standing to each other as 1:3:3:4, and therefore, although in the case of carbon a very simple connection appears between the two states of aggregation, with the higher members of the group the relations become complicated.

The specific gravity of the diamond is 3.55, according to Pelouze, and from this we get as its atomic volume the number 3-4. Although this seems to stand in no direct relation to the other values found in this group, still it affords a starting point for a number of metals, as I shall show hereafter. In connection with the carbon group the tetratomic metal zirconium is worth noticing. Its sp. gr. is given by Troost as 4:15. From this we get the atomic volume as 21:7, a value 0-3 less than four times that of graphite. This, however, may be accidental.

Another noteworthy series of relations appears between the atomic volumes of certain groups of metals. In this series the iron and zinc groups are connected, and possibly also the platinum group is involved. The equality between the atomic volumes of the members of the iron group has often been noticed, yet, for the sake of completeness, I have thought it advisable to recalculate their values. The specific gravities are as follows: Chromium 73, Bunsen; manganese S-013, John; iron 7.844, Bröling ; nickel 9:118, and cobalt 8.957, Rammelsberg; uranium 18-4, Peligot; copper 8:94, a mean of five determinations by Marchand and Scheerer. Deduced from these, their atomic volumes are respectively, 7-1, 6-7, 7-1, 6-7, 6:7, 6:5, 7.1, the average being 6:84.

The sp. gr. of magnesium is 1.743 (Bunsen), that of cadmium 8-6 (Graham-Otto's “Lehrbuch") and that of frozen mercury is given by Schulze as 14391. Hence the atomic volumes of these three metals are respectively 13.8, 13:0, and 13.9, or, very probably, equal, the average being 13.6. Zinc, which we would naturally expect to find classed with magnesium and cadmium, varies, its sp. gr. being 7.03—7.2, (Bolley) and hence its atomic volume 9-9.2. Now it has been observed that the protosulphates of magnesium, zinc, iron, nickel, and cobalt, and also the double sulphates of magnesium and copper, magnesium and zinc, and magnesium and cadmium, all of which contain 7 aq, possess equal atomic volumes. Now, since all of these compounds are formed upon precisely the same type, and since an element may possess different atomic volumes in different compounds, we should be inclined to suspect definite relations between the values of the different metals forming these salts. These metals in the free state represent three different values, viz: 6.84 for the iron group, 9.0-92 for zinc, and 13.6 for the cadmium group, yet in these sulphates all appear to possess the same atomic volume. Now it is noteworthy that 13.6 is almost exactly twice 6.84, and zinc stands between in such a manner that the three values are to each other almost exactly as 3:4:6. Whatever may be the place of zinc in this series, whether accidental or not, it is certainly very remarkable that the metals cadmium and magnesium, forming sulphates isomorphous with those of iron, cobalt, and nickel, should possess an atomic volume almost precisely double that of the latter metals. This relation must be more than a mere coincidence.

* See “Watts' Dictionary," vol. i, Art. "Atomic Volume."

Another point to be noticed in regard to zinc and mercury is an exception to a rule which has seemed to hold true with the groups hitherto given. Between the atomic volumes possessed by these metals in the solid state, and their values in the liquid condition, no direct relation is manifesi.

The platinum metals afford another remarkable instance of equality among atomic volumes, as has often been noticed. The specific gravities are as follows, according to Deville and Debray. Platinum 21.15, iridium 21:15, osmium 21:3–21:4, rhodium 12:1, ruthenium 11–11:4, palladium 11.4. Their atomic volumes are respectively 9:3, 93, 9-2-9.3, 8:5, 9:1-9.4, and 9-3. The average is 9:15, almost exactly the value for zinc, although this is probably a mere coincidence. A revision of the sp. gr. of rhodium will probably place it lower, and increase the atomic volume, so as to make the value for this group about 9:3,

Molybdenum and tungsten afford another well known examample of equality. The sp. gr. of the first is 8:64, (Bucholz,) and that of the second from 16:54—18.447, according to the state of aggregation and mode in which it was prepared, according to the observations (independent of each other) of Van Uslar and Zettnow. The atomic volume of molybdenum is therefore 11.2, and that of tungsten from 9:9-11:1. If instead of 11:1-11.2, we place the value for these metals at 11:4, we find that the latter number falls into a vacant place in the iron, zinc, and cadmium series, standing in that series so as to make the four values to each other as 3:4:5:6. This may be accidental, however,

The equality between silver and gold is also well known, the atomic volumes of these two metals being represented by the number 10-2.

A noteworthy relation to oxygen is found in the atomic volumes of the remarkably similar elements calcium, barium, strontium, and lead. The sp. gr. of calcium is 1.55 (Liés Bodart

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