22.8, bromine 27.8, iodine 37.5. Oxygen, in the radical 12-2, out of the radical 7-8. Sulphur, out of the radical 22-6, in the radical 28.6. Nitrogen, in compounds of the ammonia type 2-3, in hyponitric acid 86, and in cyanogen 17. Carbon 11. Besides these he also determined experimentally the atomic volumes of the following compounds, some of which are amended to suit the new atomic weights.

3

PCI, 93.9, PBг, 108-6, AsC1, 94-8, SbCl, 100-7, SbBr, 1168, SiCl, 122-1, SiBr, 144-2, SnCl, 1314, TiCl, 126-0. Kopp suggested at the time, that probably phosphorus and arsenic had equal atomic volumes, and added to them silicon also, whose chlorid, regarded as SiCl,, gave the number 91.6. Silicon now, however, stands apart. Tin and titanium also he regarded as having equal atomic volumes, but changing the atomic weight of silicon has brought that element near these two, so that the atomic volume of titanium agrees better with that of silicon than with that of tin.

As I shall show hereafter, tin stands by itself, having an atomic volume different from either silicon or titanium. Moreover, the fact that the atomic weights of silicon and titanium are nearer together than those of titanium and tin, goes to show that if titanium be classed with either, it should be with silicon.

As I previously stated, whenever two liquids have equal vapor volumes their atomic volumes also are equal, or nearly so. For instance, the various isomeric ethers formed by the homologues of formic acid with the methyl series of hydrocarbons, (ethyl acetate, formate, &c.,) have both equal atomic volumes and vapor volumes, and so on with all strictly isomeric bodies. Again, to cite an example of liquids diverse in their natures, benzol, butyronitrile, and bromid of ethylene, all have the vapor volume 257. Their atomic volumes, calculated by Kopp's method, are respectively 99, 99.5, and 99.6. I could cite many other examples, but it is not necessary. There are exceptions, however, though they are not common.

Suppose now we wish to determine the atomic volume of any element in its liquid compounds,-boron, for example. The terbromid of boron has the vapor volume 239. Acetic anhydrid has the vapor volume 238. Therefore the atomic volumes of these two compounds must be nearly equal. The atomic volume of the anhydrid is 109-2, calculated by Kopp's process. Regarding this as also the atomic volume of the bromid, and subtracting from it that of the three atoms of bromine, we have left as the atomic volume of boron, the number 25.8. Triethyl boron, CH,,B, has the vapor volume 157, equal to that of oenanthic acid. The calculated atomic vol

ume of the acid is 174. This, then, is also the atomic volume of triethyl boron, and, subtracting from it the atomic volume of CH, 59 we have left for that of boron the number 25.5, closely agreeing with the result obtained from the bromid. But we do not get such close agreements in all cases, and therefore in order to obtain accurate results, we must compare the numbers obtained from several of the liquid compounds of the element in question, and regard the average of them all as nearest correct. Before going farther in this direction, however, let us compare the vapor volumes of a number of similar compounds of boron, phosphorus, and arsenic.

The chlorids of these three elements have respectively the vapor volumes 257, 262, and 252. The bromids of boron and phosphorus have respectively 239 and 241. Triethyl boron, triethyl phosphine, and triethyl arsine have the vapor volumes 157, 154, and 159, and triethyl phosphate and triethyl arsenate have 132 and 130.

Kopp, from the chlorids, found the atomic volumes of phosphorus and arsenic to be probably equal. The comparison of these vapor volumes confirms this view, and adds boron as also possessing the same atomic volume as phosphorus and arsenic.

To make this still more certain I have calculated the atomic volumes of these elements from the vapor volumes of their compounds, in the manner already described.

For boron I have made calculations from eleven compounds, -the chlorid, bromid, triethyl boron, trimethyl, triethyl, triamyl, and monamyl borates, ethyl diamyl, amyl diethyl, and methyl diethyl borates, and tetraphenyl diborate. In these

compounds I obtained respectively as the atomic volume of boron in its liquid compounds, the numbers 309, 25·8, 255, 26-0, 241, 26.1, 19.7, 25·3, 31.9, 24.1, and 19.9. The average

is 25.4.

Although there are very great variations between these different numbers, it will be seen hereafter that the averages obtained by this method agree closely with the numbers found by actual experiment.

The atomic volume of phosphorus I have calculated in a similar manner in eleven of its liquid compounds, exclusive of the chlorid and bromid. I include Kopp's numbers for these last, however, for the sake of completeness in making up the average.

The list of compounds then stands as follows. The chlorid, bromid, oxychlorid, oxybromid and oxybromochlorid of phosphorus, triethyl phosphine, triethyl phosphite, diamyl phosphoric acid, triethyl phosphate, tetrethyl pyrophosphate, and the ethyl, butyl, and amyl chlorophosphites. In these, giving

Kopp's numbers for the first two, the atomic volume of phosphorus is found respectively as follows: 255, 25-2, 26·2, 25·8, 22·4, 25·5, 26·1, 23-2, 29·3, 32·3, 27·1, 27·1, and 19-7. The average of these, 258, agrees very closely with Kopp's numbers, and varies only 04 from the average obtained for boron.

The atomic volume of arsenic I have deduced from the vapor volumes of three of its compounds exclusive of the chlorid. In the chlorid the element has the atomic volume 264, (Kopp) and in triethyl arsine, triethyl arsenite, and triethyl arsenate, I obtain the numbers 25.5, 207, and 29.2. The average of all four numbers is 26.9.

If now, regarding boron, phosphorus, and arsenic, as possessing the same atomic volume in their liquid compounds, we take the average of the numbers obtained from the twenty-eight compounds in which that atomic volume has been determined, we get the number 25.8. To these three elements we can probably add vanadium, which Roscoe has shown belongs in the same group. There is but one liquid compound of this metal for which I had data to calculate from,-the oxychlorid, Roscoe's "vanadyl trichlorid," VOCI,. Calculating its vapor volume, and thence the atomic volume of vanadium, I obtained the number 27.4.

It will be seen that a number of compounds of boron, phosphorus, and arsenic gave higher results than this, and therefore, for a single compound, this number seems close enough to that found for the other three elements, to be classed with them. This view is somewhat strengthened by the fact that the atomic weight of vanadium is intermediate between those of phosphorus and arsenic.

For antimony, as already stated, Kopp determined the atomic volumes of the chlorid and bromid. Deducing the atomic volume of antimony from these, we get the numbers 32.3 and 33.4. In addition to these I have determined from their vapor volumes the atomic volumes of triethyl and triamyl stibine, and the chlorid and bromid of triethyl stibine. From these İ obtain respectively as the atomic volume of antimony, the numbers 333, 321, 32.9, and 35.9. Adding in these with the numbers from the chlorid and bromid of the metal, we get 33.3 as the average.

In the case of bismuth there is but one liquid compound for which I had the necessary data. Triethyl bismuthine has the vapor volume 138, while triethyl stibine has the number 141. These are so near together that it seems probable that bismuth in its liquid compounds has the same atomic volume as antimony. But more data are needed to decide this point definitely.

In the case of silicon, thanks to the labors of Friedel, Crafts, and Ladenburg, materials were more abundant. Apart from the chlorid and bromid, whose atomic volumes were determined by Kopp, I have calculated the vapor volumes of sixteen liquid compounds of silicon, and thence the atomic volume of silicon itself. These compounds are tetramethyl, tetrethyl, and tetraamyl silicates, diethyl, diethyl dimethyl, triethyl methyl, triamyl ethyl, diamyl diethyl, and trimethyl ethyl silicates, hexmethyl and hexethyl disilicates, ethylsilicic monochlorhydrin, dichlorhydrin, and trichlorhydrin and methylsilicic monochlorhydrin and dichlorhydrin. In these compounds I obtain respectively as the atomic volume of silicon, the numbers 310, 32.8, 33-0 30-3, 32-8, 32-2, 388, 352, 309, 303, 32-8, 36-3, 320, 390, 29.9, and 34.6. Taking also the numbers given by Kopp for the chlorid and bromid of silicon, amending them to suit the new notation and new atomic weight of silicon, and thence deducing the atomic volume desired, we get the numbers 33.0 and 30.9. Taking the average of these eighteen numbers we obtain 331 as the atomic volume of silicon in its liquid compounds. The atomic volume of titanium, as deduced from that of the chlorid, as determined by Kopp, is 34.8. Further investigation will probably show its atomic volume to be equal with that of silicon.

The atomic volume of the chlorid of tin, as determined by Kopp, and since doubled to suit the new notation, is 1314. This gave for tin the number 402. The vapor volume of the same compound gave as the atomic volume of tin, the number 401. I have also calculated the vapor volume of the following nine compounds containing this metal. Stanntetrethyl, stanndimethyl diethyl, stanndiethyl, stannethyl trimethyl, the chlorid, bromid, and iodid of stanntriethyl, and the iodids of stanntrimethyl and stanndimethyl. From the vapor volumes of these liquids I have obtained respectively as the atomic volume of tin the numbers 46.5, 42·0, 39-3, 44·0, 37·7, 42·1, 41·0, 41-8, and 440. Including the number deduced from the chlorid of tin, we get as the average 418, the atomic volume of tin in its liquid compounds.

In the case of zinc there were but three liquid compounds for which I was able to calculate the vapor volumes. These were zinc ethyl, zinc methyl, and zinc amyl. The atomic volume of zinc, deduced from their vapor volumes, I obtained respectively as 23-2, 24-2, and 23.2. The average is 23.6.

Of liquids containing selenium I have the vapor volumes of but two, the oxychlorid, SeOCl2, and monohydrated selenic acid. The latter of these, however, has never been obtained

AM. JOUR. SCI. -SECOND SERIES, VOL. XLVII, No. 140.-MARCH, 1869.

free from an excess of water, the strongest containing only about 97 per cent of monohydrate; and therefore its atomic volume, as deduced from its vapor volume, is undoubtedly a trifle too low. Be that as it may, however, in these two compounds I obtained as the atomic volume of selenium the numbers 247 and 218, the mean being 23-2. This is only 0.6 greater than the number given by Kopp as the lower atomic volume of sulphur, and, therefore, taking into account that sulphur and selenium in the solid condition have equal atomic volumes, it seems almost certain that the same equality holds true in their liquid compounds.

I determined the vapor volumes of two lead compounds, lead tetrethyl and lead triethyl, but, to my great surprise I obtained the same number for both. This is so anomalous that I am inclined to think either that there is an error in the numbers published as the specific gravities of these liquids, or else that their vapor densities do not follow the usual law. At all events I could get nothing reliable from them.

From the vapor volume of chlorochromic acid I determined its atomic volume, and thence that of chromium in liquid compounds, as 43.6. The vapor volume of the fluorid of arsenic gave me the means of ascertaining the atomic volume of fluorine, for which I obtained the number 10. But as each of these was determined from only one compound of the element, I place no great reliance upon either, regarding them merely as possible approximations to the truth.

In order to test more thoroughly this process of determining atomic volumes by means of vapor volumes, not being content with the coincidence of my numbers with those of Kopp in the cases of phosphorus, arsenic, antimony, silicon and tin, I calculated the atomic volumes of chlorine, bromine, and iodine by the same method. For chlorine, in an average of forty-one compounds, I obtained the number 22-9, Kopp's determination giving 22.8. Bromine, in an average of fourteen compounds, gave me 28.0, Kopp's number being 27-8; and iodine, calculated from nine of its liquid compounds gave the number 38.5, that of Kopp being 37.5. To this determination of the atomic volume of iodine I shall refer again hereafter.

In regard to phosphorus, arsenic, antimony, silicon, and tin, my determinations might be regarded by some as labor lost, after Kopp's examination of the chlorids and bromids. But, very frequently, the atomic volume of a single compound as calculated by Kopp's method, varies considerably from that actually found. Therefore, in order to determine accurately the atomic volume of any element in its liquid compounds it is necessary to ascertain the atomic volumes of a number of those compounds.