ART. XIII.-On Numerical Relations existing between the Equivalent Numbers of Elementary Bodies; by M. CAREY LEA, Philadelphia. Part I.

(1.)

THE determination of the chemical equivalents of the simple substances seems with each new approach to accuracy, to destroy more and more the numerical relations once supposed to exist between the equivalent numbers of certain series of elements nearly related to each other by their properties. If we except the series formed by oxygen, sulphur, selenium and tellurium, there probably remains none of those usually recognized in which the numerical relation is rigorously exact. Chlorine, bromine and iodine are represented by the numbers 355, 80 and 127, where the difference between the first and second term is 44.5, between the second and third, 47. Lithium, sodium and potassium have the numbers 6.95, 23, 39-2; difference of first and second terms, 16-05, of second and third, 16-20. Calcium, strontium and barium have 20, 43.77 and 686; difference of first and second, 23.77, of second and third, 24-83. It can be demonstrated that other relations exist, approaching quite as near to exactness as these, and some where the accuracy is perfect.

Few of the so-called elements present more directly marked analogies than nitrogen, phosphorus, arsenic and antimony, and the very interesting discoveries of Cahours and Hofmann respecting the phosphorus bases have shown that phosphorus stands in every respect intermediate between nitrogen and arsenic, forming compounds of the type 3(C,H,)PHCl, &c., like the nitrogen compounds as well as those of the type 3(C,H,)PO,, &c., like those of the arsenic and antimony groups. These authors further observe that the equivalents of phosphorus, arsenic and antimony differ by nearly the same number (44 to 45), but that nitrogen does not exhibit this relation.*

Beyond the fact of the approximate equality of these two dif ferences, the analogy has never been extended. The following considerations will show that this relation not only extends to nitrogen but may be carried with exactness to other elements.

If we form a descending arithmetical series beginning with antimony 120-3, and diminishing by a common difference of 45 (453 in one instance, 44 in several) we shall find that such a series does not cease with the third term, P=31, but gives for a fourth-14, the exact equivalent of nitrogen with a negative sign. The fifth term will be -59, the exact equivalent of tin, with a negative sign. The sixth will be 104, or very nearly the equivalent of lead (also with a negative sign). The seventh

*Kopp u. Will, Jahresbericht für 1857.

-149, very nearly the double of the equivalent of arsenic, a previous term in the same series. These results are exhibited in the following table.

It will be seen presently that the number 164, the eleventh term in the above table, occurs also in the ascending positive series, and may represent the equivalent of a metal existing but as yet unknown.

If we examine the position occupied by antimony, arsenic, phosphorus and nitrogen in the electro-chemical scale of Berzelius we shall find that in proportion as their equivalent numbers diminish, their properties become more and more electro-negative; a corresponding change is also visible in the organic radicals which these elements are capable of forming by their union with carbon and hydrogen. The passage from the positive to the negative sign in the interval between phosphorus and nitrogen is accompanied by a marked change in the nature of the organic radicals into which these elements enter-3(C,H,)N does not possess the power of combining directly with oxygen, chlorine and sulphur which 3(C,H,)P, 3(CH)As, 3(C,H,)Sb exhibit in so high a degree. The methyl compounds show the same differences as the ethyl. Standing between nitrogen and arsenic, phosphorus is every way more closely allied to the latter of

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these substances, not only by the analogies of its organic radicals, but also by the polybasic nature of phosphoric acid.* Although tin and lead represent the further members of the same series in reference to their equivalent numbers, it is evident that the increase of electro-negative relations does not extend to them. Moreover bismuth, antimony, arsenic, phosphorus and nitrogen at their maximum of oxydation combine with five equivalents of oxygen and chlorine, whereas tin unites with but two of each, and lead at most with two of oxygen and one of chlorine.

Again, if we begin with phosphorus, and form an ascending series with a common difference of 44 (except in one instance), we shall find both the number 164, the double of which constituted the eleventh term of the preceding table, and also the equivalent of bismuth, the double of which formed the thirteenth term of the same table.

These four elements exhibit strong analogies and are all isomorphous with each other.

If, taking mercury as a starting point, we subtract the number 44 from each term to find the following one, we shall obtain the series

The salts of the protoxyds of the three last of these metals are isomorphous. It may seem forced to place mercury in the same group, but its analogies with zinc are perhaps as strong as those which it exhibits with silver, next to which it has usually been classed, principally because the oxyds of both metals are reduced by heat. Mercury, like zinc, cadmium and certain other metals, is capable of replacing an atom of hydrogen in hydrid of ethyl, CH,H, and of producing in this manner the conjugate * See the very interesting paper of Cahours and Hofmann above referred to.

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organic radical mercur-ethyl, C,H,Hg, analogous to zinc-ethyl, CH, Zn. This compound has recently been isolated by Buckton.* Silver does not appear to be capable of a similar substitution; when chlorid of ethyl is made to react upon zinc-ethyl the products are ethyl, chlorid of zinc and metallic silver. It has lately been shown by Hallwachs and Schafarik that magnesium forms an ethyl-magnesium.† These metals are likewise all volatile, and it has been shown by H. St.C. Deville that magnesium, like the others, is readily distilled.

It is not a little curious that the numerically negative members of this series lead into the positive members of the foregoing; if we continue the subtraction of 44, we find for the fifth number 76, or nearly the equivalent for arsenic, for the sixth 120, very nearly that of antimony, for the seventh 164, corresponding, as before remarked, with a possible undiscovered metal, and for the eighth 208, or exactly the equivalent of bismuth. The two series thus naturally lead to each other. The equivalent for arsenic given by L. Gmelin, viz. 754, accords more nearly with some of these series and renders them more exact than that adopted by the Jahresbericht which has been here employed.

The members of these two analogous series are further united by the fact that all of them, eleven in number, are capable of uniting with the hydro-carbons of the methyl, ethyl, &c. type to form powerful organic metals, and that this capacity appears to be limited to these elements alone.

(2.)

The magnesia group includes a well marked natural family of metals, whose oxyds having the constitution RO are related with each other by isomorphism. The equivalents of these metals, according to the most recent determinations, are as follows:

[Some of the elements here enumerated are found also in the foregoing or following series. It need scarcely be remarked that no absolute classification into groups is possible; lead for instance is in some of its combinations isomorphous with the barium group, in others with the magnesia, copper in grey copThis Journal, [2], xxviii, 147.

* See this Journal, [2], xxviii, 146. There appears some reason to believe that an ethyl-aluminum may exist, which would form an exception to this law. If so, the same property may possibly be extended to others of the metals of the earths.

per ore is isomorphous with silver, while its carbonate, sulphate and seleniate are isomorphous with those of the magnesia group.] The equivalents of the above metals are related in the following manner by the number 44:

and so likewise by adding to the equivalent of lead, the equivalents of manganese, cobalt, nickel, and chromium, we obtain in each case a number almost exactly equal to three times the number 44.

To sum up with Cu and Mg, Zn and Mg the sum of each pair is 44 nearly.

With Cd and Mg, Pb and Ur, the difference of each pair is 44 or nearly.

With U and Mg, U and Fe, U and Co, U and Ni, U and Cr, Cd and Zn, the mean term is 44 or nearly.

With Pb and Mn, Pb and Fe, Pb and Ni, Pb and Co, Pb and Cr, the sum of each pair is three times 44 nearly.

It has been before pointed out that the strong analogy existing between Mg, Cd and Zn extends to their equivalents, that of Mg being added to that of Zn gives the number 44 nearly, subtracted from that of Cd, 44 exactly.

(3.)

The following metals may be classed together as tending to form acids:

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Tin,
Titanium, 25
Tantalum, 68.6
Tungsten, 92

Vanadium, 68.8
Molybdenum, 48

Tellurium, 64

Niobium, 48.82*

Relations depending upon the number 44 exist between these equivalents.

By the recent determination of H. Rose, Poggendorff, civ, ext. in this Journal, [2], xxvii, 127.