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And if to two terms of the same series A we add the equiva lent of bromine, we also find the terms of series C.

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If we add respectively the four terms of series A with the four corresponding terms of series C, we shall in each case obtain a number which is very nearly twice forty-four; that is, the mean of each pair of series is 44 nearly.

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It will be remarked that where a series leads to the equivalent of an element, but with a negative sign, that negative sign has been in all cases preserved in the further examination of its numerical relations.

(9.)

It is evident that the number 44-45 plays an important part in the science of stoichiometry, and the relations which depend upon it are supported, in some cases at least, in a remarkable manner, by analogies of atomic volume. That such analogies are a support becomes evident from the following considerations.

Solids and liquids are very far from being governed by the laws which determine the combinations of gases, in volumes either equal or having some very simple relation to one another. Therefore, if we find that in some few instances such a relation does hold good with solid substances, we may naturally expect to find a close relationship existing between those substances thus united. We may even be permitted, by way of hypothesis, to advance a step further, and finding that a given volume of silver unites with a given volume of oxygen, and that the same volume of gold unites with precisely the same volume of oxygen, to conjecture that gold may differ from silver only by a third substance, which unites with the silver without increasing its volume, or affecting the amount of oxygen which it is capable of saturating, but which, on the other hand, alters its chemical equivalent, its specific gravity, and other physical characters.

Moreover, if we find that by subtracting from the chemical equivalent of silver, half the difference between the equivalents of silver and gold, we obtain the equivalent of a third metal, copper (eu 634), which also, under equal volumes, combines with a quantity of oxygen expressed by a very simple relation

with that capable of saturating gold and silver, we may at least speculate that the three may form a series consisting of two substances combined in different proportions. It is true that we must be extremely cautious about venturing upon hypotheses involving a compound constitution of bodies which all our efforts have hitherto proved ineffectual to decompose, but on the other hand it must be admitted that when we find so-called elements arranging themselves into a series of terms having a common difference, and when we find the terms of these series united by equality or simple relation of atomic volume, we cannot grant that their elementary nature has been absolutely established. The following substances combine relations of chemical equivalents already pointed out, with analogies of atomic volume: Atomict Relation of

Differences of
Equivalents.

volume.

At. vol.

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(Where phosphorus, arsenic, &c., are compared in the solid state, the unit of relation is of course different). It has been already remarked that in point of chemical relations generally, lead and tin are less closely united with the series than the other members composing it, but the relation between the atomic volumes of lead and antimony, the latter almost the last term at the other end of the series, is almost absolutely exact. Nitrogen is of course omitted in the second table, as we do not know what would be its atomic volume in the solid state.

In the cases of nitrogen, tin and lead, the equivalents are taken with a negative sign, as before explained.

The numbers here given for the atomic volumes are calculated from the specific gravities adopted in Gmelin's Handbook, and the latest and most reliable determinations of chemical equivalents.

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It will be observed that the difference between the equivalents of copper and silver approaches very near to absolute exactness with half the difference between the equivalents of silver and gold, and as the equivalent of copper is by no means positively settled, the relation may be rigorously exact. If we take the mean between the number adopted by L. Gmelin and that adopted by the Jahresbericht (always considering cuprous oxyd as eu), we shall have for the difference between the equivalents of copper and silver the number 445, half the difference between the equivalents of silver and gold, with mathematical exactness.

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In the series Hg, Cd, Mg, Zn, similar analogies are not well marked: the atomic volumes of the three first metals are not very far apart,

Hg,
Mg,*
Cd,

Atomic volume.

7.37

6.85

6.48

but the atomic volume of zinc differs considerably; it is 4.72. In each of these different series, each term differs in its equivalent by the number 45 or a number approaching very near to 45, and yet the addition of this large amount of matter is in most cases accompanied by no change in volume, or when a change takes place, it is expressed by some simple relation to the original volume. Some of these relations of atomic volume are well known and are only here presented in view of the confirmation which they afford of the series here established, but it is believed that the connection of the atomic volume of copper with those of gold and silver, and of those of tin and lead with those of the elements of the antimony group are pointed out for the first time.

Ammermüller has noticed a fact not wholly dissimilar from this in the case of protoxyds of copper, mercury, tin and lead, which combine with a second equivalent of oxygen without change of atomic volume, the density alone increasing. But according to L. Gmelin, the specific gravities on which he based

* Taking the sp. gr. of magnesium at 1.75 as determined by Deville.

his calculations are too unreliable to render the fact well estab lished.

The numbers adopted for the equivalents in the foregoing calculations are those obtained by the latest and most reliable determinations; they are taken from the table contained in the Jahresbericht der Chemie of Kopp & Will for 1857, published in August, 1858, and the last which the author has been able to obtain at the time of concluding this paper, and have been in no case altered or modified in the slightest degree with a view to preserve or increase numerical relations, which by slight changes of this kind can be often rendered much more symmet rical. Dumas, in one of his highly interesting papers on this subject (Comptes Rendus, XLV, 709, extracted in Kopp and Will's Jahr. 1857) in his series a+xd+yd', adopts the equivalents N=14, P=31, As=75, Sb=119, Bi 207 (see Jahresbericht, p. 35, where the equivalent of Bi is erroneously printed 108, by substitution of the values given for a, x, y, d, and d', 207 is obtained): whereas the equivalent of Sb as lately found by R. Schneider, confirmed by H. Rose, and adopted by Kopp & Will is 120 3. In another place (Comptes Rendus, XLVII, 1027) Dumas has taken the equivalent of the same metal at 122, thus adopting alternately the numbers 119 and 122, neither the true one, according to the exigencies of the two series. The equivalent number of bismuth in the series just mentioned is taken at 207, whereas it should be 208. In the series a+xd we find Mg=12, Ca=20, Sr=44, Ba 68, Pb 104-the last three should be Sr 43.77, Ba 68.6, Pb 103.5. So with Li, Na, K, V, Zr, &c.

In the foregoing tables the calculated and received equivalents are placed by side of each other for comparison. The differences rarely exceed the possible errors in the determination of chemical equivalents, respecting some of which there is still much doubt. Dumas, in the paper above referred to, gives the results of many new determinations by himself, and arrives at the number 26 for both chrome and manganese, instead of the ordinarily received Cr=26·7, Mn=275. For copper his results disagreed too much to lead him to any positive conclusion.

The analogies here presented, all depending upon the same or approximately the same number, extend therefore

To the series Pb, Sn, N, P, As, Sb, Bi.

To the series Hg, Cd, Mg, Zn.

To the series Au, Ag, ¤u.

To the magnesia group, including Mn, Fe, Co, Ni, U, Co, and some of the metals also classed in the three preceding series.

The interesting paper of Prof. Cooke (Memoirs Amer. Ac., 2d ser., vol. v) to which the author's attention has been called since concluding this paper, will be more particularly referred to in the Second Part.

To the metals belonging to the group Ti, Ta, W, V, Mo, Te and No; Sn belongs also to this series as well as to the first.

To the platinum group, Rh, Ru, Pd, Pt, Ir, Os.

To Є, B, Si.

To G, Al, Zr.

The differences between Cl and Br, Br and I, approximate to the same number, as likewise do the relations between Li, Na and K, and between Ca, Sr and Ba.

This relation, therefore, extends to no less than forty-eight of the elementary bodies: to all except those as yet imperfectly understood, most of which may yet range themselves under the same law, and except the oxygen group, oxygen, sulphur, selenium and tellurium, substances which stand alone and unmistakably apart from the other elements.

Philadelphia, Nov. 10, 1859.

ART. XIV.-Remarks on the Dissolution of Field Ice; by CHAS. WHITTLESEY, of Cleveland, Ohio.

THE interesting paper of Col. Totten, U.S. A., in the November number of this Journal for 1859, upon the rapid disappearance of ice in the northern lakes, recalls some observations that I had an opportunity to make on Lake Superior a few years since.

On the 8th of March, 1855, the inhabitants of Eagle River, a village in Haughton County, situated upon the most northerly part of Point Kewenaw, were engaged in procuring ice for their summer use. The severity of winter in that latitude (47° 22′ north) had so far relaxed, that the surface of the field was slightly porous from the direct action of the sun. There had

been no rain; the atmosphere was clear and cool, but on the sunny side of houses and other objects the snow melted rapidly in the day time.

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Below the soft and moist surface, at a few inches in depth, the ice was solid and pure to the bottom, its thickness being thirty inches. The blocks which the people were cutting out, were taken about 1000 feet from the shore. One of them nearly in the form of a cube, of thirty inches on each face, was suffered to lie upon the unbroken ice, its natural surface uppermost, as represented in the figure here inserted.

Block of ice 30 inches thick. a a, upper surface.

I was thus enabled to take a direct view of the progress of its decay, as no doubt others have done many times, upon these lakes. As the force of the sun increased, the porous part on the

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