relations of these to gravity, cohesion, heat, light, electricity, and magnetism belong to the domain of physics, while chemistry is the history of their relations to each other, and of their transformations under the influences of heat, light, and electricity. Chemistry is thus to mineralogy what biology is to organography, and the abstract sciences, physics and chemistry, must precede and form the basis of the concrete science, mineralogy. Many species are chiefly distinguishable by their chemical activities, and hence chemical characters must be greatly depended upon in mineralogical classification.

Chemical change implies disorganization, and all so-called chemical species are inorganic, that is to say, unorganized, and hence really belong to the mineral kingdom. In this extended sense mineralogy takes in not only the few metals, oxides, sulphides, silicates and other salts which are found in nature, but also all those which are the products of the chemist's skill. It embraces not only the few native resins and hydrocarbons, but all the bodies of the carbon series made known to us by the researches of modern chemistry.

The primary object of a natural classification, it must be remembered, is not, like that of an artificial system, to serve the purpose of determining species, or the convenience of the student, but so to arrange bodies in genera, orders, and classes as to satisfy most thoroughly natural affinities. Such a classification, in mineralogy, will be based upon a consideration of all the physical and chemical relations of bodies, and will enable us to see that the various properties of a species are not so many arbitrary signs, but the necessary results of its constitution. It will give for the mineral kingdom what the labors of great naturalists have already nearly attained for the vegetable and animal kingdoms.

Oken saw the necessity of thus enlarging the bounds of mineralogy, and in his Physiophilosophy attempted a mineralogical classification; but it is based upon fanciful and false analogies, with but little reference either to physical or chemical characters, and in the present state of our knowledge is valueless, except as an effort in the right direction, and an attempt to give to mineralogy a natural system. With similar views as to the scope of the science, and with far higher and juster conceptions of its method, Stallo, in his Philosophy of Nature, has touched the questions before us, and has attempted to show the significance of the relations of the metals to cohesion, gravity, light, and electricity, but has gone no further.

In approaching this great problem of classification we have to exam

ine, first, the physical conditions and relations of each body, considered with reference to gravity, cohesion, light, electricity, and magnetism; secondly, the chemical history of the body, in which are to be considered its nature as elemental or compound, its chemical relations with regard to other bodies, and these chemical relations as modified by physical conditions and forces. The quantitative relation of one mineral (chemical) species to another is its equivalent weight, and the chemical species, until it attains to individuality in the crystal, is essentially quantitative.

It is from all the above data, which would include the whole physical and chemical history of inorganic bodies, that a natural system of mineralogical classification is to be made up. Their application may be illustrated by a few points drawn chiefly from the history of certain natural families.

The variable relation to space of the empirical equivalents of nongaseous species, or, in other words, the varying equivalent volume obtained by dividing their empirical equivalent weights by the specific gravity, shows that there exist in different species very unlike degrees of condensation. At the same time we are led to the conclusion that the molecular constitution of gems, spars, and ores is such that these bodies must be represented by formulas not less complex, and with equivalent weights far more elevated than those generally assigned to the polycyanides, the alkaloids, and the proximate principles of plants. To similar conclusions conduce also the researches on the specific heat of compounds.

There probably exists between the true equivalent weights of nongaseous species, and their densities, a relation as simple as that between the equivalent weights of gaseous species and their specific graviities. The gas or vapor of a volatile body constitutes a species distinct from that same body in its liquid or solid state, the chemical formula of the latter being some multiple of the former, and the liquid and solid forms themselves often constituting distinct species of different equivalent weights. In the case of analogous volatile compounds, as the hydrocarbons and their derivatives, the equivalent weights of the liquid or solid species approximate to a constant quantity, so that the density of these species, in the case of homologous or related alcohols, acids, ethers, and glycerides, is subject to no great variation. These non-gaseous species are generated by the chemical union (identification) of a number of volumes or equivalents of the gaseous species, which num

ber varies inversely as the density of the latter species. It follows from this, that the equivalent weights of the solid and liquid alcohols and fats must be so high as to be a common measure of the vapor-equivalents of all bodies belonging to the above-named series. The empirical formula C114 H110 O12, which is the lowest one representing the tristearic glyceride, ordinary stearine, is probably far from representing the true equivalent weight of this fat in its liquid or solid state; and if it should hereafter be found that its density corresponds to six times the above formula, it would follow that the equivalent of liquid acetic acid, whose density differs but slightly from that of fused stearine, must have a formula and an equivalent weight about one hundred times that which we deduce from the density of acetic acid vapor. C1 H1 О.

4

Starting from these high equivalent weights of liquid and solid hydrocarbonaceous species, and their correspondingly complex formulas, we are prepared to admit that other orders of mineral species, such as oxides, silicates, carbonates, and sulphides, have formulas and equivalent weights corresponding to their still higher densities, and we proceed to apply to these bodies the laws of substitution, homology, and polymerism, which have so long been recognized in the chemical study of members of the carbon series. The formulas thus deduced for various native silicates and carbon-spars show that these polybasic salts may contain many atoms of different bases, and their frequently complex constitution is thus explained. In the application of the principle of chemical homology we find a ready and natural explanation of the variations, within certain limits, occasionally met with in the composition of certain crystalline silicates, sulphides, etc., from which some have conjectured the existence of a deviation from the law of definite proportions in what is but an expression of that law in a higher form. The principle of polymerism is exemplified in related mineral species, such as meionite and zoisite, dipyre and jadeite, hornblende and pyroxene, calcite and arragonite, opal and quartz, in the zircons of different densities, and in the various forms of titanic acid and of carbon, whose relations become at once intelligible if we adopt for these species high equivalent weights and complex molecules. The hardness of these isomeric or allotropic species and their indifference to chemical agents increase with their condensation, or in other words vary inversely as their empirical equivalent volume, so that we here find a direct relation between chemical and physical properties.

It is in these high chemical equivalents of the species, and in certain 31

VOL. VII.

ingenious but arbitrary assumptions of numbers, that is to be found an explanation of the results obtained by Playfair and Joule in comparing the volumes of various solid species with that of ice, which they assume to be represented by H O, instead of a high multiple of this formula. The recent ingenious but fallacious speculations of Dr. Macvicar, who has arbitrarily assumed comparatively high equivalent weights for mineral species, and has then endeavored by conjectures as to the architecture of crystalline molecules to establish relations between his complex formulas and the regular solids of geometry, are curious but unsuccessful attempts to solve some of the problems whose significance I have here endeavored to set forth. I am convinced that no geometrical groupings of atoms, such as are imagined by Macvicar and by Gaudin, can ever give us an insight into the manner in which Nature builds up her units, which is by interpenetration and identification, and not by juxtaposition of the chemical elements.

None of the above points are presented as new, though they are all, I believe, original with myself, and have been from time to time brought forward and maintained, with numerous illustrations, chiefly in the American Journal of Science, since March, 1853, when my Essay on the Theory of Chemical Changes, and on Equivalent Volumes, was there published. I have, however, thought it well to present these views to the Academy in a connected form, as exemplifying my notion of some of the principles which must form the basis of a true mineralogical classification.

Mr. G. W. Hill presented a communication on the Inequalities produced in the Moon's Motion by the secular variation of the position of the Ecliptic.

Five hundred and seventy-seventh Meeting.

January 30, 1867.-STATUTE MEETING.

The PRESIDENT in the chair.

The Corresponding Secretary read a letter from Professor A. C. Kendrick of Rochester, New York, in acknowledgment of his election into the Academy.

The President called the attention of the Academy to the recent decease of M. Cousin of the Foreign Honorary Members.

Nominations for election into the Academy were presented from the Council.

In accordance with the recommendation of the Finance Committee, a special appropriation of five hundred dollars was voted for the engraving of plates to complete the publication of Dr. Storer's Memoir on the Fishes of Massachusetts. The following gentlemen were elected members of the Academy:

Dr. Gustavus Hay of Boston, to be Resident Fellow in Class I. Section 1.

Dr. Richard M. Hodges of Boston, to be Resident Fellow in Class II. Section 4.

Mr. Charles S. Peirce of Cambridge, to be Resident Fellow in Class III. Section 1.

Five hundred and seventy-eighth Meeting.

February 12, 1867. — ADJOURNED STATUTE MEETING. The PRESIDENT in the chair.

The Corresponding Secretary presented letters from Mr. C. S. Peirce and Dr. R. M. Hodges in acknowledgment of their election into the Academy.

The Committee appointed at the Special Meeting, May 8, 1866, to consider and report on the accommodation of the Academy, were discharged.

Professor Lovering reported from the Rumford Committee that the Medals voted to Mr. Alvan Clark were ready for presentation to him.

Five hundred and seventy-ninth Meeting.

February 26, 1867. SPECIAL MEETING.

The PRESIDENT in the chair.

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The President called the attention of the Academy to the recent decease of Dr. Henry Bryant of the Resident Fellows, and of Dr. Alexander Dallas Bache of the Associate Fellows.

Professor Lovering reported from the Rumford Committee