membered, 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 species 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 on 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 farther.

In approaching this great problem of classification, we have to examine-first, the physical condition and relations of each species, considered with relation to gravity, cohesion, light, electricity, and magnetism; secondly, the chemical history of the species; in which are to be considered its nature, as elemental or compound, its chemical relations to other species, and these 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 built up. Their application may be illustrated by a few points drawn from the history of certain natural families.

The variable relations to space of the empirical equivalents of non-gaseous 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 those bodies must be represented by formulas not less complex, and with equivalent weights far more

elevated than those usually assigned to the polycyanids, 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 non-gaseous species, and their densities, a relation as simple as that between the equivalent weights of gaseous species and their specific gravities. The gas, or vapor of a volatile body constitutes a species distinct from the same body in its liquid or solid state; the chemical formula of the latter being some multiple of the first, and the liquid and solid species themselves, often constituting two 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 densities of those species, in the case of homologous or related alcohols, acids, ethers and glycerids, are subject to no great variation. These non-gaseous species are generated by the chemical union, or identification, of a number of volumes or equivalents of the gaseous species, which varies inversely with the density of these species. It follows from this, that the equivalent weights of the liquid and solid alcohols and fats must be so high as to be a common measure of the vapor-equivalents of all the bodies belonging to these series. The empirical formula, C114H110C12, which is the lowest one representing the tristearic glycerid, 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 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, C,H,O,.

4

Starting from these high equivalent weights of liquid and solid hydrocarbonaceous species, and their correspondingly complex formulas, we become prepared to admit that other orders of mineral species, such as oxyds, silicates, carbonates, and sulphids, have formulas and equivalent weights corresponding to their still higher densities, and we proceed to apply to these bod ies the laws of substitution, homology, and polymerism, which have so long been recognized in the chemical study of the members of the hydrocarbon series. The formulas thus deduced for the native silicates and carbon-spars show that these polybasic salts may contain many atoms of different bases, and their frequently complex and varying constitution is thus rendered intelligible. In the application of the principle of chemical ho

AM. JOUR. SCI.-SECOND SERIES, VOL. XLIII, No. 128.-MARCH, 1867.

mology, we find a ready and natural explanation of those variations, within certain limits, occasionally met with in the composition of certain crystalline silicates, sulphids, etc., from which some have conjectured the existence of a deviation from the law of definite proportions, in what is only 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 aragonite, 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 reagents, increases with their condensation, or in other words, varies inversely as their empirical equivalent volumes; 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 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; whose constitution they assume to be represented by HO, 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 way in which nature builds up her units, by interpenetration and identification, and not 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 paper on the Theory of Chemical Changes and Equivalent Volumes, was there published. I have, however, thought it well to present these views in a connected form, as exemplifying my notion of some of the principles which must form the basis of a true mineralogical classification.

ART. XXV.-The Repsold Portable Vertical Circle; by CLEVELAND ABBE.

THE progress of practical astronomy in the United States. has already been distinguished by the suggestion of quite new ideas, as well as by improvements upon methods and instruments in use in Europe. It seems that a part of our national mission is to give a full and free development to whatever of good can be transplanted here from abroad; it is therefore unpardonable in us to neglect any opportunity of acquainting ourselves with the results of the experience of the astronomers of the Eastern hemisphere. The history of the brilliant life of F. G. W. Struve, to whom the world is indebted for the observatories of Dorpat and Poulkova, is doubtless familiar to all. The school of practical astronomy and geodesy that grew up under him at these two places, and is now officially established at the Central Observatory for the benefit of the Imperial Military Academy and other departments of the government, has, by the extent of the astronomical and geodesical works executed, made its influence felt far beyond the dominions of the Russian Czar. A residence of nearly two years at this Observatory has im pressed the writer most deeply with the correctness of that general opinion, which for years has instinctively pointed to this magnificent institution as the head-quarters of the practical astronomy of the present day.

The extent of the territory of the United States, and the oftrecurring demand for accurate topographical maps, will increase the interest with which we study the levels, barometers, base ap. paratus, universal instruments, vertical circles, prime vertical and extra-meridional transits, with which the Russian astronomers have sought to meet the demands made upon them. With them, as with us, celerity is of equal importance with accuracy. The extent of their territory must forbid them, as that of ours does us, from contemplating a minute triangulation of its entire superficies such as the smaller and more densely populated territories of the British Isles and the central European states both allowed and demanded. Our national government has rightly apprehended the importance of having the most accurate charts possible to be made of our extended Eastern and Western borders; of similar importance is the survey of our inland freshwater lakes, now in the hands of the engineers of the War Department; of great value also is the accurate survey of international boundary lines,-but the general survey and mapping of the interior presents a problem not dissimilar from that which is being solved by the Russian geographers for their own land. It was early seen that if astronomical determinations of relative

position could be made accurate to within one or two seconds of arc, the central points of reference being referred with much greater accuracy to each other and to a very few zero points, then would these relative positions, as derived from astronomical observations combined with an accurate knowledge of the figure of that portion of the earth's surface covered by these stations, suffice as groundwork for supplying the present wants of geographers and topographers. Inspired by the magnitude of the work, and supported by an interested military government, Struve and Tenner, co-working with the Norwegian and Swedish governments, carried out the astronomical and geodetical work recorded in the "Arc du Méridien de 25° 20' entre le Danube et la mér Glaciale"-at present under the authority of O. Struve and General Baeyer, co-working with Great Britain and Belgium; the field operations connected with the measurement of the arc of longitude between Valentia and Orsk are being rapidly pushed forward and will be finished in the summer of the present year. These two great works, and the similar ones that may be expected to follow in future years, when the surveys of the immense regions of Asiatic Russia come to be connected with the surveys now being carried on by the British government, furnish the necessary determination of the figure of the earth for that portion of the globe: they find their counterparts in the geodetic astronomic works in progress or already executed upon our Atlantic and Pacific sea-board, which will afford us determinations of arcs of latitude between the parallels of 26° and 48° north, and ought to be extended to the measurement of arcs of longitude of 60° on our northern, and 40° on our southern boundaries, or possibly one of 45° between Washington and San Francisco. Up to the present decade it must be conceded that the attention of geodesists has been perhaps too exclusively directed to the measurements of degrees of latitude; it is now become important to determine also arcs of longitude, and the present European international undertaking is one worthy of emulation. It is indeed with peculiar pleasure that we notice the comparatively slight expense that would attend the junction. of the present and proposed triangulations of the lake survey and of the coast survey, by a triangulation from Buffalo to Albany, leading thereby to the measurement of an arc of 18° on the parallel of 42° north between Chicago and the extremity of Cape Cod. At some future time the junction of the northwest end of Lake Superior and Cape Breton will become equally feasible, whence will result an arc of 33° on the parallel of 46° north. By the junction of the coast survey operations on the gulf of Mexico with the Pacific coast, taking advantage of the labors performed by the Mexican Boundary Survey we may be led to an arc of 33° on the parallel of 31° north, and the continuation