various epidotes give from two to six per cent of magnesia, and from one to more than two per cent of soda.*—(See Dana's Mineralogy, 4th Ed., ii, 407).

6. The composition of zoisite as already noticed by Rammelsberg is identical with that of meionite, a species which is shown by its hardness of 60 and its density of 2.6-2.7, to belong to the dimetric division of the feldspar group, where it is to the scapolites what anorthite (with the ratios 1:3: 4,) is to the triclinic feldspars. The mineral described by Boulanger as saussurite from Mt. Genèvre, with a density of 2 65, gives according to his analysis (III) the oxygen ratios 7:37:14 18: 23.75=1: 1.91 2.22, and appears to have been meionite. In de Saussure's analysis, (11) if we regard the iron as protoxyd, we obtain the ratios 5.22: 14.02: 23.50, but there is then a deficiency of 4:50 p. c. in the analysis of an anhydrous mineral. Klaproth's results (1) seem to indicate a mixture of a silicate like pyroxene or tale as in VII, while the anomalous softness of v and the facility with which it is decomposed by acids, render it difficult to form any conclusion about the saussurite of the Fiumalto examined by Boulanger. His analysis of the saussurite of Orezza (IV) gives the oxygen ratios 7.23: 14-95: 23-25-1: 2.06: 3.21, so that it has the composition of meionite and zoisite, while its specific gravity is between the two. Although inferior in hardness, it resembles zoisite in resisting according to Boulanger the action of concentrated sulphuric acid.

The saussurite of Orezza evidently demands farther study; it remains to be seen whether the verde di Corsica or verde antico di Orezza, as it is also named, (the corsilite of Pinkerton, Petralogy, ii, 78), which is regarded by d'Halloy as the typical euphotide, is not distinct from that of Mt. Rose. Delesse found the specific gravity of the Corsican euphotide to be only 3.10. The name

* Laurent in an essay on the silicates published in 1849, insisted that distinctions based on the relations between the proportions of protoxyds and sesquioxyds are of but secondary importance, since these oxyds may replace each other to an indefinite extent in many silicates, without altering the mineral type. This principle Laurent then illustrated by the epidotes among other species, showing from Hermann's analyses of thirteen specimens (of which the analyst had made three sub species,) that although the oxygen ratios of the protoxyds and sesquioxyds offered considerable variations, it was possible by admitting the substitution of the one for the other, to reduce all these epidotes to the same formula with garnet, SiO, R3, i. e., SiO+RO, in which RO, represents both protoxyds like CaO, and sesquioxyds like alO (=A1,03÷3).-(Comptes Rendus der Travaux de Chemie, 1849, p. 277).

This idea of Laurent although at the time rejected, is now universally admitted Dana has adopted it in the 4th Ed. of his Mineralogy; Hermann has recently reviewed his own analyses and accepts Laurent's view, while Rammelsberg who illustrated it in his laborious researches on the tourmalines, has recently applied it to the augites and hornblendes containing peroxyd of iron. But while there is no doubt of the general and wide application of this principle of the homomorphism of protoxyds with sesquioxyds, it is nevertheless true as Dana has remarked, that in the epidotes the variations in the oxygen ratios of the protoxyds, sesquioxyds and silica are about 1:2:3, which may be looked upon as the normal ratio for epidote, as 1:1:2 is for garnet, and 3: 2:5, for idocrase.-(This Jour., [2,] xxv, 406).

of verde di Corsica, which in the arts is applied to the rock as a whole, is by Beudant restricted to the contained smaragdite.

I have lately examined a pale yellowish-green compact and apparently homogeneous rock, which forms great beds among the crystalline schists of the Shickshock mountains in Gaspé, and has somewhat the aspect of saussurite. Its hardness is 7.0 and its density 304-309. It is exceedingly tough and sonorous, has a conchoidal fracture with a feeble waxy lustre, and is translucent on the edges. The analysis gave as follows:

The oxygen of the protoxyds and peroxyds in the above analysis equals 443 and 8.60. If to these we add the silica corresponding to 13:00 of oxygen, we shall have 61:33 parts of epidote, leaving 32-22 parts of silica uncombined. The density of the mass is that of a mixture of epidote and quartz in the above proportions, and in some specimens where the rock becomes granular, the two species are easily distinguishable. (Geol. Survey of Canada, Report, 1858). This epidote rock then is completely distinct from the saussurite of Orezza.

The two silicates zoisite and meionite offer a remarkable instance of that isomerism in mineral species upon whose importance I have long insisted. The relation of the specific gravity to the empirical equivalent weights of minerals, must enter as an essential element into a classification which shall unite the chemical and natural-historical systems. Similar isomeric relations exist between kyanite and sillimanite, rutile and anatase, and as I have elsewhere endeavored to show, among the carbon-spars. It becomes necessary in the study of mineral species to determine their relative equivalent weights, to which specific gravity must be the chief guide.-(Proc. Am. Assoc. Adv. Science, 1854, pp. 240-247).*

*The action of heat upon organic bodies of high equivalent tends to resolve them into simpler and less dense forms, (we except of course the simultaneous productions of small portions of more complex hydrocarbons). Similar results are obtained when the denser silicates are fused. Thus according to Magnus the specific gravity of garnet is lessened one-fifth by fusion, while that of idocrase is reduced from 3:34 to 294. Epidote by ignition has its density changed from 340 to 3-20 according to Rammelsberg, and saussurite is converted by fusion into a soft glass of specific gravity 28. The silicates thus modified are decomposable by acids like the basic feldspars; idocrase and garnet crystallize after fusion, the latter according to von Kobell in octahedrons. Deville found the density of hornblende and pyroxene to be reduced by fusion from 3.2 to 2-8, orthoclase from 2:56 to 2:35, and labradorite. from 2'689 to 2.525.

7. Smaragdite. The smaragdite or diallage of the euphotides appears to have been first examined by Vauquelin, who found in a specimen from Corsica with specific gravity 30; silica 50·0, alumina 21.0, lime 13.0, magnesia 6-0, oxyd of iron 5.5, oxyd of chromium 7.5, oxyd of copper 1.5=104.5. (Beudant, Mineralogie, ii, p. 134). Boulanger subsequently analyzed the diallage from the euphotide of the Fiumalto already described. It had a density of 3.10, and gave silica 40-8, alumina 12.6, lime 23.0, magnesia 11-2, protoxyd of iron 3-2, protoxyd of manganese 1.4, oxyd of chromium 20, water 5.2=99.4.—(Ann. des Mines, [3], viii, 159).

I have analyzed the grass-green smaragdite already described as occurring in masses an inch in diameter imbedded in the saussurite VI. It was to some extent penetrated by the latter mineral, and contained irregularly disseminated slender prisms of hornblende, apparently associated with talc. The analysis gave as follows:

A partial analysis of another specimen gave alumina 3.80, lime 14.22, magnesia 18.07, protoxyd of iron 2:34. The pale green color of the powdered smaragdite becomes brownish on ignition. The small portion of nickel, whose presence I have already shown in a great number of chromiferous serpentines and diallages,* gave evidence of a trace of cobalt before the blowpipe. The oxygen ratios of the silica, alumina and protoxyds in the above analysis are as 28.96: 2.12: 13-29. Its composition is evidently that of a pyroxene, with some admixture of saussurite and probably of talc. A portion of the latter mineral from one of the euphotides of Mt. Rose, was submitted to analysis, and allowing for a small admixture of saussurite, was found to have the composition of ordinary talc, being a hydrated silicate of magnesia with a little iron and a trace of nickel.

Conclusions.-1. The true euphotide is distinct from the diallagic dolerites, with which most modern lithologists have confounded it, and which are composed of pyroxene and a feldspar having the constitution of andesine, labradorite, or a still more basic variety approaching to anorthite. By the substitution of hornblende for pyroxene these dolerites pass into diorite or diabase.

* This Journal, [2,] xxvi, 237.

2. The euphotides of Mt. Rose according to my observations are composed of smaragdite (a pyroxene containing chrome and nickel,) in a base of saussurite, which is a compact zoisite, or lime-alumina epidote, containing portions of magnesia and soda, and having a hardness of 70 and a specific gravity of 3.333.38; characters which at once distinguish it from the feldspars. These euphotides also contain as accidental minerals, talc, actinolite and occasionally a vitreous cleavable feldspar resembling labradorite.

3. While the minerals analyzed as saussurite by Stromeyer and Delesse are feldspars, that from Mt. Genèvre examined by Boulanger has the composition and specific gravity of meionite, a species which is isomeric with zoisite; the saussurite from Orezza according to the same observer has a like composition but a density intermediate between these species. The saussurite examined by Thompson is apparently a petrosilex.

4. By its great density and its composition, the euphotide of Mt. Rose is related to certain rocks in which a white garnet, resembling saussurite, is mixed with serpentine, with hornblende, and with a feldspathic mineral. These aggregates associated with ophiolites, albitic diorites, and a rock made up of epidote and quartz, occur in the form of beds in the crystalline schists of the altered Silurian series in Canada.*

ART. XXXVIII.-The Dynamic Theory of the Tides; by Maj. J. G. BARNARD, A.M., Corps of Engineers, U. S. A.

IN his treatise on "Tides and Waves," Mr. Airy uses in reference to Laplace's investigation of the tides, the following language:

"If now, putting from our thoughts the details of the investigation, we consider its general plan and objects, we must allow it to be one of the most splendid works of the greatest mathematician of the past age. To appreciate this, the reader must consider, first, the boldness of the writer who, having a clear understanding of the gross imperfection of the methods of his predecessors, had also the courage deliberately to take up the problem on grounds fundamentally correct, (however it might be limited by suppositions afterwards introduced); secondly, the general difficulty of treating the motions of fluids; thirdly, the peculiar difficulty of treating the motions when the fluids cover an area which is not plane but convex; and, fourthly, the sagacity of perceiving that it was necessary to consider the earth as a revolving body, and the skill of correctly introducing this consideration. The last point alone, in our opinion, gives a greater claim for reputation, than the boasted explanation of the long inequality of Jupiter and Saturn."

*See my Contributions to the History of Ophiolites, this Journal, [2], vol. xxv, 217, and xxvi, 234.

The equilibrium-theory, manifestly false in treating the problem simply as one of statics, disregarding the motions of the fluid which must accompany the changes of its superficial form, is, at least, an explanation of the phenomenon, though not a true theory.

Mr. Airy remarks of it;

* "it must be allowed that it is one of the most contemptible theories that was ever applied to explain a collection of important physical facts. It is entirely false in its principles, and entirely inapplicable in its results. Yet, strange as it may appear, this theory has been of very great use. It has served to show that there are forces in nature following laws which bear a not very distant relation to some of the most conspicuous phenomena of the tides; and, what is far more important, it has given an algebraic form to its own results, divided into separate parts analagous to the parts into which the tidal phenomena may be divided, admitting easily of calculation and of alteration, and thus at once suggesting the mode of separating the tidal movements, and affording numerical results of theory with which they are to be compared. The greatest mathematicians and the most laborious observers of the present age have agreed equally in rejecting the foundation of this theory, and comparing all their observations with its results. And till theories are perfect (a thing scarcely to be hoped for in any subject, and less in the tides than any other,) this is one of the most important uses of theory."

If we could indeed grasp the conditions of the problem-bring into our analysis the expression of the actual form (or even a tolerable approximation to that form) of the solid nucleus whose depressions form the ocean beds, then indeed the solution would be that which we seek, not a mere explanation, but a true expression for the phenomena, as they actually occur.

While we are utterly incapable of doing this-when such a mind as Laplace's is found unable to grasp the conditions of a "Dynamic Theory," it seems to me that Mr. Airy wastes epithets upon the "equilibrium theory" which, after all, I presume no physicist ever regarded as a real theory of the tides, but rather a mere putting into mathematical form of their obvious immediate cause. If, to get over the difficulties of the true theory, and bring the problem within the grasp of our mathematics, we are obliged to make assumptions, entirely at variance with the facts which really govern the question-which cannot even approxi mate to them—we might as well, so far as the solution we seek is concerned, go one step further, and suppose there is no motion at all-or that the fluid is destitute of inertia; in other words fall back upon the equilibrium theory, for the problem is no longer that which we propose, but a mere mathematical study which may yield us some curious results.