= changing the lettering of the former. They represent crystals of the species, seen in profile. A resemblance is apparent at a glance; besides, f: ƒ (over edge n) of Euclase = 106°; I:I (over ii) Barytocalcite 106° 54'. In Barytocalcite I, I are cleavage planes, and so also the plane O; and making I, I the sides of the fundamental prism and O, the base, the planes are as lettered in the figure. The plane in Euclase corresponding to O of Barytocalcite, would be t. Taking t as O, and f for the comparison as I, the axes of the two species are as follows: = In this view, r, u, i are the clinodiagonal prisms i, i, i; the plane s 4-, k=1-3, q, a plane between s and k, mentioned by Brooke and Miller, is the plane 1, or belongs to the fundamental octahedron, having for the angle X, 128° 48′. Remembering how Anhydrite diverges from the other sulphates RS in angles and cleavage, and Wollastonite, another lime species from Augite in the same particulars, and also noting the difference in angle between Tourmaline and Calcite, it will be admitted that the homomorphism is close. Since then, calcite and tourmaline are homomorphous, and also barytocalcite and euclase, tourmaline and euclase are mutual dimorphs as well as calcite and barytocalcite; and, moreover, Tourmaline and Calcite are isodimorphous. Hence the formula of Tourmaline, analogous with that of Euclase is the right one; and condensation in writing formulas is apparently the correct method, in place of the hypothetical subdivision adopted by Hermann, and others. The Laurent School in France is obviously right in making the protoxyds and peroxyds replace one another, the parts equivalent being those having the same number of atoms of oxygen. The principle is sustained by the homomorphism of Willemite and Phenacite, Zn Si and Be Si; or if Be be written Be3, other cases show the mutual replacement of Bes and 1. It is exemplified in Augite and Spodumene, the former R Si, the latter (R3, H) Si2; and also in many other species. 15. Observations on the formulas and relations of some species. Euclase, Datholite, and Sphene.-The formulas are as follows, in accordance with the above principles. Euclase, Datholite, adopting the above view, and making 3Ĥ replace 1Ĉa as in Scheerer's theory, has the fomula, Or if 3 replace 3Ĉa, it becomes, Sphene, SECOND SERIES, Vol. XVII, No. 50.-March, 1854. 28 In Sphene there are 3 of oxygen within the brackets as in the other species. The usual formula is 2Ca Si+Ca Ti3. But the relation in form to Euclase sustains the above mode of writing it. (Ĉa+Ti) Si3 is equivalent to (R) Si*, since R=RO+RO2; so that sphene is essentially a silicate of the common form, or of Ti in which part of Ti is replaced by Ca. Some chemists write for the sesquioxyd Braunite Mn+Mn, and others adopt the same form for other sesquioxyds, denying the existence of a proper sesquioxyd. There are but few anhydrous silicates, in which the bases exceed the silica in oxygen. These are Sillimanite, Kyanite, Andalusite, Topaz, Staurotide, with Tourmaline, Euclase and Sphene. Andalusite, Topaz and Kyanite, have the same formula AlS; in Sillimanite we have both Al Si, and Al Si; and in Staurotide, homœomorphous with topaz and andalusite, 1 Si. Hence the ratio of silica varies in the same species from to (and perhaps to 1) and in the same homeomorphous group, from to 3. The formulas of Euclase, Datholite and Sphene, are therefore essentially of one type. And if this be true, then ES (under which we include (R3, or B) Si) is trimorphous. (1.) Triclinic in Kyanite and Sillimanite; (2.) monoclinic in Sphene, etc.; (3.) trimetric in Andalusite, Topaz. G. Rose considers Kyanite and Sillimanite distinct in form. But the angles of Sillimanite observed are too doubtful to enable us to decide upon this point. Beryl and Eudialyte.-These species are shown to be closely homœomorphous on page 211. The formula of Beryl is (Be+1) Si; that of Eudialyte, (R++Zr) Si. We also add that Pyrosmalite and Dioptase have the ratio 1:2, if the water and also the chlorid in the former be excluded. Groups of Anhydrous Silicates among minerals.-Making the ratio between the oxygen of all the bases, and that of the silica of fundamental value, the anhydrous silicates among minerals mostly fall into five groups, presenting the ratios 1:3, 1:2, 1: 1, 1:1, 1:(--) I. Ratio 1:3. This includes Edelforsite, Ca Si, and Mancinite, Zn Si, both species of somewhat doubtful existence. II. Ratio 1:2. Includes Wollastonite, Augite, Spodumene, Wichtyne, Beryl, Eudialyte. III. Ratio 1: 1. Includes Eulytine, Bia Sa. IV. Ratio 1:1. Includes V. Ratio 1: (to -1). Includes-Triclinic, Kyanite, Sillimanite; Monoclinic, Euclase and Sphene; Trimetric, Andalusite, Topaz, Staurotide, and perhaps Lievrite; Dimetric, Gehlenite; Hexagonal, Tourmaline. From the Formulas of Datholite, Tourmaline, Axinite, Danburite, it follows that these are not borosilicates, the boracic acid being a base. It is a general fact that all mineral species containing boracic acid are either hemihedral or oblique in crystallization. The Feldspars and some other species do not appear at first to come into this system, unless the alumina and silica are considered as replacing one another, and on this ground, any ratio between 1:1 and 1:3 may be made out. The constancy of the oxygen ratio of R to (=1:3) in the feldspars, seems to preclude our taking such a liberty with the Al and Si. The following are the species, their oxygen ratios, old formulas, and the formulas proposed. The following species also belong to the section, as they have the same ratio 1:3 for the protoxyds and peroxyds; Leucite has the composition of andesite; and sodalite, etc., that of anorthite. * The formula of Helvin, as written by G. Rose, is (Mn, Fe) MnO. But we conform as closely to the analyses, if we add it becomes as above written, or ((R+MnS)3+} Be) Si 94, protoxyd of manganese (part Fe in the analysis) 398, nese 16.3. Si+Be Si+MnS MnO++MnS, when Silica 345, glucina sulphuret of manga = Oxygen ratio. Old formula. 8. Monometric. Leucite, 1:3:8 K3 Si2+3Al Si2 Sodalite, 1:3:4 Na3 +31 Si+Na Cl Lazulite. 4. Dimetric. Nepheline, 1:3:4 R2 Si+21 Si Cancrinite, 1:3:44 R2 Si+2Äl Si+RC The formulas of the feldspars in the last column, show what is equally plain in the oxygen ratios, that the species differ in the amount of silica, and this is the great essential difference. It is least in anorthite; and from this species it increases to 4ŝi in albite or orthoclase. This increase takes place without any change of crystallization, there being only very small variations in the angles. In anorthite, the oxygen ratio for the bases and silica is 1:1; and as anorthite is common in good crystallizations, and is every way a well characterized species, it shows us that 1 of oxygen of the silica to 1 for the bases is all that the feldspar type requires. Moreover, the relation of the species to Scapolite, which has the ratio 1: 1, also favors this view. Hence 1:1 may be considered the type-ratio, upon which, variations take place according to definite proportions. When silica abounds in the rock material in process of crystallization, and the other ingredients are at hand, the species holding the largest proportions of silica would be formed. The isomorphism of Sodalite, Hanyne, and Nosean, and dimorphism with Anorthite, parallel with the dimorphism of Leucite and Andesine, show that the ratio 1: 3: 4, is their type ratio. The very unlike substances Na Cl, Ca, S, Na S, are added without modifying the form, and although chemically included, are unessential to the type. The same is true of RC in Cancrinite, which has the crystallization of Nepheline. The facts above exhibited appear to show that a type admits of some variation in the amount of silica without changing the character of the species. In Meionite, having the ratio of 1:2:3, the scapolite type is exhibited; and Bischof and Rose take this as the only ratio of the species. But the ratio 1: 2: 4 appears to be required by most analyses of Scapolite, in which there is an addition to the silica. In the same mauner R3 Si2, with an addition of Si, becomes Hornblende.* Among the feldspars, Andesine and Leucite have essentially the oxygen ratio of Augite, 1+3:8 1:2, and the formula might *The amount of silica present may be one cause leading to the formation of Hornblende in place of Augite. But in pseudomorphic changes, the same proportions may result, by a removal of part of the bases, or an addition of magnesia as Blum and Bischof have suggested. 9 be written (R3+) Si. Moreover, oligoclase has similarly the oxygen ratio of Hornblende = (R3+) Si. Hence we may look upon Leucite, and Andesine, with Pyroxene, as in a certain. sense trimorphous. Still, their relation to the feldspar series is such that they are naturally classed with the other feldspars. The zeolites, if the water be excluded, have the oxygen ratios of the feldspar-section, as shown in the following table; the oxygen of the water in the zeolites is annexed to the name of the species Some of the species are correspondingly isomorphous with feldspar species, as Analcime with Leucite, Ittnerite with Sodalite; and the ratio 1:3:12 produces oblique forms in both series. But we do not intend to draw a general parallelism, as the water whatever its relations, must in some cases modify the ratios. But as regards the origin of the species, the table is an interesting one. Bischof remarks on the identity in the ratio between the oxygen of the bases and silica in chabazite and that of Hornblende, and thereby explains the occurrence of pseudomorphs of chabazite after hornblende. Pyrrhotine (Fe S) and Greenockite (Cd S).-As Pyrrhotine and Greenockite are homoeomorphous, they are naturally arranged in the same group, although the former has a little too much sulphur. The formula 5Fe S+Fe3 S3, may perhaps be written FeS [+Fe S], the latter term being unessential to the type. ART. XXII.-On Microscopes with large Angles of Aperture; by Dr. E. D. NORTH. We have no fuller or more careful statement of the mode in which an enlarged aperture increases the efficiency of a Microscope than that of Mr. Pritchard in his "Microscopic Illustrations," which is copied by Mr. Quekett. After explaining that since the whole diameter of the front lens receives a pencil of rays from each minutest point of the object, and that, consequently, when these pencils from each point are large, more light is received from the points separately as well as from the entire object, he adds: |