sum is 111° 42', in Heulandite, 98° 40'. When the axes are equal in two cases, the inclining of the vertical axis in one, diminishes the distance of its apex from the plane of the lateral axes, and consequently, the clinodiagonal prisms, and the octahedral forms on the obtuse basal edges and angles of the fundamental prism, become more and more flattened. This is the main source of the differences in angle between Gypsum and Heulandite. It shows us that in the oblique systems, we have to look to the relations of the axes, rather than to all the angles, in tracing out the resemblance of form among species. Another inference from this case of isomorphism is that although some cases show that cleavage is a subordinate character, we may err in comparing crystals of different species, if we do not give due importance to the cleavage directions. The 4. 12 21 S. Homœomorphism of Brookite and Columbite. Through the kindness of Mr. George J. Brush, I have recently received a specimen of Brookite from the Ellenville lead mine, Ulster Co., N. Y., occurring implanted on a group of quartz crystals. mine is situated in the Shawangunk grit, a Silurian rock. The crystal has a striking resemblance in habit to that of the Columbite of Middletown, Ct., even to minor points in the arrange-iz ment of the planes. The form suggested at once the homeomorphism of the species, and this is closely sustained by the angles. ii Columbite. 119° 40' 08675: 1:08291. The isomorphism is as close as between Celestine and Barytes. a:b:c Columbite. 0.8778: 1:0.8292 Heavy Spar. 13127: 1:081413. Now it is apparent that a in Heavy Spar is 13 times a of Columbite. The relation is consequently a simple one-and so simple that the species may be considered as belonging to one and the same homœomorphous series. The plane Po of Heavy Spar and P of Columbite would be nearly identical in their inclinations on the base of the prism. Such remarkable cases of homomorphism almost show that similarity of form may exist irrespective of the elements concerned, or of any numerical ratio in the atoms of the elements present. It is obvious that crystallization must follow, or go hand in hand with composition, but not lead the way in a classification of inorganic substances. Hermann has endeavored to meet some of the difficulties produced by homoeomorphism, by supposing two or more primary compounds as the bases of a class of species, the occurrence of which in different proportions shall form all the species of an homœomorphous group. This has an appearance of propriety as regards some groups of Silicates. But what symmetry in the constitution of the two can be made out in this way when Heavy Spar and Graphic Tellurium are compared; or Sulphur and Scorodite?or Arragonite, Bournonite and Nitre?-or Chrysolite and Epsom salt? or Pyroxene, Glauber salt and Hydromagnesite?—or Brookite and Columbite?-Such facts evince that homomorphism is depedent on something beyond mere arrangement of similar atoms or of assumed parts of a species. The great principle of equality of atomic volume appears to be at the basis of it, and it would seem to matter not what the elements are; if only the resultant has a certain relation as regards atomic volume to the atomic volume of another compound, there is isomorphism. Still there is often in related groups, a numerical relation in the elementary constitution which affords an explanation of the atomic volume relation, without looking to other considerations: and this numerical relation may be extended to the whole, when the subject is better understood. Such resemblances in homologous species, as between carbonates of protoxyds, etc., are of the most obvious kind, and have long been recognised. The Gerhardtian view, that protoxyds and peroxyds may replace one another, taking three parts of protoxyds to one of peroxyd, that is parts equal in oxygen-also explains in a numerical way many seeming anomalies, as in the case of the varieties of epidote, etc. Gerhardt applies it to the oxyds themselves, and seems to show that peroxyds and protoxyds crystallize alike; for in Martite, Specular iron (Fe) occurs in monometric forms, corresponding to the form of Periclase (Mg), and of Magnetite (Fe Fe); and Laurent has recognised that the monometric and rhombohedral metals (the latter isomorphous with Al and Fe) are two corresponding series, like the two forms of a dimorphous substance. In this way, Arinite and Danburite have a like relation and both are triclinic. In axinite the ratio between the oxygen of the bases and boracic acid, and that of the silica is 1:1; and the same is true for Danburite as the recent analyses of Smith and Brush show. The formulas may be written, for axinite (R3, R, B,) Si ; for Danburite (ca, B,) Si. The propriety of reckoning the boracic acid with the bases is shown by the fact that in Tourinaline the ratio thus obtained is the only one that is constant for all *This Journal, [2], xvi, 365. varieties of the species, a fact admitted by Rammelsberg, but more particularly remarked upon in explanation of the isomorphism by Naumann. The formula of Tourmaline on this ground would be (R, H. B) Si3. But when we meet with such a case as that of the feldspars, where the only constant ratio is that of the oxygen of the protoxyds and peroxyds, the oxygen of the silica varying, the law for the replacement of protoxyds by peroxyds seems to have no application. 9. Anhydrite. Hausmann, in his paper on the system of crystallization of Anhydrite, (Karstenite), and its homomorphism with the Barytes series,* arrives at the following comparisons: A closer approximation of Anhydrite is obtained by making the prism m, the vertical prism -, and s the brachydome ¦-∞. Then the axes and the above angles become, Anhydrite, 07348610-59398 118° 35' 107° 22' 77° 4' (102° 56'). Giving the crystal the position usually adopted for heavy spar, in which the above a, 1-, and 1- correspond respectively to 1-, 1- and, the axes are ab: c = 1·368: 1:0·8083, while those of Heavy Spar in the same position are 13127: 1:081413. The prisms m and s in this view, are - and -, and the octahedral planes are m-ñ, 2m - 2ň, 3m-3ň, with m= and = . The cleavage in this case is brachydiagonal and basal, with the macrodiagonal less perfect. The divergence in crystallization of the sulphate of lime from the others of the series, is a parallel fact with that of the bisilicate of lime (Ca3 Si2, Wollastonite) from pyroxene. 10. Valentinite or White Antimony and Senarmontite. Senarmontite is described as crystalling in the monometric system and Valentinite in the trimetric, the chemical species SbO3 being therefore dimorphous. But it is a fact worthy of remark, that the prism li (P) of Valentinite is identical in angle with the angle of a regular octahedron, 109° 28'. The vertical axis and macrodiagonal in Valentinite have the ratio that subsists between the axis and intermediate diagonal of an octahedron, or ✓2 1, and the vertical axis (a) equals nearly the sum of the two lateral (b+c). * Poggendorff's Annalen, lxxxiii, 572. ART. IX.-Reviews and Records in Anatomy and Physiology ; by WALDO I. Burnett. 1. Traitè sur le venin de la Vipère, par FONTANA. Florence, 1782. p. 229. 2. Handbuch der Entwickelungsgeschichte des Menschen, von G. VAL ENTIN. Berlin, 1835. p. 268. 3. Mikroskopische Untersuchungen ueber die Uebereinstimmung in der Struktur und dem Wachsthum der Thiere und Pflanzen, von TнOS. SCHWANN. Berlin, 1839. p. 165. 4. On the Minute Structure and Movements of Voluntary Muscle. By WM. BOWMAN, in the Philos. Transact., London, 1840, pt. 1, p. 457, -also, by the same, Articles, Muscle, and Muscular Action, in Todd's Cyclopædia of Anatomy and Physiology. 1842. 5. On Fibre. By MARTIN BARRY, M.D., &c., in the Philos. Transact. London, 1842, pt. 1, p. 89,--also, by the same, Neue Untersuchungen über die schraubenförmige Beschaffenheit der Elementarfasern der Muskeln, nebst Beobachtungen über die muskulöse Natur der Flimmerhäschen, in Müller's Arch., 1850, p. 529 ;--and, On Animal and Vegetable Fibre, as originally composed of twin Spiral filaments, in which every other structure has its origin; in the Edinb. New Phil. Jour., Oct., 1853, p. 317. 6. Observations on the Minute Structure and mode of Contraction of Voluntary Muscular Fibre; by W. M. DOBIE, F.B.S.E., in the Annals and Mag. of Nat. Hist., iii, 1849, p. 109. 7. Recherches sur la Formation des Muscles dans les Animaux Verlebrès, et sur la structure de la fibre musculaire en général dans les diverses classes d'animaux; par M. le Docteur LEBERT, in the Ann. des Sci. Nat., xi, 1849, p. 349. 8. Mikroskopische Anatomie, &c.; von Dr. A. KÖLLIKER. Leipzig, 1850, Bd. II, erste Hälfte, p. 199. Ar this late period of histological research it may seem indeed a superfluous task to pass in review a subject apparently so well understood as that of the minute and ultimate structure of Muscnlar Tissue. But the truth is, that on this, as with most other subjects in microscopy, the advent of new observers, or the reappearance of old ones, in the field of research, bring with them the prestige of hitherto undiscovered facts and new truths, and so the old land-marks and positions laid down by earlier but by no means less able, faithful, and accurate observers, seem likely to be disturbed. We do not propose here to enter upon any formal discussion of the historical relations of the doctrines advanced hitherto upon this subject. We desire to pass in review what we understand to be the leading features of the histology of this tissue, and SECOND SERIES, Vol. XVII, No. 49.-Jan., 1854. 12 therein to seek the more or less definitely expressed formula of its structure-all of which will put us in a somewhat favorable position to regard critically some doctrines which are as remarkable as they are new. But first of all we will briefly refer to some of the more prominent researches which, from time to time have served as true finger-posts as each succeeding investigator and explorer has passed along the road. Although there can be but little doubt that some of those excellent old naturalists and observers of the last two hundred years, caught, with their rude magnifying powers, not erroneous glimpses of the complex intimate structure of muscle, yet any definite ideas of its real composition as explanatory of its mode of action, cannot be said to have been entertained until the days of the cell-doctrines of Schwann and Schleiden. It is true that since the time of Leeuwenhoek, or even, perhaps, before, it has been known that voluntary muscle could be split up into fine threads; but this was the limit of their real knowledge, for, if we except Foutana, none of the observers appear to have had distinct ideas of the nature of these threads. Valentin, from studies upon the development of this tissue, had perceived clearly the general character of its composition, and Schwann, a few years after, applied more or less completely and successfully his cell-doctrine to its elementary formation and constitution. These undoubtedly were very important steps; but the contribution which marks an era in the histological history of this tissue is that of Mr. Bowman, which appeared in the Philosophical Transactions of 1840. Rare are the examples in the whole domain of minute anatomy, where so much real progress has been made by a single set of researches, as in this case. In more than one particular, Mr. Bowman exhausted the subject, and it is perfectly correct to say that in the leading and essential features of the minute anatomy of voluntary muscle, the numerous microscopical observers have added but little if any thing during the thirteen years that have since elapsed. Bowman's results are so well known and even familiar to all anatomists that it is almost out of taste to repeat them; but I will state them in a brief form : A series of discs succeeding each other in a row and at regular intervals; a row of discs thus formed constitutes the primitive fibrilla. Numbers of such fibrillæ are bound together with an exact coaptation of their discs and intervening spaces-constituting the striated muscular fibre. This fibre thus composed of a bundle of fibrillæ is encased in a special sheath, the sarcolemma. And, finally, a greater or less number of such encased fibres, bound together, constitute a fasciculus, and these fasciculi make up the gross muscle. We have then muscle: fasciculus, fibre, fibrilla, disc. Fibres may be split lengthwise, forming fibrillæ, and cross |