determined by reference to the edges of the cube if the three plane angles are known which the three projections of the face of the crystal make with the three edges of the cube. Two plane angles even are sufficient, for the third can be calculated from the first two by the simple formula

tan. a cot. b cot. c;

a, b, c being the plane angles which the three projections of the face of the crystal make with three edges of the cube meeting at the same summit.

A second face of the crystal will be equally determined as regards its direction, by the three angles a, B, y, these three angles corresponding to the angles a, b, c, of the first face of the crystal, as was said above.

It follows therefore that if the three angles a, b, c, are known, or two only of those angles, and the three angles a, ß, y, or two only of those angles, we can calculate the dihedral angle of the two faces of the crystal by the formula

If x is indeterminate, it can be calculated by the formulæ

It only remains then to point out a practical means of measuring the angles a, b, c, a, ß, y.

I place in the eye-piece of a microscope a cylinder of flint glass whose index of refraction is greater than that of Canada balsam. This cylinder (the two bases of which are exactly parallel) is divided in halves by a plane perpendicular to the bases; the two rectangular faces are polished and fixed together again by Canada balsam. This cylinder is placed in the eye-piece so that its upper base is in the focus of the upper lens of the eye-piece, the two bases being perpendicular to the optic axis of the microscope, and the median plane of the cylinder passing through the optic axis and through the zero of the division of the revolving stage.

Under these conditions if the microscope receives the light in a direction parallel to the median plane of the cylinder, an illuminated field will be seen crossed by a line forming a reticle; but if the microscope receives the light obliquely to the median plane of the cylinder, the reticle will be seen to divide into two, and if the eye is inclined to the right or the left, the reticle will be bordered on one side by a black band of greater or less breadth, and on the other side by a bright band, this phenomenon being produced by the total reflexion which the luminous rays experience in traversing the cylinder obliquely and meeting the layer of balsam whose refractive index is less than that of the flint.

Consequently, if the reflecting face of the crystal has its projection perpendicular to the zero line of the microscope, a reticle will be seen equally illuminated to the right and left; but if the crystal is turned with the stage of the microscope, the reticle immediately becomes bordered on one side by a black band and on the other by a bright band. By placing the cube on the stage of the microscope, on its different faces in succession, it is easy to measure the angles which the projections of the faces of the crystal make with the edges of the eube, and it is seen that, however small a crystal may be, the phenomenon above described will be produced, provided that the crystal is able to reflect the light over a space sufficiently large to illuminate the centre of the reticle. It is sufficient that the face of the crystal should be about two millimetres, but a crystal of a thirtieth of a millimetre can be measured with an enlargement of only sixty diameters. A crystal of of a millimetre would require an enlargement of two hundred times.

In order to allow each face of the crystal to be placed successively in the axis of the microscope without changing the relative directions of the faces of the crystal, the edges of the cube, and the divisions of the stage, it is necessary to adapt to the revolving stage another stage movable in two rectangular directions by means of two micrometric screws, or, for more precision, to have a micrometric screw for the rotating movement.

To appreciate the degree of precision which this method gives, I have measured crystals of less than of a millimetre, such as the cleavages of spar, of blende, and of the microscopic crystals of quartz, and the error has never exceeded one degree.

This error is great, but these first attempts have been made with an eye-piece which is still imperfect, and I have not kept to the conditions of illumination which are necessary to obtain the best possible effect. I am convinced that, with slight modifications, great exactitude can be attained.

I have in view another system of eye-piece, also based on total reflexion, which ought to be still more sensitive than the system which I have just described, but not having yet experimented upon it, I abstain from describing it. The improvements which I have in view will, if they answer, form the subject of a further communication.*

The Microscopic Structure of the Stromatoporida, and on Paleozoic Fossils mineralized with Silicates, in illustration of Eozoon.-Principal Dawson communicated a paper on this subject to the Geological Society, which was read at the meeting of the 5th June:-The fossils included in the group Stromatoporidæ occur from the Upper Cambrian to the Upper Devonian inclusive, and are especially abundant in the Trenton, the Niagara, and Corniferous formations. The author regards Stromatopora as a calcareous, non-spicular body, composed of continuous, concentric, porous laminæ, thickened with supplemental deposit, and connected by vertical pillars, most of which are solid. The surface shows no true oscula; but perforations 'Comptes Rendu,' vol. lxxxv. p. 172.

made by parasitic animals have been mistaken for such. From the structure they could not have been related either to Sponges or to Hydractinice, and still less to Corals; they are truly Foraminiferal, and may be regarded as the Paleozoic representatives of Eozoon. Stromatopora occurs infiltrated with calcite or silica, or with its structure wholly or in part replaced by crystalline silica or dolomite. The author concluded his first section with the characters of the genera which have been included in the Stromatoporida.

In the second part he noticed a number of facts relating to the occurrence of hydrous silicates, of the nature of serpentine and loganite, infiltrating Paleozoic fossils and illustrating the mode of occurrence and mineralization of Eozoon. Instances of this kind were said to be exceedingly common, showing that such silicates, whether originating as direct deposits from water, or as products of the decomposition of other minerals, are efficient agents in the infiltration of the pores and cavities of fossils, and have played this part from the earliest geological periods.

A Microscopical Study of some Huronian Clay-slates.-At the meeting of the 19th June, a paper by Dr. Arthur Wichmann was also read, of which the following is an abstract:-Although a considerable amount of attention has been devoted during recent years to the microscopical study of clay-slates and slate-clays, yet in none of the published researches on this subject has any account of the structure of the clay-slates of Archæan age been given. The author has availed himself of the extensive series of Huronian clay-slates collected by Major T. V. Brooks in the country around Lake Superior to supply this deficiency. The succession and relation of the rocks described have been fully treated of in the work of Hermann Credner and the publications of the Geological Survey of Michigan.

The chief object of the author is to discuss the origin of the crystalline constituents in clay-slates, and at the outset he describes in detail the microscopical character of clay-slate, of novaculite or whetstone, and of carbonaceous shales and slates respectively, dwelling more especially on the crystallized minerals which can be detected in each of these rocks, and the nature of the isotropic ground-mass which sometimes surrounds them. He then points out that three theories have been advanced to account for the presence of these crystalline constituents in clay-slates. According to the first of these theories, the crystals in question are regarded as the product of chemical action in the ocean in which the original material was deposited. The second theory attributes the formation of the crystalline minerals to processes of metamorphism which have taken place subsequently to the solidification of the rocks. The third theory refers them to aggregative action going on in the still plastic clay-slate mud prior to its solidification. The first of these theories has been maintained by G. R. Credner, but against it the author adduces numerous arguments, and especially points out the difficulty of supposing an ocean capable of depositing from its waters at successive periods minerals of such different chemical composition as chlorite, actinolite, &c. In opposition to the second theory, which has received the

support of Delesse, the author points out the existence in the rocks in question of broken crystals, which have been recemented by the surrounding clay-slate substance. The author is thus led to incline towards the third theory, in favour of which some striking facts, drawn from the microscopical structure of the rocks, have already been adduced by Zirkel. He admits, however, that later metamorphic actions are not to be excluded in seeking to account for the origin of the crystalline constituents of clay-slates, and points out that four distinct stages must be considered in the series of changes by which the rocks in question have acquired their present character:-1st, the deposition of the mud; 2nd, the formation of minerals during the plastic state; 3rd, the separation of materials during solidification; and 4th, the action of metamorphic processes.

Preparations of Infusoria, &c.-Professors Cohn (of Breslau) and Stein (of Prague) commend a new process, discovered by Herr Duncker of the "Microscopic Institute" of Berlin, "after a series of long-continued and laborious researches, for preserving with the greatest possible truth to nature even the most delicate aquatic microscopic organisms, including many whose production has been hitherto considered an impossibility:" these include Confervæ, Desmidiæ, and Diatoms (with the organic parts preserved in their integrity), Rhizopods (Amoebæ, &c.), Flagellata (Volvox, Cryptomonads, Astasia), Cilio-Flagellata, Ciliata, Rotifers, Entomostraca (Cyclops, and particularly Daphnia, with the utmost possible preservation of the soft parts), Tardigradia, and Larvæ. It is suggested that such preparations will facilitate the determination of the microscopic fauna and flora of particular localities.

The Binocular with High Powers.-Suggestions have recently been revived in American and English journals that Wenham's ordinary binocular prism can be effectively used with the highest powers, inasmuch as by special modes of illumination-either by duplicating the light or directing it from two positions at a greater angle, as with a second mirror, the Paraboloid, or Powell and Lealand's condenserthe two fields may be obtained free from any defect of light at the outer margin, both with a , an, or even a object-glass. In regard to this, Mr. Wenham writes that "his own opinion of the binocular microscope, in any form where the result is obtained from half the object-glass, is that in powers higher than one-fifth it ceases to be of much utility, as the combined images cannot compensate for the loss of definition in each eye. In the form of prism by means of which the full aperture is obtained in each eye with equal illumination in both tubes, the effect is much superior, and in lengthened observations with either high or low powers it affords great relief to be enabled to use both eyes continuously without regard to any special mode of illumination."

The Germ Theory of Disease.-The number of the Linnean Society's Journal issued on 23rd May,* contains the concluding portion of Dr. Bastian's now familiar experiments with urine and potash, and

* Vol. xiv., No. 74.

includes his observations on the germ theory of disease. The author considers that" by his experiments, in addition to the disproof of a false hypothesis, he has unquestionably done one or other of two things: either (a) he has proved that living matter may be now evolved de novo, or (b) he has succeeded in bringing back to life germs which hitherto were so powerless and latent as to have been regarded by other experimenters as hopelessly dead. Even the latter is no mean result for the physician and the science of medicine, since the question of the truth or the reverse of the 'germ theory of disease is thereby almost as powerfully influenced as if the former alternative had been established with complete certainty.

Though it may be conceded that with our present state of knowledge an affirmative decision in regard to the absolute proof of the present occurrence of Archebiosis may be still withheld, there is no similar warrant for suspense of judgment in regard to the germ theory of disease, or, as it is also called, the doctrine of contagium vivum. Existing evidence is abundantly sufficient for the rejection of this doctrine as untrue; and from the evidence, more or less fully referred to in the paper, it seems to him legitimate to conclude:

First, that if we are to be guided by the analogy now dwelt upon as existing between fermentation and zymosis, it would be perfectly certain that the latter process can originate de novo, that is, under the influence of certain general or special conditions, and where specific contagia of any kind are at first absent, though they subsequently appear as results or concomitant products. So that an exclusive theory of contagion,' as the only present cause of communicable diseases, is not supported by experimental evidence.

Secondly, that some contagia are mere not-living chemical principles, though others may be living units.

Thirdly, that even in the latter case, if the primary contagious action be really due to the living units, and not to the media in which they are found, such primary action is probably dependent rather upon the chemical changes or contact actions' which they are capable of setting up, than upon their mere growth and vegetative multiplication.

Fourthly, that where we have to do with a true living contagium (whether pus-corpuscle or ferment organism), the primary changes which it incites are probably of a nature to engender (either in the fluids or from the tissue-elements of the part) bodies similar to itself, so that the infected part speedily swarms therewith. When pus from a certain focus of inflammation comes into contact with a healthy conjunctiva, and therein excites a contagious form of inflammation, no one adopts the absurd notion that all the pus-corpuscles in this second inflammatory focus are the lineal descendants of those which acted as the contagium; and the mode of action may be altogether similar when the matter containing Bacilli, by coming into contact with a wounded surface, gives rise to splenic fever and the appearance of such organisms all through the body. The old notion about the excessive self-multiplication of the original contagium is probably altogether erroneous. Thus all the distinctive positions of those who