valuable, especially if the irrelevant matter is reduced to a minimum. The small book before us contains a carefully compiled and accurate digest of many of the most prominent facts of human physiology, with incidental references to some of the best known peculiarities of a few of the lower animals, illustrated by several appropriate and well-selected diagrams, among which, however, there is an important one indicating the general distribution of the arterial system, which is unfortunately reversed, and another explaining the leverages of the body, representing a man as standing with his centre of gravity far in front of the tips of his toes. The language employed is clear and concise, whilst many of the best known terms in common use among physiologists are explained in a glossary at the end of the book. Some of the practical illustrations suggested to the pupil for his own instruction are particularly to the point. There are some explanations with which, however, we cannot agree, such as that the activity of the circulation of the blood which accompanies physical exercise is the result of the alternate compression and relaxation of the veins; and that a much vaunted theory as to the cause of cholera, which involves the purchase of a much advertised apparatus for its relief, has sufficient foundation for even the slightest mention in any book for the use of students. The non-technical character of the work will commend it to many as a useful introduction to physiology.

By

The Gardener's Year Book and Almanack, 1875. Robert Hogg, LL.D., F.L.S. (Journal of Horticulture Office.)

THIS is a very handy and valuable little book. The information it contains is of a kind that may be thoroughly depended upon. Besides a great deal of practical information of a miscellaneous sort, there are tolerably copious gardening directions for each month, besides selected lists of fruits and vegetables, and of the new plants of last year. It will be very useful to amateur gardeners, and would be still more so if it gave some short and plain descriptions of various horticultural operations-such, for example, as pruning different kinds of fruit-trees.

LETTERS TO THE EDITOR

[The Editor does not hold himself responsible for opinions expressed by his correspondents. Neither can he undertake to return, or to correspond with the writers of, rejected manuscripts. No notice is taken of anonymous communications.] Absence of Microscopic Calcareous Organic Remains in Marine Strata charged with Siliceous Ones In a letter headed "Deep-Sea Researches," and subscribed "W. C. Williamson, Owens College," in your issue of the 24th Dec. (vol. xi. p. 148), the author, after having stated that Dr. Wyville Thomson has come to the conclusion that the calcareous Globigerine and other such elements had been removed by the "solvent action of carbonic acid accumulated in the deep-sea waters," adds that, "In my memoir [1847, op. cit.] I arrived at the same conclusion."

Then follow extracts from the "Memoir" itself, alluding to the removal of all the calcareous forms, leaving only the siliceous structures," by "carbonic acid gas in solution in water.'

Finally, the author states :-"After venturing upon these conclusions in 1847, not as mere speculative guesses, but as the deliberate result of a long series of investigations carefully worked out, I need scarcely say how intense was the interest with which I read Dr. Wyville Thomson's observations, which so thoroughly sustain and confirm the accuracy of mine. My conclusions were wholly derived from the microscopic observations of earths and rock specimens which I compared with the few examples of foraminiferous ooze with which I was then familiar."

"Felix qui potuit rerum cognoscere causas."

In enumerating the different kinds of des ruction which take place in sponge-spicules generally, I have noted that the calcareous spicule is subject to one in particular, "in which there is a general breakdown of the whole fabric, which gradually

becomes resolved into a group of aqueous-looking globules, of different sizes, among which there is not a trace of the original structure to be seen. Were this change confined to those calcareous spicules which I have mounted in Canada balsam, I should have inferred that it was caused by the balsam; but I find that the same change accompanies these spicules where they may have been taken in by the kerataceous sponges to form an spicules of the Echinodermata, which may lie side by side with axis for their horny fibre; and it is worthy of remark that the them, do not appear to be similarly affected. Of what nature the origin of this disorganisation may be I am ignorant; it is a chemical question; but the destruction takes place so rapidly in many instances that I have for some time past ceased to mount any more calcareous spicules, and now preserve a record of them by immediate sketches." (Ann. and Mag. of Nat. History, vol. xii. 1873, p. 457.)

Thus it follows that a removal or an annihilation of the forms of these microscopic calcareous organisms takes place after they have been repeatedly washed in fresh water, dried under a great heat, and covered at the same time with balsam, that is, treated

artificially; as well as naturally, when they are mixed up with

other microscopic organisms to form the core of the horny fibre of marine sponges; while the same thing takes place with the Foraminifera, as testified by slides, in some of which fragments of Operculina arabica mounted upwards of twenty years ago have nearly all passed into dissolution, and others in which the spicules of calcareous sponges which were mounted not more than six years since have disappeared altogether, leaving nothing but a few aqueous-looking globules in their places respectively.

66

So that this dissolution may arise without the presence of carbonic acid gas in solution in water;" and as it is common to the calcareous organisms mounted in balsam for the cabinet, as well as in the core of horny fibre in the marine sponges of the 'deep-sea," we may fairly assume that the removal of the calcareous forms from the siliceous ones in marine deposits may be due to more causes than that assigned by the author of the letter to which I have alluded.

Moreover, even the siliceous spicules which form the core of the glassy fibre in the vitreous sponges may, with the circumjacent layers of the fibre itself, undergo absorption to such an extent, in the skeleton of these sponges, after death, as to leave nothing but a siliceous shell with hollow, continuous tube throughout.

Such are the results of my microscopic observations among these minute organisms, and therefore, in the concluding words of the letter under reference, "I think I am justified in wishing the fact to be placed on record."

Indeed, so common and rapid is the process of destruction or inherent disintegration among the microscopic calcareous organisms which I have mentioned, that I am compelled to the conclusion that it is to this chiefly, and not to "carbonic acid gas in solution in water," that we must look for a satisfactory explanation of the fact that minute calcareous organic forms are comparatively absent among the siliceous ones of marine deposits, both recent and fossilised.

The agency of decay is as difficult to comprehend as the agency of development (why we should die any more than why we should live); hence it becomes unphilosophical to limit the operations of either to any one process. All that appears certain in the matter is, that the three great attributes of the system, viz., creation, preservation, and destruction, form a cycle in which, to speak figuratively, the words "perpetual change may be enwreathed. HENRY J. CARTER

Budleigh Salterton, Dec. 26, 1874

The Constant Currents in the Air and the Sea THE Philosophical Magazine for July, August, and September contains a memoir, continued through the several numbers, by Baron N. Schilling, Captain in the Imperial Russian Navy, on "the Constant Currents of the Air and the Sea." It appears that this memoir was first published in the Russian, afterwards in the German, and finally translated and published in the English language; so that it seems to be regarded as a memoir of con-. siderable importance.

When any new and, extraordinary results are obtained in any department of important scientific inquiry, the interests of science require that the basis of these results should be critically examined before they are received; and this is especially so where,

as in this case, the results are entirely at variance with those of profound and elaborate researches in the same direction which have preceded. We propose, therefore, to examine briefly only a very few points in the reasoning from which these results have been deduced.

The author states in the commencement that equilibrium is disturbed by the three following causes :-

(4.) Alteration of the specific gravity of the water or air. (b.) The rotation of the earth on its axis.

(.) The attraction of the sun and moon.

He accordingly treats the subject under these three general heads. Under the first two he endeavours to show that none of the usual causes to which the currents of the ocean and the atmo

sphere have been usually referred can have much, if any, effect in producing them, and that they must, therefore, be due to some other cause. This seems to be designed to make way for the introduction into this subject of the new disturbing forces contained above under the last head (c). Much might be said with regard to what is stated under the first two heads in disparagement of the forces upon which these currents have been heretofore supposed to depend, but we shall confine ourselves here to a very few steps merely in the reasoning under the last head.

The author sets out under this head by assuming that the equilibrium theory of the tides is applicable to the real case of nature, and with this assumption he endeavours to show that the flood-tide rises higher above the plane of static equilibrium than the ebb-tide sinks below it. Now, it is well known by all who are familiar with tidal theories, that this theory is entirely worthless as a representative of the real tides of the ocean. Here, then, there seems to be a weak place in the very foundation of the whole reasoning, and any results based upon it should be received with much distrust, if even all the following steps in the argument were regarded as valid. In the second place, he attempts to show, by a method which is very unscientific and inconclusive, that the forces of the sun and moon tend to produce a current from the east towards the west in the flood-tide, but the reverse of this in the ebb-tide. This is then followed by another assumption in the following language:-"Since, as we have shown, the flood rises more above the normal level of the sea than the ebb sinks below it, we think we can assume, as an hypothesis, that the force of the flood-current will be greater than that of the ebb-current." From this he infers that the difference in these forces must produce a constant current in the ocean in the torrid zone from east to west, but, for reasons which

do not seem clear, the reverse of this toward the poles; and in this way, taking into account the deflections of the continents, he accounts for all the ocean currents without the aid of any of the usual causes assigned. In the case of the atmosphere he thinks that the same reasoning must hold, but admits that in this case the alteration of the specific gravity by heat toward the equator may produce some additional and modifying effects. Saying nothing with regard to the steps in the argument, these results are based upon a confessedly doubtful hypothesis, and therefore should not be received without further proof.

This is not a question to be settled by authority, but after the profound investigations of Laplace and Airy upon the tidal forces and the solution of the tidal problem, from which no constant currents around the earth were obtained, we would scarcely expect that such results would be legitimately obtained in a few pages of verbal reasoning without the aid of mathematics. It is true that more recently a very small effect of that kind has been obtained, tending to produce a westward current in all latitudes, from which, by means of friction, the earth's rotation on its axis is supposed to be slightly changed, but this effect is of an order almost infinitely small in comparison with those under consideration, and not at all contemplated in the author's reasoning, WM. FERREL

referred to above.

Washington, D.C., Nov. 7, 1874

Mud Banks on Malabar Coast

THE phenomenon of the "mud banks and of tracts of mud sus. pended in the sea" on certain parts of the Malabar coast, is not, as you suppose (vol. xi. p. 135), unexplained. The late Capt. Mitchell, curator of the Madras Museum, some years ago submitted a quantity of the mud to microscopic examination, and published the results in the Madras Journal of Literature and Science (I have not the work at hand, or I would give you volume and page). He found it to consist almost entirely of Diatomacea, of

ON THE MORPHOLOGY OF CRYSTALS*

PROFESSOR MASKELYNE, in introducing his sub

ject, said that in the assembly-room of the Chemical Society he should have to treat of Crystallography as the Science of Chemical Morphology. To the chemist the crystallisation of a substance is a familiar marvel; so familiar, indeed, that he hardly sufficiently considers its importance in relation to his own science. For the physicist, on the other hand, the instinct with which the molecules of a substance obey the laws of a sublime geometry-sublime because simple and universal-is a theme the contemplation of which has guided him to some of the most subtle and almost metaphysical conceptions that he has formed regarding the constitution of matter, and has afforded him invaluable insight into the working of the laws that control the pulsations of heat and light and other manifestations of force. But, although the morphological relations of the crystal are the external expression of the more subtle physical properties which underlie them, he stated that the purpose of the lectures he was about to deliver would be confined to the consideration only of the former.

Placing a large and very perfect crystal of apophyllite from the Ghâts of India on the table, the lecturer pointed out that certain faces carrying peculiar striations were repeated four times; that again others of a triangular form, planted on the angles of the latter, were repeated eight times, and that these had a lustre of their own; while again a plane of octagonal form was repeated only once on the top and at the bottom of the crystal, and carried a peculiar roughened surface, which was seen to be made up of innumerable small square pyramids in parallel positions. He further showed that by turning the crystal relative situations of the planes, as viewed from any round about an axis perpendicular to the last planes, the point, came always to be the same at any revolution through a quarter of a circle. A group of faces repeated with similar properties was defined as a form, the crystal in question thus exhibiting three forms; the repeated faces of each form retaining the same general aspect so long as they were not moved round through an angle greater or less than 90°. Then taking crystals of quartz which presented the same forms, he pointed out that faces that corresponded to one another on the different crystals, and even on the same crystal, have very different relative magnitudes; and that, in fact, these magnitudes were controlled by no rigid geometrical law. On the other hand, the angles which measured the inclination of corresponding faces on each other were in every case identical; hence angular inclination, that is to say, the direction in space, not relative position, that is to say, precise mutual distance, in the faces, has to be recognised as a principle

* Some notes of the Lectures delivered at the Chemical Society's rooms in Burlington House, on the Morphology of Crystals, by Prof. N. S. Maskelyne, F.R.S.

fundamental to crystallography. This may be expressed by saying that the angles of a crystal are symmetrically repeated.

The study of crystallography in its aspect as the science of chemical morphology thus resolves itself into the discovery of the laws which regulate the repetition of planes, the directions of which in space, and not their relative magnitudes, result from that geometrical instinct which guides the molecules of every individual substance as they become colligated into the symmetrical structure of a crystal.

The lecturer then went on to point out that the features of a crystal the symmetrical recurrence of which had to be studied were the faces, the edges, and the quoins (or solid angles); and he entered on a general geometrical review of the conditions under which faces in meeting produce an edge, or a quoin, or a series of edges or of quoins; and after showing the mode by which the angular inclination of two faces was measured, he dilated on one in particular among the various modes in which faces might meet, namely, that in which three or more faces intersect with each other in the same line or edge, or in edges parallel to the same line. For the crystallographer such groups of planes possess the highest significance; a group thus presenting parallel edges he denominates a zone, and it is clear that the direction of the line to which all the edges that can possibly be formed by the intersections of any and every pair of the planes belonging to the zone is indicated when we know the direction of any one of these edges. A considerable part of the earlier among the ensuing lectures will have to be devoted to the consideration of this subject of zones: and the development of the relations between the planes of a zone, under the restrictions imposed by a simple and beautiful law, will be found to involve fundamental principles regarding the symmetry which controls at once the morphological and the physical properties of the crystal in such a manner that all the systems, the symmetrical forms, and the general character of the optical, thermal, magnetic, electric and mechanical properties of the crystallised substance hang, as it were, suspended from that simple law by a chain, each link of which is a simple deduction from the link in the argument immediately above it.

Then taking a crystal of the mineral barytes, Prof. Maskelyne pointed out that certain planes upon it were repeated, some in parallel pairs, and others four times, but also in pairs that were parallel, while all of these planes presented the property already stated to be characteristic of a zone: their edges were parallel. Then, supposing a lapidary's wheel to have been passed through the middle of the crystal perpendicularly to all these edges, and therefore perpendicularly to the faces themselves, he proceeded to deal with the profile of the planes of the zone as they would be seen in such a section. He first defined such a section as the plane of the zone, or the zone-plane; and characterised it as a plane perpendicular to the edges of the zone. Then drawing a figure to represent this profile or zoneplane, he pointed out that two of the planes of the zone being perpendicular to each other, he might draw two lines through a point within the crystal and in the zoneplane parallel to the traces of those two planes, and therefore perpendicular to each other, and that now he could use these lines as axes, or as an artificial scaffolding, to which he could refer the traces of the other faces of the zone, and by the aid of which he might determine the relative directions of those faces.

The circumstance already established by the scrutiny of many crystals, namely, that the faces of the crystal might be drawn nearer or further from a point within the crystal indifferently, justified the lecturer in drawing the traces of two of the faces in the zone so as to intersect in the same point on one of the two axes thus chosen. They would thus intercept on the other axis two different

portions of that axis. Calling the former of these axes Z and the latter X, we may say that the ratio of the ntercept by either of the two planes on the Z axis to the intercept on the X axis by the same plane is the tangent of the angle formed by the trace of the plane in question with that of the plane parallel to the axis of X, or the cotangent of the angle it forms with the trace of the plane parallel to the axis Z. This tangent for the plane in question, which gave an angle of 51° 8' by measurement for the angle on the axis X, had a value 12407. The other face of the zone, being represented by the line which met the axis of X at an angle of 68° 4′, would thus yield a corresponding tangent of 24834. It will be seen, therefore, that the ratios of the intercepts for the two planes would be, for the first plane,

the X intercept the Z intercept :: 1 : 12407 for the second plane,

A third plane in the zone treated in the same would give an angle the tangent of which would lead to a ratio for the intercepts corresponding to a

a h

с

:

с : "

and

5 2 if the same process were extended to all the planes in the zone, it would be found that all of them would yield, by the simple process of measuring their inclinations and taking the tangents of their angles on the plane represented by the axis X, values that may be represented by the proportion where a and c are in the ratio above determined, and where h and always are capable of representation by rational and generally, nay, almost always, by very small whole numbers. This law thus simply enunciated for the faces of a single zone, as referred to two axes parallel to two faces of the zone here taken as perpendicular to each other, will be found, when the faces of the crystal are referred to three axes instead of two, not in the same plane, and also when they are inclined to one another at other angles than right angles, still to control the inclinations of the faces of the crystal, provided only that the axes XYZ thus taken be lines of crystallographic significance, such as lines parallel to edges formed by faces of the crystal; while the ratios abc represent the intercepts on those axes taken in the order XYZ of a fourth face of the crystal and are the numerators, while letters such as stand for the numerical denominators in the fractions that represent the ratios of the intercepts of any other fifth plane of the crystal. Any three numbers in the ratios abc represent the intercepts on the axes of the fourth or standard plane, and are called the parameters of the crystal; one parameter in particular being generally taken as unity. The numbers by which the parameters have to be divided in order to assign the ratios of the intercepts to any fifth plane of the system, namely, the simplest numbers expressive of the ratios hk, are called the indices of that plane; and when these indices are united into what is termed the symbol of the plane, by being written in brackets as (hkl), (3 2 1), &c., one understands by this that

k

point are perpendicular, and one of these bisects the angle formed by the remaining two lines, the sines of the angles taken in the proper order are in the harmonic ratio. Another point illustrated was that a sheaf of four lines presents the same anharmonic ratios of their sines as does a sheaf of four lines severally perpendicular to them. Reverting to the subject of the traces of the faces of a zone on their own zone plane, it was now seen that we can discuss the subject of relations of any four planes in the zone by considering those of their normals the angles between which are measured on a great circle of the sphere. But it remains to obtain an expression that shall connect these angles with the symbols of the poles or faces of the zone. Such an expression obtained by Prof. Miller in the first case involves a relation of the simplest kind. In short, the anharmonic ratio of four planes is the ratio which we obtain directly from the determinants of the symbols for the four planes. Since, however, the symbols for a zone as obtained from the symbols of different pairs of faces of the zone may, and generally do, differ by a common factor, it is advisable to put the expression for the anharmonic ratios of four tantozonal planes under the form of a convenient symbol given them by V. von Lang, viz., for the four planes PQRS:

[6]:[6]

=

:

m

n

sin P Q sin PS sin (PR-PQ) sin (PR-PS) where the letters on the left side of the expression stand for the symbols of the planes of which the determinants are to be taken. This very important expression offers the means of determining one unknown symbol or one unknown angle among those belonging to the four planes; another result that flows from it is the necessity for the anharmonic ratios of four planes in the zone, i.e. the magnitudes m and n, being always rational if the planes belong to a crystal. And this is another and more general way of stating the fundamental crystallographic law, that of the rationality of indices.

Prof. Maskelyne next proceeded to discuss some of the further results deducible from this great law. Firstly, since the harmonic ratio of four planes brings those planes under the requisite condition of rationality, we can say of any zone in which two of the planes are perpendicular to each other, that for any third plane of the zone inclined on one of them at an angle o, a fourth plane may also exist as a possible plane of the zone, also inclined on the first plane at the angle ; and further, the professor went on to state that if we ask the question what are the conditions for three consecutive planes in a crystal zone to include the same angle o, we find for answer that only in those cases is this possible where cos. & is rational, and that this is only so where possesses one of the values 90°, 60°, 45°, and 30°.

After a review of the results thus far obtained, the professor entered upon the subject of symmetry, and defining the different varieties of geometrical symmetry; such as, firstly, the symmetry of a plane figure to a centre of symmetry, to one or to several lines of symmetry, or to a pivot of symmetry; and secondly, that of a solid figure to a centre of symmetry, to one or to several planes of symmetry, and to one or to several axes of symmetry: he defined certain terms which would be found useful in the discussion of the symmetry of crystals. Thus, a plane figure was enthy-symmetrically divided by a single line of symmetry or ortho-symmetrically divided by two lines of symmetry perpendicular to each other; while an axis of, for instance, hexagonal symmetry became one of di-hexagonal symmetry, where each repeated element of form is itself doubled, as by reflection, on a plane of symmetry.

In applying the principles of geometrical symmetry to crystals, it was shown that the best and simplest method was that of dealing with the distribution of their poles on the sphere of projection.

The condition requisite for a single plane of symmetry to exist upon a crystal was then shown to be that this plane should be at once a zone plane and a possible face of the crystal. On the other hand, for a crystal to be symmetrical to a centre, no particular condition was requisite, since the direction and not the requisite position of a crystal plane has been seen to be the important point regarding it, while again every plane passing through the origin may be represented by the symbol of either of its poles indifferently. Now, an axial system as previously defined involves five variable quantities; namely, the three angles between the axes :

Hence, for a crystal to be centro-symmetrical, all these five quantities may vary from one substance to another. If, however, the crystal system be divided symmetrically by a plane, two of these axial elements are absorbed in satisfying the two requisite conditions of that plane being at once a crystal face and a zone-plane.

A crystal system that is simply centro-symmetrical presents the kind of symmetry characteristic of what is called the Anorthic system of crystallography; a crystal that obeys the principle of symmetry to a single plane belongs to the Oblique or Clinorhombic system.

(To be continued.)

TWO REMARKABLE STONE IMPLEMENTS FROM THE UNITED STATES

THE similarity of stone implements, both modern and prehistoric, that obtains throughout the world, has been commented upon so frequently as scarcely to need further illustration. Within a few days, however, I have found two forms of arrow and javelin points that are so unusual in their shapes, and otherwise of interest,

FIG. 1. (Natural size)

that I believe drawings of the two, and a brief note concerning them, will be welcomed by archæologists.

Fig. 1 represents a "flame-shaped" arrow-point, as this shape has been well called by Mr. E. B. Tylor (vide "Anahuac," by E. B. Tylor, p. 96, Fig. 1). Although I have collected fully ten thousand specimens of “Indian relics" from the immediate neighbourhood of Trenton, New Jersey, U.S.A., of which a very large proportion were spear and arrow heads, I have not been able before to duplicate this form, or to find any unmistakable trace of it in the bushels of fragments that here cover the ground in some places. This arrow-head, accompanied by the javelin (Fig. 2) and several of the leaf-shaped