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points, has a fine saw cut about 4th of an inch deep, made lengthwise at both ends. The wires which form the sides of the first triangle are put into one cut, and those of the second triangle into the other; and the rod may then be slid up or down along the wires, to different heights, so that when the pendulum is at rest the rod is horizontal, forming the base of one isosceles triangle, with sides of double wire, and its vertex down at the bob, and also of other two isosceles triangles, equal and similar to one another whose sides are of single wire, and whose vertices are the points of suspension in the ceiling respectively.

It is now evident that the rod is rigorously constrained to oscillate in a plane perpendicular to the line joining the suspension points, while the vertex of the triangle below the rod, which is the point of suspension of the bob, is free to move, at any instant, only in a plane at right angles to the plane of motion of the rod. As the amplitudes of the oscillations are practically made small compared with the lengths of the component pendulums, we thus obtain, with almost any desired degree of exactness, the composition of two simple harmonic motions of different periods of adjustable ratio, and in rectangular directions. It is easy also to see how, by making the wires of unequal length, and dividing them proportionally at the point of suspension of the bob, the simple component motions may be adjusted to different inclinations. In order absolutely to prevent the bob from creating indeterminate motions about its point of suspension, it would be needful to substitute, for the wires below the suspended rod, stiff pieces rigidly attached to the bob. But with due care in swinging the pendulum no very sensible motion of the bob, relatively to its suspending wires, need occur.

To record the motions of the pendulum, I have most frequently adopted the old plan of sand running out at a fine hole at the bottom of the pendulum bob. But for class experiments at the University of St. Andrews, I have also made the following arrangement :-A heavy bob of lead, in metallic connection with its suspending wires, has a metal point projecting from its lower end. Wires from an induction coil are connected, one with either of the suspension points in the ceiling, the other with a sheet of a tin foil which rests on a table, and over which is placed a sheet of paper, all but touching the point projecting from the bob. The pendulum having been first got to swing steadily, the induction coil is put in action, and the sparks, passing from the pendulum point to the tin foil, trace on the paper, if it be suitably prepared, a record of the pendulum motion. I used one of Ruhmkorff's original coils, which, with a single Grove's cell, was quite sufficient. The rheotome acted automatically, and with considerable regularity. The dots on the paper made by the sparks showed distances varying from one element of the pendulum track to another, and thus exhibited in a very interesting manner the variation in the velocity of the pendulum bob. WILLIAM SWAN

Ardchapel, Dumbartonshire, Aug. 24

PERMIT me to state that the diagrams in No. 94 of the 17th June to Mr. Hubert Airy's "Pendulum Autographs," are identical with the "Kinematic Curves" by Mr. Perigal, drawn by him upwards of thirty years ago, and discovered by Mr. Sang of Edinburgh two years previously (On the Vibration of an Elastic Spring, Ed. Ph. Tr.), autographic copies being in the possession of the Royal Society, Royal Institution, and Royal Astronomical Society. Vide my application of the Binomial Theorem to Perigal's Bicircloids (Lond. Phil. Mag. 1849-1850). Perigal calls these curves, Lemnoids, Paraboloids, &c. August 28

Mr.

S. M. DRACH

Thickness of the Earth's Crust

THE question in debate is not a mathematical one. Accepting Archdeacon Pratt's calculations as correct, they would show that certain facts in the earth's motion are what they would be if the earth were a rigid mass, or nearly so. But this at present is not disputed. What is disputed is the soundness of the inference drawn from these facts respecting the fluid or solid state of the earth's interior, for it is contended that in either case the movements in question might be practically the same, provided only they were slow enough. I do not think this is replied to by Archdeacon Pratt in his letter in NATURE, August 31.

Whatever the disturbing forces may be, they amount to a motive impulse given to some portion of the mass of the earth.

This impulse may have two effects: either it may alter the shape of the mass by causing part of it to move in some direction faster than the rest can follow, or it may alter the position of the mass by causing the whole to move together. If the portion which receives the impulse is able to move the rest as quickly as it moves itself, the whole will move together; and where there is any cohesion at all, there must be a degree of slowness at which this condition is attained.

Mr. Pratt's rope of sand, if dealt with here, is a system of particles between which there is no cohesion. They are not able, by attractive power, to move each other at all. But if hung out in free space, they would certainly assume a definite shape as a whole, and would retain it with complete rigidity" in spite of any applied force which was not able to move any of them faster than they could move each other.

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Suppose the earth were projected bodily along the line of its axis towards the pole star, what would happen to a loose stone lying on the surface at the south pole? If the earth moved northward ten feet in a second, the stone would, at the end of the first second, be still upon the surface. If the earth moved twenty feet in a second, the stone, at the end of the first second, would be a yard behind it, but before the end of the next second it would be on the surface again. Are not the relations between the rigid, the fluid, and the elastic states all illustrated here? What would be the real cohesive force in a molten earth, as compared with a congealed one, is another matter. "Molten " does not necessarily mean "limp," and the question, if determinable, has not, I imagine, been determined. The molten earth would no doubt be less compressible; and this, in some cases, may be equivalent to an increased cohesion. Let me add that I have no theory as to the earth's interior. A. J. M. Sept. 5

Spectrum of the Aurora

MAY I call your attention to an error which has occurred in the engraving of the Spectrum of the Aurora which I sent you last week. The lines are marked in strength exactly the reverse of what they should be. Thus : No. I is the strongest, and is a sharp line easily seen, and in the drawing it is the weakest; and so with the others. No. I is the brightest, No. 5 is the faintest. 47, Brook Street LINDSAY

Transparent Compass

I BEG leave to draw your attention to a contrivance that I think very suggestive, of improvements in getting up compasses for iron and wooden vessels. This I propose to effect by using glass globes with transparent needle-cards, and thus making a transparent mariner's compass, visible in all directions, that may be either supported or suspended by very simple and compact fittings wherever most convenient.

In iron vessels this transparent compass can be readily placed beyond the local attraction of the iron. In appearance like a pearl, and in good taste.

Please draw attention to this very simple remedy for so many real or alleged complaints of the deviation of the compass on board of iron vessels. GEORGE FAWCUS

North Shields, Sept. 4

A Substitute for Euclid

SINCE Prof. Tait has given the weight of his authority to the attack for me time past directed against Euclid, I, and perhaps some others who like me have sons whom they wish to educate as mathematicians, would be much obliged to Mr. Wilson, or any other of your correspondents, who would recommend a book which is suited to lay the foundation of geometry in the future. A FATHER

Monolithic Towers of Cement Rubble for Beacons and Lighthouses

IT occurs to me to suggest the trial of common rubble set in Portland or other equally good cement in the construction of beacons and seamarks, as also for lighthouses. The advantages continuous building, are the following:of employing cement rubble, not in prepared blocks but by

1. The dispensing with all squaring or dressing of materials. 2. The suitableness for such work of any stone of hard quality, thus rendering it unnecessary to bring large materials from a distance, or to open quarries for ashlar,

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A straight line has a certain direction; we all know what is meant; it is an inherent property of a straight line. The answer to the question what property two parallel straight lines have (independently of their being produced) is that they have the same direction. I do not invite discussion on the propriety of this definition, but only call attention to the fact that the words exist by which this conception of parallels can be expressed. Now to speak of planes. A plane has a certain parallel planes have the same The same what? Again, here are two theorems, which are, in fact, reciprocal (1) planes parallel to given straight lines are themselves parallel; and (2) if two intersecting planes are respectively parallel to two other intersecting planes, the lines of intersection are parallel; which may be better enunciated as follows :-(1) two directions determine one ; and (2) two determine one direction.

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The German geometers have no difficulty about it. They say, "Durch 2 Richtungen ist eine Stellung, durch 2 Stellungen eine Richtung bestimmt." J. M. WILSON

Rugby, Sept. I

The Nucleus of Adipose Tissue

WILL you allow me to make one or two observations upon the remarks made by the writer of the article on the last part of the "Physiological Anatomy and Physiology of Man?" In few words the reviewer has drawn attention to several of the most important points advanced in this part, and for this I feel much indebted to him. But with reference to adipose tissue, he observes that I convey the impression that the adult fat cell "consists merely of an envelope containing oily matter-no mention being made of the fact that by proper treatment a nucleus also can be almost always demonstrated." This is strange, for I believe I was the first to demonstrate the "nucleus in the fat cells of adult adipose tissue. In my lectures at the Royal College of Physicians in 1861, I showed specimens illustrating the fact, and in the work reviewed I have endeavoured to show that the so-called "nucleus" (germinal matter or bioplasm) is concerned in the formation of the fatty matter, and in its removal from the fully formed fat vesicle (p. 305) whenever we get thin from the absorption of fat. In fig. 198, plate xx., fat vesicles in various stages of development are represented, the "nucleus" being given in every one, while in fig. 132, plate xv., are shown some fat vesicles in cartilage, the nucleus being seen in every instance. If I have not made this point sufficiently clear in my description, it arises from the circumstance that I desired to leave as much as possible of the general description given by my predecessors in the first edition. In the early part of the chapter the nucleus has not been mentioned, which is to be regretted, but in the latter part, containing the new matter, very frequent allusion to it has been made.

It is this constant presence of the "nucleus" (bioplasm) in all tissues, at every period of life, at least as long as their activity lasts, to which I have long attached such great importance. I have endeavoured to show that this nucleus matter (bioplasm or germinal matter) is alone instrumental in the formation and removal of all textures, and at every period of life. This alone, of all the matter of the body, is in a living state, and capable of formation. Contrary to the generally received opinion, I have proved its presence even in all forms of yellow elastic tissue, and have shown that this texture is formed upon the same principles as other tissues.

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Eclipse Photography

It

FROM letters I have received, it appears that the table of exposures given in my "Notes" is not correctly understood. is necessary to explain again that the reason why the plate exposed 8 secs. gave a better result than the one exposed 30 secs. was because the eclipsed sun was nearly covered by cloud during the long exposure, and was quite clear during the short. The 30 secs. plate would have been greatly over-exposed for certain details, but the outer corona would probably have been more clearly defined. By giving some plates short and others long exposures, it was intended to show different effects, as would certainly have been the case if we had been favoured with a cloudless sky.

I am informed that it is proposed to attempt to obtain uniformity of results by using the same kinds of instruments and chemicals at all the stations. So far, good. But where is the certainty that the hands that will use the chemicals and instruments will produce equality of results? It is about the same as giving to a dozen men pens, ink, and paper, and expecting from them twelve specimens of caligraphy all alike. It would be preferable to decide beforehand whether negatives, or positives, or both are to be taken, and then to allow the operators to choose their own methods. A. BROTHERS

The Museums of the Country

It must be obvious to any scientific person visiting the provincial museums of this country, how inefficient they are for the purpose of preserving Geological and Natural History collections, which are being formed more or less throughout the land.

Whilst the British Association directs so much attention towards the advancement of science by means of investigation, and grants money for the purpose, it is short-sighted on its part to neglect the subject of Local Museums as means for preserving collections for the benefit of science and of posterity.

To give an illustration of the way in which such museums are too often conducted. In a west-country museum there has lately been an addition, consisting of a valuable collection of cave bones, and that is well-preserved and arranged, but why? In a great measure because one of the members of the local society happens to take an interest in that department. But in what condition is the local geological collection? In a state of neglect and disorder, because in that department no one takes an interest. In other museums, where there is nobody to take an interest in the subject, the state of the collections may be imagined.

It is much to be regretted that museums should remain in such a condition. The formation and preservation of local collections ought not to depend upon impulse, or the chance enthusiasm of individuals, but should be the result of a generally recognised business-like system; and it should be the interest of the various local societies to provide competent curators. It should also be the duty of these societies to preserve for the museum of the district the collections which have been formed, by local geologists or collectors, and not to permit them to be scattered or added to those in the British Museum and to that in Jermyn Street, where they may be said to become buried, and where the geological collections are already of an unmanageable size.

Thunderstorms

F. G. S.

THE prevalence of thunderstorms accompanied by serious accidents during the last two months has led me and many others to consider whether the phenomena of electrical discharges are thoroughly understood. We have heard of several instances in which the electric fluid "came down the chimney, filled a room with sulphurous vapour," and terrified or injured persons sitting near the fire-places. One fatal accident took place within a few hundred yards of my own house. A gentleman's coachman driving along the turnpike road was instantaneously killed on his box, "the lightning," it is said, "having struck him on the head and passed through his body to the iron work of the carriage, and thence to the ground." From the appearance of the body there is no doubt that the fluid did pass through the poor fellow and caused his death, but my opinion is that he was killed by an ascending current which was attracted to the wheels of the carriage, passed upwards through his body, issued at his head, and shivering his hat (made of felt, and therefore a bad conductor) to fragments, passed to the cloud above. During the same storm I was watching the lightning playing on the hill which is

separated by a valley from my house. Every flash I observed
was double, composed I imagine of an ascending and de-
scending current. In every instance one of the two flashes
was brighter then the other; but I could detect no difference
of time; as far as the eye could judge they were simu'-
taneous The inference I am disposed to draw from these facts
is this, that during thunderstorms ascending currents are to be
guarded against no less than descending ones; that when chim-
ney-pieces are shivered and people sitting by the fire side are killed,
the electric fluid has not come down the chimney at all, but has
proceeded from the earth, and, having found a good conductor
in the fender and grate, has passed through them harmlessly, and
has then overflowed, so to say, into the room, or shattered the
non-conducting masonry. Continuous lightning-conductors, on Sir
Snow Har is's principle, afford sufficient protection to public
buildings, but me al pinnacles terminating below in masonry or
woodwork are likely to cause mischief, and iron pillars, unless
insulated below by some non-conducting substance, must be equally
objectionable.
C. A. JOHNS

SIR WILLIAM THOMSON ON THE LAW OF
BIOGENESIS AND THE LAW OF GRAVI-
TATION

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greater than that which may be attributed to the dogma
no life except from life." It is the fact that within
human observation the law of gravitation is a true state-
ment; it is also the fact that within human observation
the dogma "no life except from life" is a true statement;
but how can it be for a moment supposed that this places
the two statements in the same position of sureness?
Does not all depend on that term "within human obser-
vation?" Will not the sureness depend on the extent and
thoroughness of the observation? And is it not the case
that whilst human observation of bodies in relation to the
law of gravitation is of the most vast character-embracing
not only all varieties of terrestrial matter, but innumerable
extra-terrestrial bodies-the human observation of the way
in which living matter originates or grows, is a mere trifle
Sir William Thomson speaks of being "deeply impressed
so insignificant in extent that it is as a drop in the ocean?
by the evidence put before us by Prof. Huxley," and is
thereupon ready to adopt an article of scientific faith
true through all space and time." What was the evidence
in question? The merest fragment, as Prof. Huxley would
himself acknowledge (though associated with much more
evidence upon allied matters)-simply this by no means
astonishing though much controverted fact, that when out of
the unspeakably many kinds of mineral matter which you
might take, you take one or two and boil them and seal them
up and submit them to a variety of processes, the object of
which is not to produce favourable conditions for the evo-
lution of life, but to prevent the access of already living
matter-you don't get life produced. The whole of this
kind of experiment, and of the evidence which so much
impressed Sir William Thomson, cannot-attended as it
is with negative results-have anything to do with the
general question of the de novo origin of living matter. Such
evidence merely relates to a particular supposed case of such
origin, one out of thousands conceivable. Yet this is what
it seems to me-I write with diffidence-Sir William
Thomson has taken as evidence of the same value as that
on which rests the law of gravitation. Because it seems
rather more probable than not that organisms do not
arise de novo in boiled and sealed solutions of tartrate of
ammonia, in hay-decoctions and turnip-juice, therefore it
is true through all space and all time that dead matter
never becomes living without the action of living matter;
therefore nowhere to-day on the whole earth-in the sea
charged with gases, open to sunlight and atmosphere,
holding salts and complex semi-organic compounds,
suspended and in solution-is this process go.ng on;
in no pond; under no moss; and not only to-day, but we
are to conclude that never at any time did Nature in her
great laboratory produce life from mineral matter, because
in certain arbitrary, crude, and utterly artificial conditions
of isolation she refuses to do so. Is it true that the law of
gravitation is no surer a teaching of science than the
dogma about the origin of life which rests on such logic?
That I have not misrepresented the utter poverty of
observation upon the origin of life will, I believe,
be admitted by all naturalists- possibly individuals
unacquainted with biological phenomena may have
conceived it to have been relatively more extensive.
We have been able to trace the commencement of so
many of the various living forms to eggs, that it becomes
waste of time to examine into cases of alleged spontaneous
origin of complex forms from mineral matter; and biologists
have now to look for the formation of simple organic material.
Observations therefore which merely tend to disprove the
spontaneous productions of maggots, worms, ciliated

PASSAGE in the address of the President of the British Association appears to me so remarkable, and so much at variance with the notions entertained by biologists of various shades of opinion, that I am surprised that no observations were made upon it during the sectional meetings, and beg now to draw attention to it. I may mention that in the discussion on spontaneous generation in Section D on the last day of the meeting, I did say substantially what I now write to you, but no one present defended Sir William Thomson's position. The passage in question is as follows: "But science brings a vast mass of inductive evidence against this hypothesis of Spontaneous generation, as you have heard from my predecessor in the Presidential chair. Careful enough scrutiny has, in every case up to the present day, discovered life as antecedent to life. Dead matter cannot become living without coming under the influence of matter previously alive. This seems to me as sure a teaching of science as the law of gravitation. I con ess to being deeply impressed by the evidence put before us by Prof. Huxley, and I am ready to adopt as an article of scientific faith, true through all space and through all time, that life proceeds from life, and from nothing but life." In the first place it is to be remarked upon this passage, that the reference to his "predecessor in the Presidential chair," and to the evidence put before us by Prof. Huxley," is made in such a way as would lead an uninformed person to suppose that not only was the speaker simply availing himself of that evidence, but also merely following or re-enunciating a belief previously expressed by Prof. Huxley. This I do not for a moment suppose was in any way the meaning of Sir W. Thomson, who unintentionally has made it appear that Prof. Huxley comes to the same conclusion from the consideration of certain facts, as he does. So far from this re-assuring concord having an existence, I doubt if any single biologist of name (of whatever philosophic tendencies) would venture to assert that it is as sure a teaching of science as the law of gravitation that dead matter cannot become living without coming under the influence of matter previously alive, and conclusions derived from a consideration of a vast series of facts prohibit an evolutionist from accepting such a doctrine without the most complete and widely-reaching evidence in its favour. Sir William Thomson's autho-infusoria, and fungi, are not to be reckoned as "evidence rity must be accepted as unquestionable as to the amount of sureness which may be attributed to the law of gravi ation; but with great deference to him, I should like to ask if he would definitely maintain that it is no * NATURE, Vol. iv., I. 269.

on the origin of life," they do not bear on the question as it now presents itself, the working hypothesis of science being, not that animals or plants originate de novo, but that organic matter has at one time done so, and is doing so still. It is, I believe, just to assert that observation bearing on this hypothesis is almost entirely wanting, and

indeed, the few experiments of the French observers, and of Gilbert Child and Bastian in this country are the only ones at present made.

The reason is obvious, the conditions of the experiment and observation required are so difficult that we have not yet mastered them. They are first, to ensure all the favouring circumstances in the laboratory experiment which natural stations afford, and, of course, to ensure them it is necessary to know or have some idea (which biologists have not) as to what they may be; second, to exclude simultaneously all living matter; third, to make the observations throughout with the greatest minuteness which the microscope permits a necessary condition, on account of the possible smallness of particles of living matter. When we have had experiments performed in this way with a vast variety in the first-named set of conditions, so as to obtain and study the action of various natural circumstances which might possibly be present in the de novo origination of living from mineral matter-then we may speak of evidence on the question. As it is, we have but a very incomplete and discordant series of observations on one class of conditions in which there is a presumption of spontaneous generation (the case of Bacterium), and which have been selected for experiments on account of a supposed facility for isolation, without interference with the conditions, but of which very little is understood at all. I venture to submit that this single case, in which there has been some little investigation with, be it granted, negative result, so far from warranting the enunciation of a dogma, which is declared to be as sure as a great law expressing the concurrence of almost infinitely numerous, varied, and reiterated observations, does not even justify an opinion; it has no possible bearing upon the source of the minute protoplasmic particles which the microscopist finds abundantly in sea-water, nor upon the origin of the atmospheric germs which are so largely invoked by some persons. It leaves us necessarily to a priori considerations in regard to the origin of life on the earth, and until direct researches are made, the hypothesis developed by a priori argument must have far more claim on the adhesion of an unbiassed mind, than a pseudo-law, though the latter bear an authority so great in some departments of science as is that of Sir William Thomson.

E. RAY LANKESTER

RECENT FRENCH ZOOLOGICAL DISCOVERIES
Tw
'WO naturalists, who have been more than usually
successful in their investigations of the faunas of
distant and little-known countries, have recently returned
to France, and are now engaged in working out the results
of their arduous expeditions. These are M. le Père
Armand David, and M. Alfred Grandidier.

David during the recent exploration of Mopin, as this portion of the Celestial Empire is termed by the French writers, have of late years seldom been equalled in any part of the world for extent or variety. The fauna of these mountains seems to be a sort of pendant to that of the Himalayas, which, some years ago, was so successfully investigated by Mr. Hodgson. The singular Ælurus or Wah, of Nepal, is replaced by a larger and even stranger form, the Eluropus of M. Milne-Edwards, a large bear-like mammal, quite distinct from anything previously known. A long-haired monkey inhabits the pine forests, remarkable for the development of its nose, which the same naturalist has proposed to name Rhinopithecus. The Takin of the Mishnees of Upper Assam (Budorcas taxicolor) is represented by a second species of this most singular genus of Ruminants. A new form of Cervidæ is remarkable for its small horns and well-developed canines; and there are a host of interesting novelties belonging to the insectivorous and rodent orders in Père David's series. In birds, M. Jules Verreaux, to whom the working out of this part of M. David's collections has been assigned, has already discriminated upwards of thirty new species. Amongst these many belong to the remarkable genera discovered by Mr. Hodgson in the hill-forests of Nepaul, and hitherto unknown to occur elsewhere. Perhaps the most noteworthy of them is a small Passerine form allied to Paradoxornis, which has only three toes, a phenomenon hitherto unknown in that typical order of birds. The Reptiles and Batrachians obtained by Father David in Moupin are also said to contain many novelties. Since the lamented death of Prof. Duméril, their investigation has, we believe, been undertaken by Prof. Blanchard, who has within these few last days brought before the French Academy a notice of one of the most extraordinary animals of the latter group. This is no other than a gigantic aquatic Salamander allied to, but distinct from, the now well-known Sieboldia maxima, of Japan. The discovery of this form of life in continental Asia is a fact of the highest significance as regards geographical distribution, as it was previously believed to be in the present epoch confined to the Japanese Islands, though remains of a closely allied animal (Andrias scheuchzeri) are found in the tertiary freshwater deposits of Central Europe.

We have mentioned only a few of the principal discoveries of M. David, but enough has been said to show the importance of the additions he has made to zoological science, and to heighten the interest attaching to the complete investigation of the fauna of the Chinese fron tier of Tibet, which this distinguished naturalist has thus inaugurated.

His

While Father David has been labouring among the snows of Central Asia, another not less arduous devotee of science has been risking his life in the tropical forests of Madagascar, and has likewise made many brilliant M. le Père Armand David is a missionary priest of the discoveries. M. Alfred Grandidier, who has now returned Order of Lazarists, who was for many years resident at from, we believe, his third voyage of discovery in that Pekin. Here he devoted much time and attention to the strange island, has shown that the riches and eccentricifauna of the surrounding country, which was at that period ties of its fauna have not yet been exhausted. little known, and entering into communication with the collections, which have only reached the Jardin des authorities of the Jardin des Plantes of Paris, supplied Plantes very recently, although brought to France before that establishment with many interesting novelties. the political storm of last autumn commenced, have not Amongst these one of the most remarkable was a new yet been fully examined. But they are said to contain deer with very peculiar horns and a long tail, which was very full series of several species of Lemuridæ, the comnamed by M. Alphonse Milne-Edwards Elaphurus davidi-parison of which is likely to lead to important results, anus, after its indefatigable discoverer. But about two besides examples of a new genus of Rodentia, and many years ago Father David moved the seat of his investiga- other Mammals of high interest. M. Grandidier has tions into still more promising quarters. It was, we also paid much attention to the fossil deposits of believe, the magnificent new species of Pheasants trans- Southern Madagascar, which contain the remains of the mitted by Bishop Chauveau from Ta-tsien-leou-a town extinct gigantic bird, Epyornis maxima, and has arrived in Western Szechuen upon the frontiers of Tibet-that at some important results (such as the former presence first called his attention to the probable richness of this of Hippopotamus in Madagascar) which may ultimately district in other departments of zoology. Nor have his tend to modify some of the views generally held conexpectations been in any way disappointed. The collec- cerning the true nature of the fauna of this island and tions of Mammals, Birds, and Reptiles, obtained by Father its origin. P. L. S.

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FIG. 11.-Proportion 3: 4.-Cusped type. pairs, for comparison of relative motions, I found that the two upper joints alone were able to make good their title to independent periods of swing: the third joint acted merely as subsidiary to the second, merely serving to facilitate the bend at the second joint, and always synchronous with that bend, never able to establish a proper period of its own. All three joints conspired to allow undeviating vibration in a plane at right angles to that allowed by the topmost joint alone, just as though there

FIG. 12.-Proportion 3: 4.-Looped type.

had been only two joints at right angles. I also tried three joints at angles of 90° and 30°, and two joints at an angle of 60°. They all gave similar results. It is clear that the planes of slow and quick vibration are determined solely by the position of the topmost joint, the former being that in which the pendulum can swing by the topmost joint alone, and the latter that in which the topmost joint takes no share at all, or the least possible share, at right angles to the first. However the joints may be

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