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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 intended for this or any other part of NATURE. No notice is taken of anonymous communications.]

Supposed Horn-Sheaths of an Okapi. MR. R. LYDEKKER, F.R.S., lately directed attention in the columns of NATURE to a specimen of the okapi sent home by Dr. Christy from the Congo State, which was stated to be provided with corneous sheaths to its horns, resembling those of an antelope. The specimen has been mounted by Mr. Gerrard, of Camden Town, and is still in his workshop, whilst the skull has been purchased by the Royal College of Surgeons. I have been given the opportunity of examining both the mounted skin and the skull. The skull is of an individual of nearly the same size and age as that presented to the Natural History Museum by the late Captain Boyd Alexander, carefully figured under my superintendence with many other skulls of the okapi in the atlas of my "Monograph of the Okapi," published in 1910 by the trustees of the British Museum. With the new skull acquired by the College of Surgeons, and apparently belonging to the same animal as the skin, is a pair of small ossicones, not yet ankylosed to the skull, measuring about 2 in. along the longer side from point to base. They are of the same shape and little shorter than those of Boyd Alexander's specimen. In neither skull is there as yet a tuberculated surface of the frontal bone developed for the attachment of the ossicone. In the Boyd Alexander specimen each ossicone stood up as a projecting cone, and was covered with the hairy skin except for a small area at the free end, where the hair seems to have been rubbed away, or removed in preparing the skin, as may be seen in the mounted specimen in the Natural History Museum. In Major Powell-Cotton's specimen, of which both skin and skeleton are in the museum, each ossicone is longer, slightly compressed from side to side, and claw-like in shape, the point curved downward and backward; and each ossicone rests on a pitted and tuberculated surface of the frontal bone, to which it is closely fitted but not yet ankylosed.

In older specimens, e.g. that in Paris and that in Edinburgh, figured in my atlas, there is complete ankylosis of the ossicone with the frontal bone, and a wide extension of its base. The ossicones of the Powell-Cotton specimen are 3 in. in length, and are closely covered with hairy skin except, for a length of about in., at the tip, which pierces the skin. This "tip" of the okapi's horn, or ossicone (not yet developed in the Boyd Alexander specimen), consists, as I have described in the Proc. Zool. Soc., 1907, of peculiarly dense bony substance, which acquires a bright polished surface, and is sharply marked off like a nipple, by its raised margin from the rest of the bony substance of the ossicone, as seen in all adult specimens, of several of which I have published drawings. It emerges through the skin as a tooth does, when it is said to be "cut."

It is only in their pointed claw-like shape and the penetration of the skin by the hard, tooth-like apex that the okapi's paired ossicones differ from the paired ossicones of the giraffe. It is, however, remarkable that the foetal giraffe has already before birth two soft haircovered growths corresponding in position and proportionate size to the paired ossicones of the adult, and that the bony ossicones develop in these soft upstanding structures soon after birth. The young okapi

has no such tegumentary growths, and the ossicone makes its appearance when the animal is nearly full grown or completely so as a free button-like ossification lying beneath the integument, which is pushed upwards by it as it grows. The dense emerging point of the okapi's ossicone forms for the animal a very efficient weapon. The giraffe's ossicone never penetrates the skin, but its apex is broad and flat and clothed with a tuft of long black hair. The axis of the okapi's ossicone is not at right angles to the horizontal plane of the skull, but is directed backwards so as to form an angle of 45° with that plane.

Mr. Gerrard tells me that wrapped in the bundle with the skin of Dr. Christy's specimen as received by him were two hollow, bluntly ending corneous horn-sheaths of about 2 in. in length, which he was led to suppose belonged to the animal. He has mounted these two hollow horn-sheaths on the top of the animal's head over the holes in the skin made in originally clearing it from the ossicones (when the skin was prepared in Africa) which have gone with the skull to the College of Surgeons. These hollow horns do not fit well to the cut skin, and there is no intrinsic evidence forthcoming to justify the association of them with the okapi's skin. They have the appearance of young horn-sheaths of some species of antelope, and show a few ring-like markings on the surface. They taper only slightly from base to tip, and the tips are rounded and blunt. It is, I admit, conceivable that in the early period of its growth before the completion of its ivory-like point and the cutting by it of the skin, the ossicone of the young okapi might develop a temporary corneous sheath to be shed during further growth and replaced by hairy skin. The prongbuck sheds its hornsheath yearly, and very young cavicorns have been observed to shed a first sheath before acquiring a permanent one. Hence it is not impossible that a temporary corneous sheath should develop from the skin covering the young ossicone of the okapi.

The real question in such a matter is what is the evidence in favour of the unlikely but possible occurrence? The fact that between fifty and a hundred skins and skulls of the okapi have reached Europe in the last twelve years, and that no such hornsheaths have hitherto been seen or heard of, is important. It is also important to bear in mind that it is quite certain that when once the okapi is full grown and its ossicone is ankylosed to the skull, it is covered by hairy skin like that covering the skull, from which its naked ivory-like point emerges.

The evidence is as follows. Mr. Gerrard tells me that he was led to believe that the small horny sheaths sent with the skin of the okapi actually belonged to the specimen by the fact that when removed from the parcel a label was found tied to them on which was written, "Horns of the Okapi." This would certainly seem to justify Mr. Gerrard in mounting them on the head, as he did.

He has, however, since I saw the specimen, sent me a note just received by him from Dr. Christy. This is headed, "Details of Okapis obtained with numbers of cases and dates of dispatch." It is signed by Dr. Christy, and dated Khartoum, February 10, 1915. It appears that Dr. Christy has been employed on a mission in the Congo State during 1913-14 by the Belgian Government, and that he had forwarded during those years specimens collected by him to Brussels to be sent on to Mr. Gerrard, acting as his agent, in London. Seven specimens of okapi are mentioned in the list before me, and the date of shooting and the name of the ship and route by which they were dispatched are given. Some were sent off in 1913, others in 1914. Mr. Gerrard tells me that only one the one he has mounted-has reached him in

London. It is impossible to say whether the others arrived in Brussels, and, if so, what has now become of them. Dr. Christy's list is a very interesting one, and I will venture to give extracts from it. The specimens are distinguished by numbers. "No. 507, juv., not full grown; shot by myself, April 10, 1913. Skin good, skeleton complete." "No. 531, ♂, full grown. Shot by a Congo official, out shooting with me, May 22, 1913. Horns 1 in., skincovered. Skin good, skeleton complete." "No. 686,

, big. Shot by myself, October, 25, 1913. Skin good, skeleton complete.' "No. 717, ♂, old. Shot by Reid. Skin good; horns and hoofs attached to skin. Skeleton complete. Horns 4 or 5 in. long, and bare at tips." 'No. 532, ? 8. Skin only from natives." “No. 533, ?. Skin only; from natives.' "No. 695, juv., ?sex; half-grown, 1913. Skin dried by natives. Skeleton complete.'

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In this list it will be observed that nothing is said about horn-sheaths." It is perfectly certain that, as a sportsman and naturalist acquainted with the okapi, and the only educated" European who has himself shot the okapi, Dr. Christy would have directed attention in his notes to the presence of "hornsheaths" if he had discovered such structures to exist.

Only one of the seven specimens mentioned in Dr. Christy's list has come through to London. I have no doubt that it is the specimen No. 531, shot on May 22, 1913, at Mawambi, by a Congo official out shooting with Dr. Christy. The horns (ossicones) are stated definitely to be skin-covered. This agrees with my inference from a comparison with the Boyd Alexander specimen and the state of growth of the ossicones. It makes the "horny-sheaths" impossible. The measurement given by Dr. Christy for the horns (ossicones) is 1 in. This is their vertical height from base to apex. As they are pyramidal in shape, the measurement along the side of the pyramid from apex to edge of the expanding base, is as given above by me, about 2 in.

I think that Dr. Christy's own notes settle the question against the horny sheaths which it was already really impossible to "fit" satisfactorily to the specimen with which they reached Mr. Gerrard.

As to how this label-with "Horns of the Okapi ' written on it became attached to these little hornsheaths it is possible to form various conjectures. Perhaps some busy, well-intentioned servant, being told to be sure to see that the little horns (ossicones) were not omitted from the parcel, mistakenly picked up the small horn-sheaths belonging to some antelope skin, left by chance with other skins and skulls in the disorder of packing or preparing a mass of specimens, and conscientiously but erroneously labelled them Horns of Okapi," and packed them with specimen No. 531, destined to produce astonishment and confusion on arriving two years later in London.

Dr. Christy is to be congratulated on the fine series of specimens of okapi which he obtained and sent to Brussels en route for London. We must hope that they may escape destruction or seizure by the enemies of mankind, and eventually yield their contribution to our knowledge of the okapi, especially since among them are the first specimens seen alive and shot by a competent European observer.

March 9.


The Spectra of Hydrogen and Helium. MR. E. J. EVANS has described recently some interesting experiments on the "4686" and Pickering series, which were obtained from vacuum tubes containing helium from which hydrogen was apparently completely eliminated. Stark has also observed the "4686" line in a vacuum tube showing no trace of the

hydrogen lines. The experimental evidence of a helium origin of the lines in question would thus appear to be strong, and Prof. Fowler, from analogy with the enhanced line series of the alkaline earths, has also concluded that the lines are due to helium. According to Dr. Bohr, who first suggested that the lines were due to helium, the series in question owe their origin to the binding of an electron by a helium atom from which two electrons have been removed. Dr. Bohr's theory involves a modified value of Rydberg's constant for these lines, and Prof. J. W. Nicholson, in a letter to NATURE of February 11, has pointed out that it can be put to the test by an accurate measurement of the lines of the "4686" series, from which the value of the constant can be calculated.

Although the spectroscopic evidence is in favour of helium as the origin of the lines, it may be pointed out that this evidence is not conclusive. Although 4686 does not appear in hydrogen in the absence of helium, the same may be said of ultra-violet members of the Balmer series, which do not appear in vacuum tubes containing pure hydrogen, but which make their appearance when helium is present. The difficulty of preparing vacuum tubes free from hydrogen is well known, and the fact that the ordinary hydrogen lines are absent from the spectrum cannot be taken as conclusive evidence that hydrogen is not present. In view of this fact, the writer has conducted experiments to determine the relative mass of the atom from which the "4686" series originates, by measur ing the limits of interference of the "4686" line and the lines of helium and hydrogen. The circumstances which control the breadth of spectrum lines have been discussed by Lord Rayleigh in the current number of the Philosophical Magazine.

At low pressures the order of interference at which fringes are still visible is proportional to the square root of the atomic weight of the atom from which the radiation originates. It is hoped shortly to publish a full account of the experiments, but the following may be stated as a preliminary result. A vacuum tube containing helium and hydrogen at a low pressure was excited by an induction coil with capacity and a spark-gap in the circuit, the spectrum consisting of helium lines, 4686, and the hydrogen lines. With an interference apparatus giving a suitable difference of path, moderately sharp ring systems can be obtained for all the helium lines, whilst no trace of interference can be detected in the 4686 line or the hydrogen lines.

Further observations are required to determine the exact limits of interference of the 4686 line and the hydrogen lines, but the results indicate that the mass of the atom from which 4686 originates is definitely smaller than that of the atoms concerned in the production of the ordinary helium spectrum.

T. R. MERTON. University of London, King's College, March 15.

Musical Sand in China.

AMONG the immense mass of ancient Chinese records and manuscripts brought back from the buried cities and caves of ancient Khotan, in Central Asia, and now stored in the British Museum, is one called the Tun-Huang-Lu, a topographical description of part of Khotan itself. This little geography was written in the time of the Tang dynasty, in the seventh century, but probably contains matter from earlier authors.

Among the specially interesting natural phenomena of the country described in the Tun-Huang-Lu is a large sandhill, which at certain times gave forth strange noises, so much so that a temple in its vicinity was entitled the "Thunder Sound Temple."

The geographer, speaking specially of the sandhill, says:The hill of sounding sand stretches 80 li east and west and 40 li north and south. It reaches a height of 500 ft. The whole mass is entirely constituted of pure sand. In the height of summer the sand gives out sounds of itself, and if trodden by men or horses, the noise is heard 10 li away. At festivals people clamber up and rush down again in a body, which causes the sand to give a loud rumbling sound like thunder. Yet when you look at it next morning the hill is just as steep as before."

Mr. Lionel Giles, from whose translation of the Tun-Huang-Lu these extracts are made, mentions that this sounding sandhill is referred to in another old Chinese book, the Wu Tai Shih.

JOSEPH OFFord. 94 Gloucester Road, South Kensington, S.W.

The Green Flash.

I CAN confirm Dr. Schuster's observation of the green flash at sunrise, as in September last I saw a green segment herald the sun as it rose from the sea into a sky which was free from atmospheric glare (see the Observatory, December, 1914). Observations had previously been made at sunset, in one of which the eye was unquestionably fatigued, and the green flash was seen upon turning away from the sun at the instant after sunset. In a later sunset experiment precautions were taken to prevent retinal fatigue, and again the flash was seen.

My opinion is confirmed by Prof. Porter's experiment that "the reason why doubt has been cast upon records of the green flash is that the colour may arise in two different ways (complementary colour due to retinal fatigue, or dispersion by the atmosphere), and that the observer has not always been careful to avoid retinal fatigue, as was the case in my first (sunset) observation."

My observation, No. 2 (loc. cit.), is also in agreement with Dr. Schuster's experience, that with a very red sun no flash is to be seen.


University College, Reading, March 6.

Measurements of Medieval English Femora. As the Editor of NATURE has insisted upon the great pressure at present upon his space I propose to reply to Dr. Parsons's letter, in the issue of March II, adequately elsewhere. KARL PEARSON.


Galton Laboratory, March 15.

THE PRINCIPLE OF SIMILITUDE. HAVE often been impressed by the scanty attention paid even by original workers in physics to the great principle of similitude. It happens not infrequently that results in the form of "laws" are put forward as novelties on the basis of elaborate experiments, which might have been predicted a priori after a few minutes' consideration. However useful verification may be, whether to solve doubts or to exercise students, this seems to be an inversion of the natural order. One reason for the neglect of the principle may be that, at any rate in its applications to particular cases, it does not much interest mathematicians. On the other hand, engineers, who might make much more use of it than they have done, employ a notation which tends to obscure it. I refer to the manner in which gravity is treated. When the question under consideration depends essentially upon gravity, the symbol of gravity (g)


makes no appearance, but when gravity does not enter into the question at all, g obtrudes itself conspicuously.

I have thought that a few examples, chosen almost at random from various fields, may help to direct the attention of workers and teachers to the great importance of the principle. The statement made is brief and in some cases inadequate, but may perhaps suffice for the purpose. Some foreign considerations of a more or less obvious character have been invoked in aid. In using the method practically, two cautions should be borne in mind. First, there is no prospect of determining a numerical coefficient from the principle of similarity alone; it must be found if at all, by further calculation, or experimentally. Secondly, it is necessary as a preliminary step to specify clearly all the quantities on which the desired result may reasonably be supposed to depend, after which it may be possible to drop

one or more if further consideration shows that in the circumstances they cannot enter. The following, then, are some conclusions, which may be arrived at by this method :

Geometrical similarity being presupposed here as always, how does the strength of a bridge depend upon the linear dimension and the force of gravity? In order to entail the same strains, the force of gravity must be inversely as the linear dimension. Under a given gravity the larger structure is the weaker.

The velocity of propagation of periodic waves on the surface of deep water is as the square root of the wave-length.

The periodic time of liquid vibration under gravity in a deep cylindrical vessel of any section is as the square root of the linear dimension.

The periodic time of a tuning-fork, or of a Helmholtz resonator, is directly as the linear dimension.

The intensity of light scattered in an otherwise uniform medium from a small particle of different refractive index is inversely as the fourth power of the wave-length.


The resolving power of an measured by the reciprocal of the angle with which it can deal, is directly as the diameter and inversely as the wave-length of the light.

The frequency of vibration of a globe of liquid, vibrating in any of its modes under its own gravitation, is independent of the diameter and directly as the square root of the density.

The frequency of vibration of a drop of liquid, vibrating under capillary force, is directly as the square root of the capillary tension and inversely as the square root of the density and as the 1 power of the diameter.

The time-constant (i.e., the time in which a current falls in the ratio e: 1) of a linear conducting electric circuit is directly as the inductance and inversely as the resistance, measured in electro-magnetic measure.

The time-constant of circumferential electric currents in an infinite conducting cylinder is as the square of the diameter.

In a gaseous medium, of which the particles repel one another with a force inversely as the nth power of the distance, the viscosity is as the (n+3)/(2n-2) power of the absolute temperature. Thus, if n=5, the viscosity is proportional to temperature.

Eiffel found that the resistance to a sphere moving through air changes its character somewhat suddenly at a certain velocity. The consideration of viscosity shows that the critical velocity is inversely proportional to the diameter of the sphere.

If viscosity may be neglected, the mass (M) of a drop of liquid, delivered slowly from a tube of diameter (a), depends further upon (T) the capillary tension, the density (o), and the acceleration of gravity (g). If these data suffice, it follows from similarity that

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We see that in all cases h is proportional to and that for a given fluid F is constant provided v be taken inversely as a or b.

where F denotes an arbitrary function. Experi-,
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Within these limits Tate's law that M varies as
a holds good.

In the Eolian harp, if we may put out of account the compressibility and the viscosity of the air, the pitch (n) is a function of the velocity of the wind (v) and the diameter (d) of the wire. It then follows from similarity that the pitch is directly as v and inversely as d, as was found experimentally by Strouhal. If we include viscosity (v), the form is


where f is arbitrary.

As a last example let us consider, somewhat in detail, Boussinesq's problem of the steady passage of heat from a good conductor immersed in a stream of fluid moving (at a distance from the solid) with velocity v. The fluid is treated as incompressible and for the present as inviscid, while the solid has always the same shape and presentation to the stream. In these circumstances the total heat (h) passing in unit time is a function of the linear dimension of the solid (a), the temperature-difference (0), the streamvelocity (v), the capacity for heat of the fluid per unit volume (c), and the conductivity (k). The density of the fluid clearly does not enter into the question. We have now to consider the "dimensions" of the various symbols.

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In an important class of cases Boussinesq has shown that it is possible to go further and actually to determine the form of F. When the layer of fluid which receives heat during its passage is very thin, the flow of heat is practically in one dimen sion and the circumstances are the same as when the plane boundary of a uniform conductor is suddenly raised in temperature and so maintained. From these considerations it follows that F varies as v, so that in the case of the wire

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the remaining constant factor being dependent upon the shape and purely numerical. But this development scarcely belongs to my present subject.

It will be remarked that since viscosity is neglected, the fluid is regarded as flowing past the surface of the solid with finite velocity, a serious departure from what happens in practice. If we include viscosity in our discussion, the question is of course complicated, but perhaps not so much as might be expected. We have merely to include another factor, vw, where v is the kinematic viscosity of dimensions (Length) 2 (Time)-1, and we find by the same process as before

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inclined at 45° to the direction of the incident light. These mirrors were mounted in a tube and separated a convenient distance (Fig. 1).

For modern trench warfare the convenient separation is about 18 to 24 in., and the mirrors are mounted in tubes, in boxes of square or oblong section, or attached to a long rod. In each case it is necessary that the mirrors should be fixed at the correct angle, and that there should be no doubling or distortion of the image.

The principal requirements of these trench periscopes are portability, lightness, small size and inconspicuous appearance, and large field of view. When there are no lenses the field of view is exactly the same as would be obtained by looking through a tube of the same length and diameter. Thus, with mirrors of 2 in. by 3 in. and a separation of about 22 in., a field of view of 5° would be obtained; and by moving the eye about, this field could be nearly doubled.

By using a box of oblong section the horizontal field of view can be increased without unduly increasing the size of the periscope. As the field of view is somewhat limited in any case, the principal objection to the use of a telescope or binocular, viz., the reduced field, no longer applies, and many periscopes are arranged to be used with a monocular or a binocular telescope.

Most periscopes can be used with a magnification of two or three, i.e., with one tube of an ordinary opera glass; but when higher magnification is to be used the mirrors must be of better quality, both as regards flatness of surfaces and parallelism of the glass. When the mirrors are large enough-8 to 10 centimetres wide-both telescopes of the binocular may be used, but in this case the requirements for the mirrors are even more stringent, as the images formed by the two telescopes will not coincide unless the mirrors are plane. When suitable lenses are placed between the mirrors, the size

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When longer tubes are used or larger fields are required, the design should approximate to that used in the submarine periscope.

This optical system has been steadily developed since its first introduction by Sir Howard Grubb in 1901.

The system consists of two telescopes, of which one is reversed, so that the image would be reduced in size, while the other magnifies this image, so that the final image is of the same size as the object, or is magnified one and a quarter or one and a half times. (As a very large angular field of view is required in these periscopes, the beam reflected into the tube must cover a large angle, and would soon fall on the sides of the tube; the reversed telescope, however, reduces the angle of the beam, and so enables it to pro

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