the tables of these satellites should be brought to a high degree of perfection; and as, according to the opinion of the most distinguished mathematicians, the observation of all the phenomena which are presented by one of these satellites in superior or inferior conjunction is the best means of determining certain elements of the theory of the satellites of Jupiter, it was useful to give in the collection of ephemerides not only the epochs of the eclipses, but also those of the contact of the shadow of the satellite with the planet. Tables for the observation of the satellites at the time of their maximum elongation would also be very desirable.

From the mariners' point of view, for whom the moon is the principal heavenly body, the positions of the moon calculated for noon and midnight of every day would be insufficient on account of the considerable proper movement of our satellite. To obtain the longitude of a place by means of the observation of the passage across the meridian of one of the limbs, there would be required an excessively laborious calculation; the use of that method, however convenient, was then illusory. It was necessary to give the right ascension and the declination for every hour of the day, for the purpose of avoiding the employment of second differences except in cases where very great precision was sought for.

Then, when accurate tables of the movements of the planets were obtained, it was useful to add to the distances of the moon from the sun and from the stars, the distances of that body from the principal planets, the observation of which is more convenient and more certain than that of its distances from the stars.

46

But it was necessary to consider not only astronomers in observatories and sailors on board their ships, it was useful to enable astronomers on an expedition, and sailors when in a foreign harbour, and also geographers, to obtain the geographical_co-ordinates of their station with ease and accuracy. From this point of view the method known as that of the Lunar Culminations holds the first rank, a method to which a beautiful work by Nicolaï gave a capital importance. The learned director of the Observatory of Mannheim showed with what facility the observations of the passage of the moon combined with those of a certain number of stars, called stars of the moon," bordering on its parallel, and passing the meridian a little before or a little after (halfan-hour at the most), could give, sufficiently approximately, the difference of the longitudes of two places, even with a meridian instrument which was not perfect. On the other hand, Bessel and Hansen had given simple methods for calculating the horary movement of the moon. To apply this method of lunar culminations, it was then necessary to choose "stars of the moon," and to publish their positions every year, day by day, at the same time as those of the moon at the moment of its passing the meridian. This addition had, moreover, this advantage, that by indicating by an asterisk the stars comprehended between 4° and 14° of declination, the observers of the two hemispheres would have the elements most useful for improving continuously (d'une façon continue) the value of the lunar parallax. The phenomenon of the occultation of the stars of the moon offers, besides, an excellent means of determining longitudes. It was then important thus to calculate in advance and to publish all the elements likely to serve for predicting all the occultations in a given place, for the purpose of rendering the employment of this method casy to the navigator.

Finally it was indispensable, as well for the astronomical operations of observatories as for those connected with an astronomical or a geodetic expedition, that the collection of ephemerides should contain, for epochs sufficiently close to permit calculation for intermediate dates

"Uber die Methode, längen durch Rectascensions Differenzen gewählten Vergleichsterne vom Monde zu bestimmen" (Astronomische Nachrichten for 1823 and 1824.)

by simple proportion, the apparent positions of a very large number of stars of the greatest magnitude, and distributed both in the north and south hemispheres. It was useful, moreover, to join to this catalogue the values for very close epochs of the constants of Bessel, which enable one to pass from the mean position of a star at the commencement of the year to its apparent position on any day whatever.

For the principal circumpolars, a and & Ursa Minoris, the importance of which is so great in determining the various constants of a meridian instrument, and whose apparent positions vary much more rapidly than those of stars at a distance from the pole,-the apparent positions ought to be given every day.

Such is, with the exception of a few unimportant details, the list of reforms which the general opinion of astronomers demanded in England and Germany. (To be continued.)

ON THE SECONDARY WAVES IN THE SPHYGMOGRAPH TRACE

Na letter printed in this journal a short time ago (vol.

viii. p. 464), Dr. Galabin refers to a paper which has been since published in the Journal of Anatomy and Physiology (No. XII. p. 1), for a fuller account of his views as to the theory of the pulse, of which we gave a short notice and criticism in a former number (vol. viii. p. 330). This second and more detailed description calls for further remark, especially as the author has found reason somewhat to modify his opinion on one important point.

As is well known, the sphygmograph trace of a pulse beat (see Fig. 1) consists of a primary rapid rise, followed by a more gradual fall, broken by a considerable undulation, termed the dicrotic wave, which varies in its distance from the next primary rise according to the rapidity of the pulse. Between the primary and the dicrotic rises in the trace, the descending curve is sometimes interrupted by another small undulation termed the "tidal" wave, by Mr. Mahomed, though the name predicrotic is better, as it does not involve any theoretical conceptions. It is the development in the trace of these predicrotic and dicrotic waves that Dr. Galabin discusses and his explanation of the former is the following.-The separation of the primary and tidal (predicrotic) waves is due to an oscillation in the Sphygmograph, caused by the inertia of the instrument. In some cases the lever may be separated slightly from the knife-edge on which it rests, but generally the oscillation takes place in the instrument as a whole, and it may be followed by others in a descending series. With reference to this interpretation, it may be first remarked that it seems almost impossible that the whole sphygmograph should acquire a momentum in each pulsation, for it should be so adjusted on the arm that no part except the tip of the spring is in any way in contact with the artery, and when such is the case it is difficult to conceive of any shock being communicated to the whole. Again, any sudden upward impulse given to the instrument itself would be attended with a descent in the trace, for as the lever is only attached at one end, and there only on points, its pen would be slow to participate in the general movement of the framework, and would not rise so rapidly as the recording paper. The momentum acquired by the lever is a different thing. Marey and Sanderson have both shown that the primary rise in the trace may be attended with a sudden sharppointed wave, in the production of which the lever leaves the knife-edge on which it rests, returning to it after a very short excursion. To prevent the excessive development of this imperfection Marey has employed a small secondary spring to depress the lever; this spring Dr.

Galabin persists in not employing, because he thinksthough the evidence he brings forward on the subject is extremely small-that it increases the number of minor vibratory undulations. Nothing of the kind, however, is the case. Nearly all properly-taken tracings from the pulse in health present, if there is a secondary spring employed, no percussion wave at all; and when it is present the true predicrotic wave is quite independent, as may be seen in Fig. 2, which is from a powerful, healthy pulse of 44 a minute, in which the rise a is the percussion, b the primary, c the predicrotic, and d the dicrotic wave. This true predicrotic wave) varies in development with

that a proper trace can be obtained; because then only is it possible to see the full extent of the true predicrotic wave, uncomplicated by the superposition of the extraneous percussion wave. The latter does not appear as an extra element of the curve, but entirely disguises its true nature, on account of its being developed quite independently. when the lever is no longer in connection with the rest of the instrument, and therefore unaffected by whatever change may be occurring in the artery.

The cause of this predicrotic wave, which Marey gives of the similar one that appears in the hæmadromometer trace (Fig. 3, B) though considered by Dr. Galabir scarcely worthy of refutation, is supported by a large number of facts, especially by the hæmadromometer trace itself (Fig. 3, a, B). Its commencing in the radial artery as well as the carotid, at the moment of closure of the aortic valve, is also strongly in favour of the supposition that it is of shock origin; and that a shock may be transmitted through a column of fluid, which Dr. Galabin and some others seem to doubt, can be easily proved by suddenly closing an ordinary tap through which a large volume of water is passing, whereupon several oscillations of the retained liquid occur, producing a series of blows against the tap and perhaps the side of the tube, which are heard without difficulty.

The hæmadromometer trace (Fig. 3) shows also how completely the dicrotic wave is the result of the closure of the aortic valve, as Dr. Galabin also thought

wwwwww

FIG. 1.-Sphygmograph tracings of hea'thy pulses, drawn to one scale, with rates between 44 and 170 a minute. They read from left to right.

different pulse rates, being much more conspicuous in very slow pulses, and entirely absent in very quick ones, in which last a slight percussion wave is frequently found (see Fig. 1). Dr. Sanderson has previously described these two waves as co-existing, and he is undoubtedly right, as any who have had any considerable experience in Sphygmography in health will agree. It is Dr. Galabin who is in error, and it is but little compliment to other workers in the same field even to suppose that they have been sufficiently simple-minded to study and describe as physiological phenomena, instrumental errors so uncomplicated in origin and so readily comprehended. The

chief argument he brings forward in favour of his explanation is that by placing a weight on the lever at different parts, and so altering its moment of inertia, the length of the predicrotic wave is varied. That the percussion wave which is developed when no secondary spring is employed is so affected, no one will doubt, because the resistance of the pen is less significant when the lever is heavy than when it is light, and therefore the wave is of shorter duration when it is weighted. This wave, however, is even then of such considerable length that it has not ceased before the true predicrotic wave has commenced, and it therefore disguises the true nature of the trace. It is, therefore, only when the secondary spring is employed

FIG. 3.-Hamadromograph trace rom the carotid. a, Curve of direction and force of blood current, all above the dotted line indicating an onward and all below a heartward stream. 8, Simultaneous sphygmograph

trace.

in his earlier paper; but in his second he attributes it to the oscillatory result of the inertia of the arterial walls, and the lateral momentum acquired by the blood. The mass of the arterial walls, and the lateral movement of the blood during distension are so slight, that neither are in any way competent to explain a movement so constant and so considerable as the dicrotic wave, especially when one so much more reasonable is to be obtained as the result of the valve closure. At all events no theory can be considered at all satisfactory which does not explain, in one way or another, the hæmadromometer trace, which is one of the foundations of arterial dynamics, and has been verified in all its details by Dr. Lortet of Lyons. Neither Dr. Galabin's theory, nor that of Mr. Mahomed, can be said in any way to take Cognizance of the facts which it discloses, and they are incapable of doing so, therefore they must be considered inaccurate. Both these authors complicate their results by arguing from the analogy of a schema or model of the circulation constructed with elastic tubes; the arteries, however, are not simple elastic tubes, but tubes cut in elastic solids, being surrounded on all sides by yielding tissues, and they are not therefore comparable with tubes experimented on in air, and will not allow of comparative deductions being drawn from them.*

A. H. G.

*The blocks for Figs. I and III. are kindly lent by Prof. Humphry.

the "polariser" and the "analyser ;" and the two together are included under the general name of "polariscope."

The four principal processes by means of which a ray of light may be polarised are, reflexion, ordinary refraction, double refraction, and scattering by small particles. These methods will be considered in order; but before doing so, it will be convenient to describe the phenomena of polarisation as exhibited by some instrument tolerably simple in its action and of easy manipulation. For such a purpose a plate of crystal called tourmalin will perhaps serve better than any other to begin with. Tourmalin is a crystal of which there are several varieL

FIG. 6.

ties, differing only in colour. Very dark specimens generally answer the purpose well, excepting that it is difficult to cut them thin enough to transmit much light. Red, brown, or green specimens are usually employed; the blue are for the most part optically unsuitable. Some white, or nearly white, specimens are very good, and may be cut into thicker plates without loss of light.

If we take a plate of tourmalin cut parallel to a particular direction within the crystal called the optic axis (the nature and properties of which will be more particularly explained hereafter), and interpose it in the path of a beam of light at right angles to the direction of the beam, the

a

g

FIG. 8.

FIG. 5.

ances, whereby a ray of light may be brought into the condition in question, "or polarised." And it is a fact both curious in itself and important in its applications, that any one of these processes (not necessarily the same as that used for polarising) may be used also as a means of examining whether the ray be in that condition or not. This latter process is called "analysation." When two instruments, whether of the same or of different kinds are used, they are called respectively

FIG. 7.

only effect perceptible to the unassisted eye will be a slight colouring of the light after transmission, in consequence of the natural tint of the particular piece of crystal. But if we examine the transmitted beam by a second similar plate of tourmalin placed parallel to the When the former, the following effects will be observed. two plates are similarly placed, i.e. as if they formed one and the same block of crystal, or as it is technically expressed, with their optic axes parallel, we shall perceive only, as before, the colouring of the light due to the tints of the two plates. But if either of the plates be then turned round in its own plane, so as always to

remain perpendicular to the beam, the light will be observed to fade gradually, until, when the moving plate has been turned through a right angle, the light becomes completely extinguished. If the turning be continued beyond the right angle, the light will begin to revive, and when a second right angle has been completed, the light will be as bright as at the outset. In Figs. 1 and 2 a, b, c, d, e, f, g, h represent the two plates; in Fig. 1 the two plates are supposed to be in the first position; in Fig. 2 the plate e, f, g, h has been turned through a right angle. Of the parts which overlap, the shading in Fig. I represents the deepened colour due to the double thickness of the crystal; in Fig. 2 it indicates the complete extinction of the light. The same alternation of brightness and extinction will continue for every right angle through which the moving plate is turned. Now it is to be observed that this alternation depends only upon the angle through which one of the crystals has been turned, or, as it is usually stated, upon the relative angular position of the two crystals. Either of them may be turned, and in either direction, and the same sequence of effect will always be produced. But if the pair of plates be turned round bodily together no change in the brightness of the light will be made. It follows, therefore, that a ray of ordinary light possesses the same properties all round, or as it may be described, in more technical language, a ray of ordinary light, is symmetrical in respect of its properties about its own direction. On the other hand a ray of light, after traversing a plate of tourmalin has properties similar, it is true, on sides diametrically opposite to one another, but dissimilar on intermediate sides or directions; the properties in question vary in fact from one angular direction to another, and pass through their phases or an entire period in every angle of 18 degrees. This directional character of the properties of the ray, on account of its analogy (rather loose, perhaps) to the directional character of a magnet or an electric current, suggested the idea of polarity, and hence the condition in which the ray was found to be was called polarisation.

Having so far anticipated the regular order of things on the experimental side of the subject, it will perhaps be worth while to make a similar anticipation on the side of theory. It is considered as established that light is due to the vibrations of an elastic medium, which, in the absence of any better name, is called ether. The ether is understood to pervade all space and all matter, although its motions are affected in different ways by the molecules of the various media which it permeates. The vibrations producing the sensation of light take place in planes perpendicular to the direction of the ray. The paths or orbits of the various vibrating ethereal molecules may be of any form consistent with the mechanical constitution of the ether; but, on the suppositions usually made, and none simpler have been suggested, the only forms possible are the straight line, the circle, and the ellipse. But in ordinary light the orbits at different points of the ray are not all similarly situated; and although there is reason to believe that in general the orbits of a considerable number of consecutive molecules may be similarly situated, yet in a finite portion of the ray there are a sufficient number of variations of situation to prevent any preponderance of average direction.

This being assumed, the process of polarisation is understood to be the bringing of all the orbits through out the entire ray into similar positions. And in the case of the tourmalin plate the orbits are all reduced to straight lines, which consequently lie in one and the same plane. For this reason the polarisation produced by tourmalin, as well as by most other crystals, is called rectilinear, or more commonly, plane polarisation. This property of tourmalin may also be expressed by saying that it permits only rectilinear vibrations parallel to a particular direction determined by its own internal structure to traverse it.

Adopting this view of polarisation as affected by a plate of tourmalin, it would be interesting to ascertain the exact direction of the vibrations. And a simple experiment will go far to satisfy us on that point. The argument, as now stated at least, is perhaps based upon general considerations rather than upon strict mechanical proof; but the experimental evidence is so strong that it should not be denied a place here. Suppose for a moment that the tourmalin be so placed that the direction of vibration lies either in or perpendicular to the plane of incidence (that is, the plane containing the incident ray, and a perpendicular to the surface on which it falls at the point of incidence; then it is natural to expect that vibrations executed in the plane of incidence will be far more affected by a change in the angle of incidence than those perpendicular to that plane. In fact the angle between the direction of the vibrations and the surface upon which they impinge, will in the first case vary with the angle of incidence, but in the second case it will remain unchanged.

In Figs. 3 and 4, n, o represents the ray of light; the arrow the direction of vibration, a, b, c, d, a, b, c', d', the plate in two positions, turned in the first instance about the direction of vibration, in the second about a line perpendicular to it.

Dismissing, then, the former supposition, and supposing that nothing whatever is known about the direction of vibration; then, if all possible directions be taken in succession as pivots about which to tilt or turn the second tourmalin, it will be found that for one direction the intensity of the light diminishes more rapidly with an increase of tilting (or, what is the same thing, with an increase of the angle of incidence) than for any other. And further, that for a direction at right angles to the first, the intensity of light diminishes less than for any other; while for intermediate directions the diminution of inten sity is intermediate to those above-mentioned. In ac cordance, therefore, with what was said before, we may conclude that the vibrations are parallel to the line or pivot about which the plate was turned when the diminution of light was least.

Secondly, polarisation may be effected by reflexion. If light reflected from the surface of almost any, except metallic, bodies be examined with a plate of tourmalin, it will in general be found to show traces of polarisation that is to say, if the plate be caused to revolve in its own plane, and the reflected rays be viewed through it, then in certain positions of the plate, the reflected light will appear less bright than in others. If the angle at which the original rays fall upon the reflect ing surface be varied, it will be found that the amount of alteration in brightness of the light seen through the revolving tourmalin (or analyser) will also vary. This fact may also be expressed thus: in polarisation by re flexion, the degree of polarisation, or the amount of polarised light in the reflected rays, varies with the angle of incidence on the reflecting surface. But at a particular angle, called on that account the polarising angle, the polarisation will be a maximum. This angle (usually measured between the incident ray and the perpendicular to the reflecting surface) is not the same for all substances; in fact it varies with their refrac tive power according to a peculiar law, which, when stated in the technical language of science, may be thus enunciated: the tangent of the polarising angle is equal to the refractive index. considerations, combined with the usual expressions for Simple geometrical the laws of reflexion and refraction, will show that this relation between the polarising angle and the refractive index may be also expressed in the following way. If light be incident at the polarising angle, the reflected and refracted rays will be at right angles to one another.

In Fig. 5, s, i represents the incident, i, f the reflected, and i, r the refracted ray. Then s, i will be incident at the polarising angle when the angle s, ↳, I is a right angle.