but owing to the difficulty of determining iridium accurately, it is doubtful if these figures can be considered reliable.

If calculation were made from South African iridosmium, the osmium figures would be larger, as this iridosmium apparently runs much above the average in osmium; on the other hand, osmium analyses are apt to be low, owing to volatilization. The palladium is lower than would be anticipated; in the Sudbury ores the palladium runs much higher in proportion to the platinum. The ruthenium is unexpectedly low, but is probably approximately correct.

JAS. LEWIS HOWE

WASHINGTON AND LEE UNIVERSITY, LEXINGTON, VIRGINIA

THE RECTA OF FROGS

So far as I know Paramoecium has not been definitely shown to encyst in nature nor in laboratory cultures. In fact, most of the investigators who have worked with this organism state that they have never seen it encyst and are of the opinion that it does not possess the ability to do so. Hence the following observations, though incomplete, seem worthy of record.

Two to three c.c. of rich, milky-white cultures of Paramoecium (species not determined) were injected (by attaching a short catheter to a syringe) into the recta of frogs, with the result that encystment occurred in about two per cent. of the frogs injected. In all, encystment has been observed in three frogs. When it was first observed, two hours had elapsed since the paramoecia were introduced into the rectum. When a portion of the rectal contents was examined a fair number of individuals were observed in what later seemed to be the beginning of encystment, although at first they were very nearly overlooked for Opalina. More careful observations, however, disclosed a very thin membrane-like substance surrounding them. By continued observations it was finally possible to observe six individuals regain their normal Paramoecium shape, appearance and activity by freeing themselves of the peculiar substance enclosing them. It was really not possible until the organisms had freed themselves of the membranes to determine whether I was observing Paramoecium, some undescribed parasitic ciliate of frogs, or Opalina in an abnormal condition, because they presented a very unusual appearance due to the fact that they were folded and rounded so as to occupy about half their normal space. Others, however, were not able to free themselves and, after an hour or two, became more and more rounded and definitely enclosed within what, by this time, could be called a definite membrane perhaps a cyst membrane.

In another frog which was examined five and a half hours after injection per rectum only encysted paramoecia were present. These were placed in three depression slides, four organisms on one slide and

several on each of the others, and kept in a moist chamber and observed several times daily. No change was noticed for the first three days, but on the fourth day some of the cysts were undergoing fission, and on the fifth day two organisms were seen within a single cyst. A fairly heavy cyst wall was clearly visible. On the fifth day some paramoecia excysted.

When a considerable amount of tap-water was added, it was noticed that very soon the movement, which had been quite slow, was gradually increased and in three instances was observed to bring about excystation after two hours. As the movement of the organism became more rapid the cyst wall became thinner and thinner until the organism was finally able to free itself and swim away. Shortly before the organism was free, it could be seen pushing against the cyst wall which by this time had become a very thin membrane which would bulge out as the organism pushed against it from within. Several of the cysts produced in this experiment were observed for eight days when they were accidently lost due to evaporation of the water containing them. None of the encysted paramoecia were ever observed to lose movement entirely, although movement in some was very feeble indeed.

In another instance paramoecia were injected into the recta of five frogs. After four and a half hours the frogs were examined; four contained a few free and fairly active paramoecia and no cysts, and one contained cysts with thick heavy walls and no free paramoecia.

In many instances the paramoecia were all dead within three to four hours after injection into the frog's rectum. A very high percentage were killed and disintegrated (digested perhaps) within one to two hours, or before encystment was ever observed to occur.

All attempts to bring about encystment in removed recta, in removed rectal contents, in the recta of killed frogs, and in the stomach and intestines failed.

We may have in these meager observations an inkling as to the origin of parasitism; during the protection afforded by encystment a free-living organism may gradually become acclimatized or adapted to its new and unfavorable environment and finally become a parasite. It would perhaps be a worth while undertaking to place in the alimentary tract and in the tissues of animals the cysts and free forms of some of the well-known free-living ciliates which form cysts readily in nature and in culture. After thousands of failures it might be possible to find an organism that could excyst and then maintain itself on the intestinal bacterial flora.

L. R. CLEVELAND

NATURAL AND EXPERIMENTAL INGESTION OF PARAMOECIUM BY COCKROACHES ABOUT thirty cockroaches were collected in the basement of a department store in Baltimore between eight and nine in the morning. They were placed in a dry bottle and carried to the laboratory where several were dissected about two hours later and their stomach and rectal contents examined microscopically.

Three of those examined had Paramoecium in their stomachs. No attempt was made to determine the species of Paramoecium, but the observation was verified by three individuals in the laboratory who were familiar with this well-known organism. The usual parasitic protozoa were seen in the rectal contents, but Paramoecium was only observed in the stomach. The remaining cockroaches (17 in all) were left to be examined later to see if Paramoecium remained present and if it reached the rectum. These were all opened up and observed between three and four in the afternoon, seven to eight hours after they were collected, and no living paramoecia were present in any of them, but the remains of paramoecia were clearly visible in the stomach contents of two individuals.

In order to determine how long Paramoecium would live in cockroaches, approximately two hundred individuals were collected and were starved in dry petri dishes from one to ten days before being fed a rich, milky-white culture of Paramoecium, containing hundreds of individuals per drop. In most of the experiments the cockroaches were starved four or five days because it was somewhat difficult to get them to ingest paramoecia after one to two days' starvation. Each cockroach was placed in a petri dish and was observed until it ingested from one to three drops of the culture, the time was noted, and then the cockroach was removed from the petri dish with forceps, swabbed off with cotton, and placed in another petri dish with blotting paper in the bottom. A hundred and fifteen observations were carried out in this manner. The cockroaches were dissected at intervals from five minutes to three days after having been observed to feed on Paramoecium. The contents of their alimentary tracts were examined microscopically, with the result that few, if any, of the paramoecia were killed during the first two hours after ingestion and that all were killed by the end of five hours except in a single instance where three actively motile paramoecia were found in the stomach contents six hours after ingestion. When the stomach contents were examined three and four hours after the ingestion of paramoecia, mostly broken up or disintegrating organisms were observed together with three or four normally active individuals. This, then, makes it highly probable that the cockroaches in which Paramoecium naturally occurred had fed on water containing a fair number of these organisms shortly before they were collected and brought to the laboratory-perhaps a rather unusual occurrence. L. R. CLEVELAND

DEPARTMENT OF TROPICAL MEDICINE,
HARVARD UNIVERSITY MEDICAL SCHOOL,
BOSTON, MASS.

VOL. LXVI SEPTEMBER 9, 1927 No. 1706

CONTENTS

The British Association for the Advancement of Science:

The Outstanding Problems of Relativity: PROFESSOR E. T. WHITTAKER

Charles Fuller Baker: COLIN G. WELLES

Scientific Events:

International Electrical Congresses; The Field Museum Paleontological Expedition in South America; The Bartol Foundation; The New Bureau of Chemistry and Soils

Scientific Notes and News

University and Educational Notes
Discussion and Correspondence:

Age of the "Satsop" and the Dalles Formations
of Oregon and Washington: DR. JOHN P. BUWALDA
and BERNARD N. MOORE. More Data: E. H.
MCCLELLAND. Assimilation of Fixed Nitrogen by
Havana Tobacco: A. B. BEAUMONT and G. J.
LARSINOS. Standard Mathematical Symbols: PRO-
FESSOR BURTON E. LIVINGSTON
Quotations:

A Portrait Painter of Birds

223

229

230

233

235

236

237

THE SCIENCE PRESS

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Entered as second-class matter July 18, 1928, at the Post Office at Lancaster, Pa., under the Act of March 8, 1879.

THE OUTSTANDING PROBLEMS OF

RELATIVITY1

It was in January, 1914, that Einstein2 made his great departure from the Newtonian doctrine of gravitation by abandoning the idea that the gravitational potential is scalar. The thirteen eventful years which have passed since then have seen the rapid development of the new theory, which is called general relativity, and the confirmation by astronomers and astrophysicists of its predictions regarding the bending of light rays by the sun and the displacement of spectral lines. At the same time a number of new problems have arisen in connection with it; and perhaps the time has now come to review the whole situation and to indicate where there is need for further investigation.

Speaking from this chair I may perhaps be permitted to recall that my first experience of the British Association was as one of the secretaries of Section A nearly thirty years ago; and that my secretarial duties brought me the privilege of an introduction to the distinguished mathematical physicist, Professor G. F. FitzGerald, of Dublin, who was a regular and prominent member of the section until his death in 1901. FitzGerald had long held an opinion which he expressed in 1894 in the words "Gravity is probably due to a change of structure of the ether, produced by the presence of matter."3 Perhaps this is the best description of Einstein's theory that can be given in a single sentence in the language of the older physics: at any rate it indicates the three salient principles, firstly, that gravity is not a force acting at a distance, but an effect due to the modification of space (or, as FitzGerald would say, of the ether) in the immediate neighborhood of the body acted on; secondly, that this modification is propagated from point to point of space, being ultimately connected in a definite way with the presence of material bodies; and thirdly, that the modification is not necessarily of a scalar character. The mention of the ether would be criticized by many people to-day as something out of date and explicable only by the circumstance that FitzGerald was writing thirty-three years ago; but even this criticism will not be universal; for Wiechert and his fol

1 Address before Section A-Mathematical and Physical Sciences-the British Association for the Advancement of Science, Leeds, 1927.

2 Zeits. f. Math. u. Phys. 63 (1914), p. 215.

3 FitzGerald's Scientific Writings, p. 313.

lowers have actually combined the old ether theory with ideas resembling Einstein's by the hypothesis that gravitational potential is an expression of what we may call the specific inductive capacity and permeability of the ether, these qualities being affected by the presence of gravitating bodies. Assuming that matter is electrical in its nature, it is inferred that matter will be attracted to places of greater dielectric constant. It seems possible that something of this sort was what FitzGerald had in mind.

C2

Let us now consider some of the consequences of Einstein's theory. One of the first of them is that when a planet moves round a central attracting body in a nearly circular orbit, the perihelion of the orbit advances by (approximately) 6лv2/c2 in each revolution, where v is the planet's velocity and c is the velocity of light. This gives for the motion of the perihelion of Mercury almost exactly the amount (42′′ per century) which is found from observation. Another consequence is that light-rays which pass near a massive body are deflected, the bending at the sun's limb being 1"75. This was confirmed observationally by the British expeditions to the eclipse of May, 1919, and still more decisively by the Lick Observatory expedition to the Australian eclipse of September, 1922: the Lick observers found for the shift 1"-72 ± 0′′-11, which differs from Einstein's predicted value by much less than its estimated probable error. Yet another result of general relativity is that, by the principle of equivalence, light which reaches us from a place of different gravitational potential (such as the sun) must exhibit a kind of Doppler effect. This "gravitational shift of the solar spectral lines" is now generally admitted to be confirmed by comparisons of wave-lengths at the center of the sun's disc with wavelengths from the arc in vacuo; and in 1925 the effect was observed, on a much larger scale, by W. S. Adams in the spectrum of the companion of Sirius.

Besides the effects which have been verified observationally there are many consequences of Einstein's theory which are of interest as opening up new fields or presenting new interrelations of phenomena in astronomy and physics. For instance, there is a contribution to the precession of the equinoxes which, unlike ordinary precession, does not depend on the oblateness of the earth. Again, the bending of the rays of light near a gravitating body, which has been observed in the case of the sun and the companion of Sirius, may, theoretically at any rate, be so pronounced that the ray is permanently captured by the attracting body, and describes forever a track round and round it, which approaches spirally and asymptotically to a circle whose center is at the center of gravitation. Yet another deduction is that an electrified body, or a single electron, which is at rest in

2

where AV is the Beltrami's second differential parameter for the form ds2 = Za dж¿ dx which specifies the line-element in the three-dimensional space, Ti is the energy-tensor, and N is the velocity of light at the point. This equation reduces to Laplace's equation in one extreme case (when no matter or energy is present at the point) and to Poisson's equation in another extreme case (when the energy is entirely in the form of ordinary matter), but it offers an infinite variety of possibilities intermediate between the two, in which energy is present but not in the form of ordinary matter. It is possible that this equation, which evidently suggests an approach to the new wave-mechanics, may play as important a part in the microphysics and astrophysics of the future as the equations of Laplace and Poisson have played in the ordinary physics of the past.

Let us take another consequence of the new theory. Consider the field due to a single gravitating particle. Take any plane through the particle, and in this plane draw the family of concentric circles, whose center is at the particle. The length of the circumference of these circles will, of course, diminish as we take circles nearer to the center: and at one place we shall have a circle whose circumference is of length

4rẞM/c2

where ẞ is the Newtonian constant of attraction, M is the mass of the particle in grams, and c is the velocity of light in empty space. When we arrive at this circle we find that the element of length directed radially towards the center is infinite: that is to say, the space within the circle is impenetrable. Every gravitating

T

In particle has a ring-fence around it, within which no other body can approach.

It will be noticed that in all that I have said I have used the ordinary language of three-dimensional physumerical space, and have avoided mention of that fourons dimensional world of space-time which looms so Ne largely in most expositions of relativity. The reason is that I have been speaking only of phenomena belonging to the statical class, i.e., those for which the field does not vary with the time: and for such phenomena, as Levi-Civita showed in a famous paper on the Rendiconti dei Lincei of 1917, the four-dimensional problem can be reduced to a three-dimensional one of the same kind as physicists have been accustomed to deal with. It may be consoling to those who distrust their own powers of doing research in four dimensions to know that in general relativity there are enough important unsolved problems of the statical type, for which capacity in three dimensions is sufficient to keep all the investigators of the world busy for at least another generation.

TESE

ce's

SL

(r =1, 2, 3)

d SL =0 dt 8x, δωτ just as in the classical dynamics: but L is not now a simple difference of terms of the "kinetic energy" and "potential energy" types. It shows the sound instinct of the creators of the old dynamics that they almost always studied the equations without making the assumption that L consists of terms of kinetic and potential type: and thus their discoveries remain perfectly valid in the dynamics of general relativity.

The fundamental researches of Einstein and Hilbert, with the discovery of the field equations of gravitation, were published in 1915. At that time German scientific journals did not reach this country regularly, and British physicists and mathematicians were mostly occupied in one way or another with duties arising out of the great war; so that comparatively little notice was taken of the new theory on this side of the North Sea during the first year or two of its existence, and indeed it was not until the end of the war that most of us had any opportunity of studying it. In Germany, however, it was quickly realized that general relativity was one of the most profound and far-reaching contributions that had ever been made to science. Its successful prediction of new phenomena of a most unexpected kind was an event of the first importance, but still more significant was its complete subversion

of the foundations of physics and reconstruction of the whole subject on a new basis. From time immemorial the physicist and the pure mathematician had worked on a certain agreement as to the shares which they were respectively to take in the study of nature. The mathematician was to come first and analyze the properties of space and time, building up the primary science of geometry; then, when the stage had thus been prepared, the physicist was to come along with the dramatis persona-material bodies, magnets, electric charges, light and so forth-and the play was to begin. But in Einstein's revolutionary conception, the characters created the stage as they walked about on it: geometry was no longer antecedent to physics, but indissolubly fused with it into a single discipline. The properties of space, in general relativity, depend on the material bodies that are present; Euclidean geometry is deposed from its old position of priority and from acceptance as a valid representation of space; indeed its whole spirit is declared to be alien to that of modern physics, for it attempts to set up relations between points which are at a finite distance apart, and thus is essentially an action-at-a-distance theory; and in the new world no direct relations exist at all except between elements that are contiguous to each other.

The scheme of general relativity, as put forward by Einstein in 1915, met with some criticism as regards the unsatisfactory position occupied in it by electrical phenomena. While gravitation was completely fused with metric, so that the notion of a mechanical force on ponderable bodies due to gravitation attraction was completely abolished, the notion of a mechanical force acting on electrified or magnetized bodies placed in an electric or magnetic field still persisted as in the old physics. This seemed to be an imperfection, and it was felt that sooner or later everything, including electromagnetism, would be reinterpreted and represented in some way as consequences of the pure geometry of space and time. In 1918 Weyl proposed to effect this by rebuilding geometry once more on a new foundation, which we must now examine.

Weyl fixed attention in the first place on the "lightcone," or aggregate of directions issuing from a worldpoint P, in which light-signals can go out from it. The light-cone separates those world-points which can be affected by happenings at P, from those points whose happenings can affect P; it, so to speak, separates past from future, and therefore lies at the basis of physics. Now the light-cone is represented by the equation ds2 = 0, where ds is the element of proper time, and Weyl argued that this equation, rather than the quantity ds2 itself, must be taken as the startingpoint of the subject; in other words, it is the ratios of the ten coefficients 9pq in ds2, and not the actual