TOWARDS A UNIFIED COSMOLOGY

by     Reginald O. Kapp

PART V - APPENDICES

Appendix E - The Shrinking Earth


E.1: Further Means of Estimating the Half-Life of Matter
These appendices are, as I have said already, to be regarded as research programmes. One of the subjects on which research is needed is the half-life of matter. A reason has been given in Appendix C why this cannot be much greater than 4 x 108 years and why it is probably not much less than 3 x 108 years. In this appendix further means for estimating the half-life will be given. They contain some uncertainties, which the future may remove ; and in view of these more importance must here be given to the method than to the estimated number of years to which it leads. It will be shown that more accurate knowledge than we have at present is likely to lead to an estimated half-life not greater, and perhaps substantially less, than 4 x 108 years.

It has been suggested in Appendix D that the elements of which the earth is composed were formed out of hydrogen in Jupiter at a time when that planet was much more massive than it is now. It is this hypothesis that can help with an estimate of the half-life of matter.

There is evidence that some of the earth's sedimentary rocks were laid down 2 x 109 years ago. It may, for all I know, be impossible to decide whether this happened while the earth still formed a part of the substance of Jupiter or after it had become a planet. But the former view would seem difficult to maintain and, in the absence of evidence to the contrary, most of us, I feel sure, would assume that the first sedimentary rocks on the earth were formed after this planet had been hurled into independent existence. When this happened the speed of rotation of Jupiter must have been such that centrifugal force substantially exceeded gravity.

The most recent estimate for the age of radium-bearing rocks is greater than that of sedimentary rocks, namely 2.6 x 109 years. This is the time that, according to the revised double star theory, has elapsed since the heavy elements were synthesized in Jupiter. When it happened the speed of rotation of Jupiter must have been such that gravity substantially exceeded centrifugal force.

These figures show that the speed of rotation of Jupiter must have risen greatly during less than 6 x 108 years. At the beginning of this interval it was such that gravity produced the pressure needed for the heavy elements to form. At the end of the period it was so much greater that the effect of gravity was more than cancelled; there was a surplus of centrifugal force sufficient to overcome the cohesive strength of the material.

It has been shown in Appendix D that only one reason can be suggested for a large increase in the speed of rotation of a solid star not subjected to an external couple, namely loss of mass by extinction. Hence the time interval between the birth of the heavy elements and the birth of the earth could help with an estimate of the half-life of matter. One would have to know the centripetal force needed to form the heavy elements and the centrifugal force needed to eject the planets. The sum of these forces would be a measure of the increase in speed of rotation between the two events. This, in turn, would be a measure of the loss of mass by extinction. It ought to be possible to arrive at rough estimates of all the quantities that enter into the calculation. It seems to me that a threefold increase in speed of rotation during 6 x 108 years is of the right order of magnitude; and this corresponds to a half-life of 4 x 108 years.

Another clue is given by the present ratio of the mass of Jupiter to that of the sun.

According to the revised double-star theory Jupiter has never been quite as massive as the sun, but it seems to me that it must at one time have been nearly as massive, for I doubt whether a double star can form at all unless the masses of both stars are about equal during growth. If one of them were much less massive than the other, one would expect it to be absorbed by its larger neighbour during an early stage of its development. Hence each partner of a binary star system probably begins to form at about the same time as the other partner and to grow at about the same rate until both have become so massive that income by capture of surrounding matter and loss by extinction roughly balance. A small difference in the income and loss account would then be critical.

This would be the moment when a difference between the two masses would decide the subsequent course of events. Incapable of competing successfully with its larger partner for surrounding matter, the smaller star would find itself after a certain time on the wrong side of the balance sheet; it would be losing mass. The net loss rate would be small at first, for it would be but a small difference between the rate of extinctions and the slightly lower rate of captures. But as the difference between the masses of the two neighbouring stars increased, the rate at which the smaller one replenished its substance by capture would also decrease; the discrepancy between the two masses would become ever more accentuated. While the larger star would continue to balance its accounts and might even continue to grow, the smaller one would in time become so small that its income from capture became negligible and its future size would be wholly determined by the half-life of matter.

If the above reasoning is sound, the sun's mass has not changed by a large factor since it reached its maximum value a certain number of thousands of millions of years ago and Jupiter had the same mass at one time; the present mass of this planet is then one-thousandth of the maximum value that it ever reached. The reduction began slowly, while loss was being partly compensated by capture, but became more rapid when capture practically ceased. The curve connecting the mass of Jupiter with time must then have had the general shape shown in Fig. 6.

X 109 YEARS AGO

Fig. 6. Relation between mass (vertical scale) and time (horizontal scale) for Jupiter, if the half-life of matter is 4 x 108 years. The figures on the vertical scale give the past mass of Jupiter as a factor of the present mass.

The curve has been drawn for a half-life of matter of 4 x 108 years. Other curves could have been drawn to the left for shorter and to the right for longer half-lives. But they would all have to begin at the past time when Jupiter and the sun were both about equal and when both began their existence as complete stars. Estimates seem to vary as to when this was, but I cannot recollect one greater than 7x109 years ago. It is difficult to draw a convincing curve that shows the mass of Jupiter to have been 1000 times its present value 7 x 109 years ago and that also corresponds to a half-life greater than 4 x 108 years. So I should like to adopt this estimate provisionally while hazarding the guess that more reliable data will lead to a rather shorter estimate.

E.2: The Diminishing Value of g
Let the mass of the earth t years ago be m0 and its present mass m. Let the radius of the earth that corresponds to m0 and m be, respectively, r0 and r, and let the half-life of matter be Tm. It can be shown easily that the following relations hold for small values of t:

m0 / m = 1+ 0.69t / Tm
r0 / r = 1 + 0.23t / Tm

From these equations, and if Tm is taken at 4 x 108 years, the following conclusions are reached:

(a) The value of the gravitational constant, g now expressed in metres per second square as 9.80665, had more nearly the value 9.80667 in Newton's time and will have the value 9.80663 in the year 2250.
(b) The radius of the earth is diminishing by nearly 4 mm. per year.
(c) During the geological period known as the Cambrian the earth had about two-and-a-half times its present mass and its radius was about 13.5 per cent. greater than now.
(d) During the time, two thousand million years ago, when the first known sedimentary rocks were laid down the mass of the earth had thirty-two times its present value and the radius was more than three times as great as it is now.
(e) At the time when these sedimentary rocks were laid down water boiled at 140oC. Its great weight must have caused it to have an enormous scouring action on rocks. Sedimentation must have been a much more rapid process than it is now.
(f) If it were not for the slowing down effect of the tides, the continuous decrease in the earth's radius of gyration would lead to a continuous increase in its angular velocity. It follows that tides dissipate more energy than has hitherto been supposed.

The astronomical, geological and biological consequences of this slow but unceasing reduction in the earth's mass and volume must be significant. If my theory that the half-life of matter is finite is true, it must therefore provide extensive and rewarding fields for new research by experts in these three disciplines. This appendix is not a suitable place for considering in detail the nature of this research, but it is worthwhile to consider some samples of the problems that continuous extinction raises in each of these disciplines.

The astronomical field seems to be the least promising of the three, for the astronomical changes that would result from shrinking of the earth are likely to be the least easy to detect.

One such change would be the earth's hold on the moon, which must be steadily loosening as g decreases. It has already been mentioned in Appendix C. Another would be the increase in angular velocity that must accompany reduction in the earth's radius of gyration. As just mentioned, this speeding-up of the earth's rotation must go some way towards counter-acting the slowing-down effect of the tides. But I cannot think of any astronomical observations precise enough to detect the predicted changes in g and in the radius of gyration.

These changes would affect the exact times when eclipses occur. One can calculate these times very accurately for past eclipses on the assumption that the earth's mass was no greater then that it is now and could then compare the result with historical records. If observations thousands of years ago had been as precise as they are today, one might be able to discover from a discrepancy between the calculated and the observed moments whether the earth's mass has changed or not.

But to be sure one would also have to disentangle the two effects that influence the length of the day: tides, which tend to make the day grow longer, and contraction, which tends to make it grow shorter. For this one would have to know accurately how much energy is dissipated by tides and this is, in fact, hardly possible to estimate. The conclusion is, I am afraid, that precise astronomical observation and calculations are too recent and knowledge of some of the relevant quantities too incomplete, for the gradual shrinking of the earth to have an observable effect in astronomy.

E.3: Geological Implications of Shrinking
In geology the position may be more hopeful. The finite half-life of matter may, for instance, succeed in explaining the formation of mountain ranges. The only explanation of these that has so far seemed at all possible is that the ranges are the consequence of shrinking of the earth. But it has hitherto proved impossible to find a satisfactory cause of the shrinking.

At one time it was believed that this cause was thermal. In remote geological times, it was thought, the earth's core was much hotter than it is now. As it cooled it contracted and the more rigid crust ceased to be a tight fit. Surrounding the contracting core loosely it came under the influence of strong shear forces, which caused it to pucker into mountains and depressions. 'Like the skin of an apple', it used to be said.

It was always difficult to understand how mere thermal causes could suffice to explain the contraction; for the change in the volume of a solid substance with change of temperature is not great and puckering seems to occur only if the change of volume is rather great. It must be remembered that what has to be accounted for is not one single pucker but a succession of many such at irregular intervals of time.

The earliest ranges have long since been weathered down by the action of water. Their broken and distorted remains have sometimes been raised into new ranges by a subsequent upheaval. Mountains arose in Great Britain, Norway and Greenland during the Silurian period, 350 million years ago. They have been largely obliterated and have given place to later mountains, often on the same sites. The more recent Appalachian Mountains were formed in the days when the great reptiles lived and crawled, we are often told, in swamps. These mountains were followed still later by the Sierra Nevada, the Rocky Mountains and the Andes, which arose in the Cretaceous period. The youngest arrivals are the Alps, the formation of which coincided with some of the higher mammals. A considerable amount of continuous or repeated shrinking is needed to account for so much.

Thermal shrinking can certainly not do so and the theory that it did has long since been abandoned by geologists. The earth has cooled but little, if at all, during geological times, as is demonstrated by sedimentary rocks. These have been precipitated out of the sea and some of them were formed, as has been mentioned already, more than two thousand million years ago. So apparently the sea existed at that remote time. The average temperature of the surface of the earth must therefore have been below the boiling point of water during the geological ages in which it is known that the mountain ranges were formed. It is still above the freezing point of water. If the average temperature of the earth has differed at all from one geological upheaval to the next, the difference must have been negligibly small.

Such considerations have led geologists to seek some other explanation for mountain ranges. There are at least four but it would not be helpful to discuss them here in detail. None can be said to hold the field. The conclusion at which one arrives is that it is almost, if not quite, impossible to account for the puckering of the earth's surface if there has been no shrinking and it is, similarly, almost, if not quite, impossible to account for any sufficiently pronounced shrinking so long as one assumes the half-life of matter to be infinite. The best that can be said for the various rival theories about the origin of mountain ranges is that they are valiant attempts to explain what still seems to be inexplicable.

In these circumstances it is worthwhile to consider whether the puckering of the earth's surface could be the consequence of the kind of shrinking that results from the continuous extinction of matter. To prove that this was indeed so would be to provide somewhat sensational support for Symmetrical Impermanence. But it can only be done if a rather serious difficulty can first be surmounted. Its nature must claim our attention for a moment.

The extinction of an elementary component of the material universe is accompanied, it has to be remembered, by the simultaneous extinction of an equivalent volume of space. Hence we have to face the following question: when an elementary component becomes extinct, does the space occupied by this component become extinct as well? If it does, the extinction does not leave a void. The matter that has been adjacent to what has disappeared is not adjacent to the place where that was, for the place, too, has disappeared. The compacting of matter is, on such an interpretation, exactly the same after a disappearance as it was before.

If continuous extinction has to be interpreted in this way, the extinction of matter within the earth would change its size without changing its density or its shape. If nothing happened to the earth except continuous extinction, the earth would, at any particular moment, be an exact reduced scale model of what it had been before. Shrinking of this kind would not impose any shear forces and could not lead to any puckering. If the extinction of matter is accompanied by extinction of the space previously occupied by that matter, the origin of mountain ranges must remain as inexplicable as ever it was.

But I am not sure that this is the correct interpretation of continuous extinction. The relation between matter and space is still very obscure and no one can honestly say that he has no difficulty in appreciating the meaning of the relativistic view that space is a constituent of the material universe. For most of the time we tend to ignore this conclusion and continue to regard space as a container. Much clarification of thought has still to be done before any of us can hope to discuss adequately the relation between space and matter. At present we can ask the question whether it is true that space and matter originate together and become extinct together. But we cannot hope to answer the question until we understand its meaning much better than we do today.

Having uttered this warning against both hasty acceptance and hasty rejection of any conclusion about the relation between space and matter, I venture to draw attention to a conclusion that will be put forward tentatively in Appendix H. This is that, when an elementary component of the material universe becomes extinct, the space that becomes extinct, too, is not that occupied by the component, but surrounding space. It will be shown that it is more consistent with the relativist notion of a differentiated space to assume that a wave of contracting space travels outwards from the site of an extinction without causing disappearance of the site.

If this conclusion does, in fact, follow from a correct appreciation of the relation between space and matter, a void is left behind whenever an elementary component of the material universe becomes extinct. As extinctions are occurring continuously in all substances, such voids are also occurring continuously. Their subsequent fate must depend on whether or not the substance is subjected to a compressive force. If it is not, the voids remain and the substance loses mass without losing volume. Its density decreases with time and would be halved in time Tm But if there is a compressive force, the voids are squeezed up. The loss of mass is accompanied by a loss of volume and the density is not changed.

These conclusions can be applied to the shrinking earth. The consequence of continuous extinctions is that the core, which is subjected to the weight of the superimposed layers of the earth and the atmosphere above the earth's surface, loses volume as well as mass, while in the first instance the outer crust loses mass only and does not lose volume until gravitational forces and the weight of the air above compress it. Hence the crust ceases to be a tight fit and the puckering that geologists attribute to contraction takes place.

I have purposely not elaborated the above theory and I put it forward with considerable diffidence. I should not do so at all were it not that the formation of mountain ranges, like many other scientific mysteries, calls for the collaboration of specialists in many fields of study and the hypothesis of continuous extinction does at least offer a prospect, be it but a faint one, that this mystery will be solved by a joint effort of geologists, mathematical physicists, nuclear physicists and relativists. There are occasions when an author ought to withhold a new theory until he has tested it from every point of view. But when the testing calls for the combined efforts of many, his proper course is to offer the theory to the world while it is still in a tentative state.

Let me add that, according to this theory, there is no filling up of voids when there is no compression. There is none on the surface of the moon or on Mars, which have no atmosphere to weigh on the solid surface. One should therefore expect the surfaces of these bodies to have become more and more spongy with time. Mattel there must be in a condition unknown and unreproducible on earth - solid, yet with a very low specific gravity. If my theory is correct, comets must consist of similar substance, for they must be the degenerate remnants of larger chips thrown off Jupiter.

E.4: Continental Drift
At the beginning of this century there was much discussion of a theory that was called, after its originator, the Wegener Hypothesis. According to this the earth's geography has undergone radical changes during geological times. The Eastern and Western continents are supposed, for instance, to have been joined together into a single huge landmass. If it was so, some cataclysm must have broken the mass into two pieces, of which one is now the two Americas and the other the combined continents of Europe, Africa and Asia. After their severance the two pieces must have drifted apart, leaving the Atlantic Ocean between them.

At least four arguments have been urged in favour of this hypothesis and one against it. Here there is neither the space nor the need for their detailed presentation. As I have said already the purpose of these appendices is to stimulate research and not to provide an exhaustive study of each of the many subjects on which Symmetrical Impermanence seems to throw a new light. Those who are qualified to explore the effect of continuous extinction on the earth's geology and geography must be acquainted with the extensive literature on the Wegener Hypothesis and the recent revival of interest in it. So a brief enumeration of the arguments for and against it will suffice.

The Wegener Hypothesis has never been presented as an inference from accepted basic facts and principles. It is an ad hoc hypothesis devised to explain certain observations for which no other explanations have been found. Its strength is its considerable explanatory power. Its weakness is that it itself calls for an explanation and this has not been forthcoming. The first set of observations explained by the Wegener Hypothesis is biological. Certain species of animal, for instance, occur on both sides of the Atlantic that are nearly related and must have had a common ancestry in times that are recent by the geological time scale. Descendants of these common ancestors must at some time have crossed from the one land mass to the other. But they would have had to cross the sea to do so if the masses had always been separated, as they are now.

One might suggest that the masses were joined only at their Northern ends, where they are now nearer to each other than anywhere else. But if so, descendants of the common ancestors would have travelled a very long way; for existing nearly related species are to be found, respectively, in the Southern ends of South America and South Africa. If the present species have descended from emigrants successive generations would, during their wanderings, have been adapted to the variety of climate that occurs between arctic, moderate and equatorial latitudes. But there is no evidence for such an evolutionary history. The hypothesis that is most consistent with the biological observations is that the Southern tips of South America and Africa were joined together at the time when the common ancestors of the present species lived.

The second set of observations is purely geological. The East coast of the Western continents and the West coast of the Eastern ones fit together like pieces in a jigsaw puzzle. The fit between the edges of the continental shelves of the two landmasses is even closer than that between the coastlines that appear on an ordinary map and that show only the limit of the land that is above sea level. There is, moreover, a ridge running from North to South in the Atlantic such as one might expect if there was a continental break at that place.

It has also been shown that the remaining landmasses, such as Australia and Greenland, can, with a little ingenuity and rotation, be fitted together. This has led to the suggestion that the whole of the earth's land surface was continuous at one time. Sundry bits are supposed to have broken off occasionally. But when they did they can never have stayed close to each other for long. Something must always have caused them to drift apart.

The third set of observations is from mineral deposits. Gold is found near the East coast of South America and in the corresponding part of the West coast of Africa. The gold is alluvial and such as one should expect in the lower reaches of a river. It is so on one side of the Atlantic but not on the other. Its presence there is therefore difficult to explain. But it would be quite explicable if the gold in each country had been deposited by the same river when the continents were joined together.

The fourth set of observations is of certain magnetic rocks. Particles of iron ore in these are little magnets, each with a North and a South pole. In a given sample of rock all the magnets point the same way.

The best explanation of this uniform direction that has been offered is that the particles aligned themselves to the direction of the earth's magnetic field at the time when the magnetism occurred. But the alignment today is often far from the direction of the poles. One explanation of this would be that the direction of the earth's magnetic axis has changed greatly in past ages. But there is no other evidence for this, besides which the geographical distribution of the rocks in question and their ages are hardly consistent with this explanation.

The explanation that does seem to fit many, though not all, the facts is that the particles oriented themselves to the magnetic poles when they were in one latitude and longitude and have been carried since on the landmass that they occupy into other latitudes and longitudes.

The objection to the theory of continental drift is that no reason can be found why the landmasses should drift apart. Even supposing something did cause a crack to occur right across the earth's crust, from one end to the other, why should the two pieces not stay near each other? It is true that the earth's crust floats on a more or less plastic mass. A force applied horizontally to a portion of the crust would overcome the stickiness of the plastic material and cause movement. One could argue that the force need not be very great if the movement is very slow. But for even slow movement there must be a force of a significant magnitude and friction has to be overcome; potential energy has to be converted into frictional energy, into heat. So long as no force at all of the required magnitude and direction and no suitable source of potential energy are accounted for, the Wegener Hypothesis has to be abandoned.

It is here that the hypothesis of the continuous extinction of matter promises to help. It can explain both the breaking off of landmasses and their subsequent movement.

Let us consider an extensive continent floating on a plastic mass. If continuous extinction causes a reduction in the earth's radius such as is given by the inferred half-life of matter there will be a tendency for the more rigid continent to retain the previous radius while the plastic substratum acquires the new one. When this happens the continent will form a cantilever. If it is too rigid to bend it will break. At the place where the break occurs one should expect the crust to be firmly embedded in the plastic mass. Some of the crust would be left there, as the stump and roots of a tree are left in the ground when a gale blows the tree over. The ridge that stretches along the Atlantic may well be the 'root' of attachment of the earlier continent, of which two pieces now form, respectively, the Western and Eastern worlds.

For the reason why the pieces should drift apart one has to turn to one of the theories that have been brought forward in the hope of explaining the formation of mountain ranges. It is as follows:

Radio-active materials within the earth are a source of its heat. It is the disintegration of the atoms in these materials that has enabled the earth's temperature to remain approximately constant during thousands of millions of years. The heat is radiated away at about the same rate as it is produced. But the rate of radiation cannot be the same for all parts of the earth's surface. The continents form a blanket and keep the heat in while the oceans allow it to escape readily. From this one must assume that the earth is hotter deep below the continents than it is below the oceans.

The higher temperature must be accompanied by thermal expansion. This will produce an upwards thrust under the continents, which will be opposed by their weight. But when a crack has occurred there is nothing to restrain the plastic mass below the site of the crack from expanding and raising the edges of the crust at each side of the crack. These edges will then be further from the centre of the earth than the outer edges. Thus two inclined planes are formed and the separating continents slide down them in opposite directions.

The force that causes continental drift is, according to Symmetrical Impermanence, gravity. The original source of the energy that overcomes friction is radio-activity within the earth. This is converted into heat and thereafter, to a small extent, into the potential energy of position that is measured by the raising of the ground level where a crack occurs.

Thus a person who had no other reason to postulate continental drift would, nevertheless, postulate it if he accepted Symmetrical Impermanence. This, in other words, transforms the Wegener Hypothesis from the category of ad hoc hypothesis into that of inference.

E.5: Biological Implications of Shrinking
Biological considerations must claim our attention next. Here there is a more immediate prospect that a study of the consequences of a shrinking earth will be rewarding. For a large change in the mass of the earth could hardly fail to have its pronounced effect on the things that live on it. If the half-life of matter is of the order of magnitude that I have estimated, conditions must have been significantly different in those remote days when those plants and animals were alive whose fossils have been discovered. One should expect the difference to be reflected in their structure and their habitats.

According to the now accepted view that the half-life of matter is infinite, there is no reason to suppose that physical conditions on earth have changed very significantly during the past two thousand million years. I have already pointed out that the temperature must have been about the same in the remote past as now. There must have been sea and land and the same atmosphere. Science fiction may speak of swamps and twilight and a primordial slime, but geology does not seem to justify such flights of imagination. Nothing is known against the conclusion that the same plants and animals that live today, including man, would have found the earth a congenial place in those distant times. Why then, one is led to ask, did they not occur for so many hundreds of millions of years? Was the earth really, it has to be asked, hospitably ready so long ago for the forms that exist today and did they really wait all that while before they accepted the invitation? If the earth had the same climate and other physical conditions so long ago, why the grand evolutionary cavalcade, in which species evolve, have their brief era of dominance, become extinct and are succeeded by others? Why did those species that occur now not evolve earlier? Why did the early species not survive to this day?

One possible answer is that evolution is a slow process and that during those past hundreds of millions of years plant and animals have been adapting themselves ever better to conditions on this planet. But the answer is hardly tenable. We know that evolution is not as slow as all that. Pronounced evolutionary changes come about during periods of time that are quite short by the geologist's time scale. The complex history of mammalian evolution was completed in only a couple of hundred million years. At this rate one should expect that evolution from amoeba to mollusc would have been completed at least eighteen hundred million years ago. But the first known molluscs seem to date from Cambrian times, only five hundred million years ago. Fifteen hundred million years for evolution of the first thing that could leave fossil remains is too long. It does not equate with modern genetic knowledge.

We also know that the species that are now extinct must have been well adapted to their surroundings, for they did survive for many generations. On a rational interpretation of evolution there can have been but little scope for improvement. Yet no species that lived in Cambrian times has descendants today that resemble their ancestors sufficiently to be classed as the same species.

A possible answer to the question why every early species has become extinct is that there was too much competition with more successful rivals. According to this view every kind of plant and animal that ever lived on earth would have living descendants like itself today were it not that it was either preyed upon or starved to the point of extinction by more competent later arrivals. To say this is to say that adaptation to the physical circumstances of the inanimate environment was perfected a long while ago and that since then adaptation has always only been to the competitive circumstances introduced by living things.

This answer might explain the occasional extermination of a few species but not, it seems to me, that of every species that existed a few hundred million years ago. It is true enough that Nature, as the poet said, is red in tooth and claw; the struggle for survival is indeed fierce. But the opposed forces are closely balanced. The conflicts that we observe today rarely result in the complete elimination of one of the warring species. What more often happens is that the one gains no more than a relative ascendancy over the other. The world is, moreover, not so densely populated that the various species are in continuous conflict. Many survive by the simple process of avoiding those stronger than themselves. Animals that are preyed upon remorselessly go on having descendants for many millions of years. Why should the day have come for every one of them when there could be no more descendants of the same Form?

The answer that physical conditions have been steadily changing seems to me to provide a far more satisfactory explanation of the evolutionary trend than the answer that the sole cause of change has been competition. But no other reason for a change in physical conditions seems to have been found except the change in the mass of the earth that I am claiming. This change means a corresponding change in the value of g and must have very pronounced and varied effects. In this research programme I do not pretend to give an exhaustive list of them, but only to mention some samples .in the hope that others may further explore the field. I feel sure that it will prove a rewarding one.

If the half-life of matter is 4x108 years, the weight of everything was more than three times its present weight two thousand million years ago. rhis must have caused the earth to be a very different place to the congenial earth that we know.

The air pressed on the earth with a force of over 3 kg per square cm. The atmosphere was squeezed into a much thinner, if denser, blanket than our present atmosphere. There will have been but little evaporation of water into the dense air. Clouds must have been rare. Far from the twilight postulated by the romancers, the land and the sea must have been under a fierce glare. When clouds did form and shed their rain, each heavy raindrop must have fallen with a great speed and reached the ground with a truly destructive impact.

At the high density of the air small local differences in temperature must have caused large displacements of air, so that average wind velocities must have been very high. At the same time even a low velocity, such as would be a gentle breeze today, must have had the force of a hurricane when the air was so much denser. The gales that swept the land must have been devastating and will have carried sand and pebbles, even great boulders, along with them.

When conditions on land were so violent, the sea must have been the only safe place for living things. If any vegetation at all could maintain .itself on land, it must have been of the kind that clings to rocks like some of the present lichens. Anything that protruded a frond above the rock face would have been torn off by the raging tempests.

Before there were plants to put oxygen into the air and to provide food there could be no animals and as there could be no land plants until g had fallen to a level at which the earth had a tolerable climate, one should not expect land animals to have appeared until comparatively late in geological times. Even sea animals must have kept themselves well out from land. For only the tiniest of creatures could have survived the violence with which waves must have broken on the seashore in those times.

When g had several times its present value, a branched tree was an impossibility. For no kind of wood would have been strong enough to support those cantilevers that we call branches. Stalks could not have borne the weight of fruit. Even leaves would have been a burden. If a plant could find a place to grow sheltered from the gale, it would yet have to have such a structure that its leaves would not drop off by their own weight.

Similar considerations apply to the early animals. No bull could have been strong enough to support its cantilever-like head. Bones and muscles could not have supported the tissues of any large animal. So one need not be surprised that, right up to the carboniferous period, there were no large animals. It was only then, when, by my estimate, g had not much more than twice its present value, that the amphibians began to evolve.

When g is great it is obviously easier to crawl than to walk. Hence the great saurians, which lived in the days when our coal deposits were being formed, were eminently adapted to terrestrial conditions of the time. It may also well be that they did really live in swamps. For they could then keep their heavy bodies submerged so that some of the weight would be borne by the water. As g decreased, their descendants will have raised more and more of their bodies above the surface. But nimble four-footed creatures had to wait until the weight of the mammalian body had dropped to a value at which slender stilt-like legs can support it; and then the first such creatures could only be small ones.

So far I have only discussed those conditions that, from our present point of view, seem to have made the earth increasingly hospitable. I have spoken of the conditions that made later arrivals possible. But did the decreasing value of g not perhaps make the earth less hospitable to its previous inhabitants? Was there no change of the kind that would make the earth impossible for them?

There must have been such changes, too, and a rewarding field of research would be to discover what they were. I shall be content to mention one obvious one. It is the decreasing density of the air. The heart, the blood and the lungs of the great saurians must have been adapted to the air pressure of their day. As this pressure decreased, they must have found themselves starved of oxygen. It may be that the descendants of us, who are alive today, will become extinct for the same reason. According to the hypothesis of continuous extinction, the time must come eventually when the earth will have so little mass that, like the moon now, it will no longer retain its atmosphere. But long before then the air will have become so rarified that creatures adapted to a pressure of one kg per square cm will not be able to get enough air to support life. Neither a violent cataclysm, nor cold, nor heat, but lack of oxygen seems most likely to bring the end about.

If gases and solids have been heavier in the past than they are now, so, of course, have liquids. When g was much greater than it is now, sap could not have risen in a tree. Nor could any animal have had a heart powerful enough to pump the heavy blood to a level much above that of the heart. The shape of a lizard was then better adapted to environment than the shape of a giraffe. While the heavier air could support the heavy body of a flying animal, monkeys could not readily have swung from branch to branch of trees.

In particular, one may surmise that man's erect posture and the enormous development of his brain had to wait until g had fallen to an appropriate value. A creature that held its head well above the ground and whose brain needed so copious a supply of blood could not have survived in a world where blood weighed much more than it does now.

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