changes such as are now in progress, chiefly-one may say, altogether-under solar influence. On the other hand, regarding the sun's emission of heat as resulting, in the main, from the contraction of his mass, we find that, assuming his density uniform, or nearly so, the contraction of his mass to its present dimensions, even from a former infinite extension, would have resulted only in generating as much heat as would last, at the present rate of emission, about twenty millions of years. We do not gain by supposing the rate of emission less in former ages of the earth, for then, the rate of solar work on the earth being less, the length of time necessary to complete the work which has actually been done would have been proportionately greater.

The difficulty is very serious. Dr. Croll, who was one of the first to call attention to it, suggested the explanation, which I take to be inconceivable, that our sun was generated by the collision of several orbs which had been rushing through space with enormous velocity, and that his supply of heat represents the energy of those rushing suns, as well as that resulting from compression. My own solution of the difficulty is one which is confirmed by other researches, including an important investigation by Mr. G. Darwin, that the sun is not of nearly uniform density throughout his apparent globe, but that he is enormously compressed towards the centre, and that, in point of fact, the surface we see lies very far above the real surface of the sun.

Dr. Ball believes that in the former proximity of the moon we may find a complete answer to the enigma. In the primitive oceans, he says, the moon raised tides as she does now, but when she was nearer the tides were much higher than at present. For instance, when the moon's distance was but forty thousand miles, or roughly, a sixth of her present distance, her tide-raising power was not six times, but two hundred and sixteen (six times six times six) times greater than at present. So far Dr. Ball's reasoning is sound; but I cannot follow him in saying that, therefore,

the tides would have been two hundred and sixteen times as high as at present. (There is no such simple relation as this between tide-producing energy and the height of the tidal wave.) Still, we may admit that the tides were very much higher then than now.

'These mighty tides,' says Dr. Ball, are the gift which astronomers have now made to the working machinery of the geologist. They constitute an engine of terrific power to aid in the great work of geology. What would the puny efforts of water in other ways accomplish when compared with the majestic tides and the great currents they produce? In the great primæval tides will probably be found the explanation of what has long been a reproach to geology. The early paleozoic rocks form a stupendous mass of ocean-made beds, which, according to Professor Williamson, are twenty miles thick up to the top of the Silurian beds. It has long been a difficulty to conceive how such a gigantic quantity of material could have been ground up and deposited at the bottom of the sea. The geologists said, "The rivers and other agents of the present day will do it if you give them time enough." But unfortunately, the mathematicians and the natural philosophers would not give them time enough. The mathematicians had other reasons for believing that the earth could not have been so old as the geologists demanded. Now, however, the mathematicians have discovered the new and stupendous tidal grinding engine. With this powerful aid the geologists can get through their work in a reasonable period of time, and the geologists and the mathematicians may be reconciled.'

I am disposed to doubt seriously whether mathematicians and astronomers have done more than to somewhat alleviate the pressure of the difficulty we are considering. That they have subtracted somewhat from the work which had formerly been assigned to the sun must be admitted. We need not inquire what was the former height of the tides, or discuss the action of the tidal wave in detail. If we consider only that the tidal wave, according to the very theory we are considering, has, by its reaction against the earth, reduced the earth's rotation-spin from a rate of one rotation in perhaps not more than three hours, certainly not more than six, to one rotation only in twentyfour hours, we see that the work done on the earth's crust

must have been enormous. It represents the frictionproducts, so to speak, of all that work. The wonder might rather be that the ocean-made beds are not much thicker than they are, than that they are so thick. But here is our difficulty returning to us in another form. Is it clear that the beds considered by Dr. Ball were not made subsequently to the time when the moon was at the comparatively small distance he mentions? Can we for a moment imagine that the tremendous work of checking the earth's rotation-spin to less than a quarter of what it was, has only left such traces as these? Must not that work have been done while still the greater part of the earth's mass was fluid, and the water tidal wave have begun its work long after? Geologists have other reasons than the thick ocean-made strata for their belief in the vast periods of time which form the great difficulty of the problem. There is the evidence derived from the study of organic matter, the evidence derived from the remains of once-living creatures—animal and vegetable. The moon might have raised a tidal wave as high as Chimborazo without hastening the progress of what may be called the development of the earth-nay, she would very seriously have checked this progress. It may be doubted, even, whether life, belonging to any save the lower forms, could have existed during the time when such tidal waves as Dr. Ball pictures careered round the swiftly rotating globe.

It remains to be noticed that, though the day will continually increase as the moon recedes, and, vice versâ, the length of the month, measured in days, attained long since its maximum. It was then-some millions of years ago— about twenty-nine days long, and is now but twenty-seven and one-third days, as days are now. As the moon recedes, the lunar month-which is also the moon's day-will contain fewer and fewer of our terrestrial days. For our days grow longer, now, at a greater rate than the lunar month increases. Our day will continue to grow longer and longer as the moon recedes. In one hundred and fifty millions of

years, or thereabouts, our day will be about one thousand four hundred of our present hours long; this period, also, will then be that in which the moon circles around the earth-about fifty-eight and one-third of our present days. Dr. Ball goes on to consider how the sun would affect this state of things. There would be a tide raised by the sun on the earth after the moon had ceased to raise any tide (the earth's rotation exactly synchronising with the moon's revolution); and, as a result of this, Dr. Ball says, that the earth would begin to rotate in a longer time than the moon circles round her. It appears to me that the moon's action would check any tendency of this sort, just as the earth's action on the moon has, as we know, prevented the moon from rotating in a longer period than that of her revolution round the earth. The state of compromise with a moon circling once in one thousand four hundred hours round the earth rotating in the same time, the moon also so rotating, would be, I believe, a state of stable equilibrium. It is not a very pleasant future to look forward to. Fortunately it is very remote.

THE BIRTH OF THE MOON.

FOURTEEN years have passed since, in the first series of my Light Science for Leisure Hours,' I discussed the change which the tidal wave is slowly but surely producing in the length of the day. Certain researches, which had then recently been made into the moon's motions, had shown astronomers that there must be some force at work retarding the earth in her rotational spin. 'In this difficulty,' I wrote at that time, 'we are not left wholly without resource.' We are not only able, I showed, to say that the discrepancy between the moon's motions and theory is due to a gradual retardation of the earth's rotation-movement, but we are able to place our finger on a very sufficient cause for such a retardation. One of the most firmly established principles of modern science is this, that where work is done, force is in some way or other expended. The doing of work may show itself in a variety of ways-in the generation of heat, in the production of light, in the raising of weights, and so on; but in every case an equivalent force must be expended. If the brakes are applied to a train in motion, intense heat is generated in the substance of the brake. Now, the force employed by the brakesman is not equivalent to the heat generated. Where then is the balance of force expended? We all know that the train's motion is retarded, and this loss of motion represents the requisite expenditure of force. 'Now,' I asked, 'is there any process in nature resembling, in however remote a degree, the application of a brake to check the earth's rotation ?' There is,'