GEOLOGY is not one of the exact sciences with a mathematical basis, like chemisky or electricity. Nevertheless, problems arise now and then which are capable of mathematical investigation. The problem of the earth's antiquity, or rather that of the duration of geological time, which is not the same thing, is one that has attracted much attention, and has led to a long controversy between certain physicists on the one hand and geologists on the other. According to the “nebular hypothesis” now generally accepted, our planet had cooled down from a molten and somewhat viscous state long before geological time began—that is, before a watery ocean settled down by condensation from a heated atmosphere, and left our air as it now is, mostly composed of the incombustible element nitrogen, with a little oxygen, a variable amount of aqueous vapor, and a trace of carbonic acid. How many reons passed away before this state of things was arrived at, no one can say. Such times were pre-geo- logical. But at last an ocean formed, then, perhaps, later on, dry land appeared; the wind blew and the rains fell, as they do now, and the earth reached a phase which geologists believe to have been, generally speaking, not very unlike that of the present day. The question of geological time is the question of the duration of this phase. The great series of stratified rocks (including lava flows and intrusive igneous rocks such as “dikes “) were formed during geological time; and these are the pages on which the earth has recorded her history. Naturally, therefore, the geologist endeavors to seek for some means of calculating the length of time required by Mother Earth to write hei- autobiography.Now the earlier modern geologists, Hutton and his followers, who, by teaching the great principle of uniformity in geological actions, placed the science on a sound and reasonable basis, and gave it an enormous impetus, were. unfortunately, so greatly impressed with this idea that they could see no trace of a beginning or sign of an end. Sir Archibald Geikie, in his recent address as president of the British Association, assembled in Edinburgh, has thus eloquently described their state of mind: “When the curtain was then first raised that had veiled the history of the earth, and men, looking beyond the brief span within which they had supposed that history to have been transacted,* beheld the records of a long vista of ages, stretching far away into a dim, illimitable past, the prospect vividly impressed their imagination. Thus the idea arose and gained universal acceptance, that, just as no boundary could be set to the astronomer in his free range through space, so the whole of bygone eternity lay open to the requirements of the geologist.... This doctrine was naturally espoused with warmth by the extreme uniformitarian school, which required an unlimited duration of time for the accomplishment of such slow and quiet cycles of change as they conceived to be alone recognizable in the records of the earth's past history.” This extreme teaching, in itself a reaction against the old-fashioned previous teaching, produced another reaction, and the pendulum of opinion swung back to some extent; only slightly, but still sufficiently to raise a controversy. The physicists, led by Lord Kelvin (Sir William Thomson), began to look about for some means of checking these enormous demands. Lord Kelvin considered the question of the world's antiquity from the physical standpoint. His arguments, or rather calculations, were based on three important considerations. These we must notice; but as our object in this paper is to consider purely geological measures of time, and his methods can only be judged by the mathematician and astronomer, we must content ourselves with a very brief account of his conclusions. Lord Kelvin arrived at a very different conclusion, and this was derived from three distinct lines of reasoning, ori'ather calculation. First, he considered the internal heat, and rate of cooling of the earth; secondly, the tidal retardation of the earth's rotation; and thirdly, the origin and age of the sun's heat. With regard to the earth's heat: the rate of increase of temperature downward from the surface is known, for a certain distance, by observations in mines. As many of our readers are already aware, it is about 1” F. for every 50 or 60 feet. But this rate is not maintained, and becomes less at great depths. Then with regard to the earth's present temperature— about 36” l!^. at the bottom of the oceans. From such available data he calculated that the earth could not have consolidated, from its former molten state, less than 20 millions of years ago, nor more than 400 millions. In the one case the underground heat would have been greater than it actually is; in the other there would have been no sensible increase in temperature downward. He afterward inclined toward the lower limit rather than the higher one, and said that we ought to be quite satisfied with 100 millions of years for the duration of geological time. Professor Tait would even limit the period since the earth's consolidation to 10 or 15 millions of years. We pass on to the argument from the tides. It is generally admitted that the daily tidal waves must, in some degree, diminish the rate of rotation of the earth on its axis. Its action has been compared to that of a brake on a wheel. At one time, then, the rotation was more rapid; in other words, the earth's day was shorter, and has since been steadily getting longer. If we assume any antiquity for the globe greater than 100 millions of years, he thinks the flattening at the poles would be greater, owing to greater centrifugal force having been formerly exerted by the more rapid rotation. Lastly, Lord! Kelvin has attempted calculations based upon the radiation of heat from the sun, and also upon the amount of heat generated by the falling together of meteoric masses, such as by clashing together may have given rise to the sun. He admits, that his conclusions from this source are, from the nature of the case, less reliable. Still, like the other calculations, they point to a comparatively small number of millions of years, perhaps about twenty. The sun may, however, have continued to receive showers of meteorites, and thus to be replenished with heat; which would disturb these calculations. Moreover, certain chemical changes may be the means of liberating heat in the sun. But we will not dwell on these difficulties here. It is hardly necessary to say that most geologists consider that conclusions such as these are too sweeping. Seeing what vast changes have taken place on the earth— so many thousands of feet of solid rock formed by slow deposition in water, so many new forms of life introduced at certain epochs, while others were extinguished—the geologist cannot bring himself to believe that all the changes (only fully realized by those who study the record of the rocks) could have taken place within 20 or even 100 millions of years. Some, doubtless, would demand much more time, and refuse to accept even the limit of 400 millions. No one distrusts the actual calculations; but many do seriously distrust the data (or want of data) upon which they are founded. Hence a serious difference has arisen between geologists and physicists with regard to the duration of geological time. Mathematics are an excellent mill, and will grind out beautiful results; but what you get out of this mill depends very much on what you put into it, and if you put in material based upon certain assumptions, you must not be surprised at getting a result tainted with similar uncertainty. Let us quit this somewhat unsatisfactory region of speculation and see what further light can be gained from the science of geology. It will be interesting to compare any results that may be obtained with those above mentioned, and to see whether they harmonize. The geologist knows only two time-keeping processes; one is rock formation (deposition), the other rock destruction (denudation). A third is sometimes referred to, namely, changes in the organic world involving the appearance, from time to time, of new species, genera, families and O!'ders of plants and animals—changes which are comprehended under the one word “evolution.” But this kind of change, which has been going on ever since the oldest (Archrean) rocks were first formed, concerns the biologist more than the geologist. The biologist, as Professor Huxley said, has no clock, and must take his time from the geological clock. In other words, when, on passing from one rock formation to another, a great change in the fossils is noticed—as, for instance, in passing from primary rocks to secondary or from secondary to tertiary—the lapse of time required to bring about such evolutionary change can only be gauged by the thicknesses of the strata in which the different fossils are found, and partly, in the two cases above quoted, by the “strati- graphical break” between the two sets of strata; that is, the amount of rock denuded during the interval between the two eras. As the Greeks used to detect “the lazy foot of time” by the slow dropping of water from a clepsydra, so the geologist measures his periods by the work of water, either as a rock destroyer or as a rock former. This is our water clock, and our two measures of time are (1) depth of rock denutled, (2) depth of rock deposited. Now the condition of the-water clock's accuracy as a time keeper was uniformity of action, that the drops should continue falling at same rate; so with the geological clock. These two processes, so closely related to each other, must be supposed to have been working throughout geological time (that is, the time during which the great series of stratified rocks were being formed) with considerable uniformity. This brings us back to the “theory of uniformity,” originated by the illustrious Hutton, and expanded and explained by Playfair and Lyell. Readers of Knowledge will hardly need to be told that “denudation” is chiefly effected by “rain and rivers.” The consequence of “denudation” in one place is rock formation in another; the one is complementary to the other. In other words, the debris of continents is carried by rivers into lakes, seas and estuaries, there to settle down and “sow the dust of continents to be.” Now rivers depend for their supplies on rainfall hence rainfall is one of the main factors in problems about denudation. Geologists believe (from a mass of evidence in the stratified rocks which it would take too long to expound here) that the rainfall has, in past periods, been pretty much what it is now in various parts of the world—not necessarily in Europe. It may, however, have been somewhat greater as far back as the Archrean and Palreo- zoic times, when, perhaps, the earth was ostensibly warmer and the sun sensibly hotter. Hence, geologists consider that they are justified in attempting to form some kind of estimate of former periods of time from the two processes above referred to. Not only is it possible thus to compare one period with another and to say which was the longest, but we venture to think that it is justifiable to attempt to calculate the limits of geological time on the basis of the rate at which strata may be formed. We want to translate feet of rock formed into years. To give a mathematical basis to geology is one of the great problems of the future. What degree of success awaits such efforts we cannot say, but certain attempts have been made to gauge denudation, and to see at what rate it goes on. With regard to deposition of strata, very lit tie, if anything, has been done, and we cannot help thinking that important results might be obtained in this direction; but of that we shall speak presently. Let us briefly consider the first operation, namely, the wearing away of land. The subject of atmospheric denudation has been arithmetically investigated, in order to ascertain at what rate a given continent, or portion of a continent, is at present being worn down by” rain and rivers.” Take the great area drained by the Mississippi, which is what geographers call its “basin.” The area of this basin is reckoned to be 1,147,000 square miles. It is clear that all the mud. sand, etc., brought down by this great river to the Gulf of Mexico must be derived from the rocks and soil in that area; the next step is to find out how much solid matter is brought down every year. Most extensive and accurate determinations upon this subject have been made by the United States government. As the mean of many observations carried on continuously at different parts of the river for months' together, Messrs. Humphreys and Abbot, the engineers employed to investigate the physics and hydraulics of the Mississippi, found that the average proportion suspension, they observed that a large amount of coarse detritus is constantly being pushed along the bottom of the river. They estimated that this moving stratum carries every year into the Gulf of Mexico about 750,000,000 cubic feet of sand, earth, and gravel. Their observations led them to conclude that the annual discharge of water by the Mississippi is 19,500,000,000,000 cubic feet, and consequently that the weight of mud annually carried into the sea by this river must reach the sum of 812,500,000,000 pounds. Then, taking the total annual contributions of solid matter, whether in suspension or moving along the bottom, they found them to equal a prism 268 feet high, with a base of one square mile. But, besides all this, there is in every river a large amount of matter chemically dissolved. This consists chiefly of carbonate of lime, dissolved by rain water in filtering through rocks before it reaches the river. Properly to estimate the loss sustained by the surface of a river basin, we ought to know the amount of mineral matter thus removed, as well as that referred to above; and to make sure of good results, we ought to have the total volume of water discharged, from measurements made at different seasons and extend:!ng over a series of years. Such data have not been fully collected from any river, though some of them have been ascertained with approximate accuracy, as in the cases of the survey of the Mississippi and the Danube. As a rule, more attention bas been paid to the amount of mechanically suspended matter than to the amount in solution. We must, therefore, confine ourselves to the former, but it must be borne in mind that the following estimates are under-statements of the truth, because the amount of dissolved matter is left out. Some of the results obtained are as follows: The Mississippi, with a basin of 1,147,000 square miles, discharges annually 7,459,267,200 cubic feet of solid matter; the Rhone, with a basin of 25,000 square miles, discharges 600,381, 800 cubic feet of solid matter; the Danube, with a basin of 234,000 square miles, discharges 1,253,738,600 cubic feet; the Po, with a basin of 30,000 square miles, discharges 1,510,137,000 cubic feet. Now as all this solid matter comes off the surface of so much land, the area of which is known, it can easily be calculated what thickness of rock must have been removed (on an average) to produce the amount brought down to the sea, as given in cubic feet. On elevated land, where mountain streams run faster, more rock is removed than over low plains or gentle slopes, where rivers run slowly. But we only want. a general average for the whole area. An illustration may serve to make this clear. Given a lump of butter, containing so many cubic inches, and a slice of bread, with area so many square inches; any school boy could find what the thickness of the butter would be when spread evenly over the bread. The results for the great rivers were as follow: The Mississippi removes so'no foot from its area in one year, or one foot in 6,000 years; the Rhone removes or one foot in 1,528 years; the Danube removes or one foot in 6,846 years; the Po removes 'fl., or one foot in 729 years. Now these are very important results, and since the phy,sics of the Mississippi have been more carefully studied than those of perhaps any other river, and as that river drains so extensive a region, embracing so many varieties of climate, rock and soil, we shall probably get the best results by taking the Mississippi rate of denudation as a fair one. Let us see, then, what that rate means. It means that the surface of its basin will be lowered 10 feet (generally) in 60,000 years; supposing the rate to continue, 100 feet in 600,000 years, and 1,000 feet in 6,000,000 years. Apply this to the whole of North America, the mean height of which, according to Humboldt, is 748 feet above sea level, and we find that this continent would be worn away in about 472' millions of years. The same kind of calculation, based upon the rate of denudation by the Upper Ganges, has been applied to the continent of Asia, and a shorter length of time was found to be required to wear it all down to sea level. But the Ganges rate seems to be hardly a fair one, so we will keep to the Mississippi. Such calculations are made on the assumption that no serious changes take place in the way of earth movements, raising or depressing a continent. Upheaval would undoubtedly quicken the rate of denudation, by giving greater velocity to the rivers (on account of increased fall), and in the same way depression would check the rate of denudation. But in spite of this possible element of disturbance, the result above given is an important one. Now the amount of denudation that might thus take place over the North American continent is a mere trifle compared to the vast denudation which must have taken place in order to provide the prodigious amount of solid matter contained in the whole series of stratified rocks. Their total estimated thickness is about 100,000 feet! It is clear, then, that a much greater number of millions of years was required to lay down this great series of sedimentary rocks on ocean beds. especially when we reflect that such material had to be distributed by ocean currents over vast areas, and also that many of these rocks were built up very slowly in the deeper parts of oceans by the slow accumulation of organic remains. This applies, for example, to the carboniferous limestone, the oolites, and the chalk formation. Evidences of great denudation abound both in Great Britain and in Europe, and in all parts of the world. Thousands and thousands of feet of solid rock have been removed, and yet such phenomena were by no means spread over the whole of geological time. We can often prove that even in the interval between two successive periods enormous denudation took place, and the mind is bewildered in endeavoring to combine with any reasonable amount of time required for such intervals the much greater periods required for the accumulation of the subsequent or overlying strata. Any student who is familiar with geological sections can caU to mind numerous examples of great denudation. For instance, what a vast period of time is indicated by the upheaval and subsequent denudation of the pre-Cambrian (or Archrean) rocks before those of the Palreozoic era were deposited on their upturned edges ! No attempt has been made to estimate in years this interval. Or, to take another case, it is found that in many parts of our country a great thickness of the carboniferous rocks, especially the coal measures, was denuded away before the advent of the Secondary or Meso- zoic era. Sir Andrew Ramsey has calculated (from sections drawn to scale) that a covering of rock to the depth of one mile was removed from the surface of the Men- dip Hills, and most of this destruction took place during the above interval. No one has yet attempted to apply a rate of denudation to this case, for the uncertain elements in such a problem are many. The Mississippi rate of one foot in 6,000 years would hardly be applicable, being an average for a large area including mountains, valleys, and plains; whereas the Mendip Hills are a small hilly area. If we could find the rate at which some of our present mountainous regions are being worn down, and obtain an average therefrom, it might bejustifiableto apply such anaverage to the case in point. But mountains are composed of hard and often crystalline rocks, and this fact would tend to counteract the more rapid erosion due to the velocity of mountain streams. We will now endeavor to point out a method that might possibly lead to valuable results if followed, and from Which an averagerate of rock formation might be obtained. Take the ease of the Mississippi. What becomes of all the solid matter brought down by this river ? It mostly find8 its way xato the Atlantic, for the Gulf of Mexico is swept by that powerful current the GulfStream. It would not be spread all over the Atlantic bed, for some may be carried up to the North Sea and Arctic Ocean; and again, there are large areas in the Atlantic where no sedimentary deposits are forming, but only globigerina ooze, pteropod ooze, or the red clay (believed to be volcanic and even cosmic dust). These areas are far from land, and some of them are the deepest recesses of the Atlantic. Suppose that all the debris from the North American continent were being washed into the Atlantic only. N ow this ocean is larger than North America in actual area, but we may subtract the areas devoted to globigerina ooze or red clay. What these areas are could doubtless be estimated by Mr. Murray, of the Challenger expedition. We do not know how much they are; but let us suppose that when this is done an area remains equal to the continent of North America. Then it would follow that all the rock material removed from that surface of land settles down to form new rocks on an area equal to that of the land from which it camp.. Now if, taking the Mississippi rate, one foot is removed from the former area in 6,000 years, it follows that about one foot is added to the latter surface in the same time. It would really be rather more, because the new material would be soft and unhardened by pressure, while the old rocks from which it came were compressed and hardened before they came up to form a land surface. But this difference may be neglected. It will thus be seen that a result of some value is obtained, namely, just what we have been seeking—an average rate of rock formation. The question arises, “Is this rate of rock formation over a large area of sea bed, viz., one foot in 6,000 years, too rapid ?” We are inclined to think that it is. It might apply to strata formed in shallow waters, but it seems too high a rate for those formed in deeper waters, and certainly is inapplicable to slow-growing deposits like globigerina ooze. However, let us see what we can make of it. The whole series of stratified rocks is generally estimated at 100,000 feet—taking all the formations and adding their thicknesses together. Here would be a measure of geological time, if only we knew the average rate at whi(jhthey were built up. Suppose we app!y the rate just obtained and see what it leads to. If one foot is formed in 6,000 years, 100 feet will be formed in 600,000 years, and 100,000 feet in 600,000,000 years. Six hundred millions of years ! This is more than Lord Kelvin's extreme limit for geological time, or the time since the earth consolidated from a molten state. And yet we have taken a rate of rock formation that appears not to err on the side of rapidity; and. moreover, this calculation makes no allowance for those great “gaps “or “breaks” in the 100,000 feet of the geological record with which the student will be familiar. Again, it makes no allowance for the necessarily slow rate at which organic deposits were formed, and formations of this kind occupy no small fraction of the whole series of rocks. For example, the liivat mountain limestone in one district is 4,000 feet; hi% l the chalk in the Isle of Wight is 1,000 feet thick; then there are the oolites between, to say nothing of Silurian limestones below. It is, therefore, not surprising that geologists are dissatisfied with the limits laid down by Lord Kelvin and others. They demand much more time than he will allow, and we think that the calculation above given justifies such a demand. His later estimate of only 100 millions of years certainly seems too small. Prof. Huxley, some years ago, endeavored as it were to make peace between the two parties in this controversy by taking the latter limit of 100 millions and applying it to the stratified rocks. If 100,000 feet of rock were formed in 100 millions of years, then the rate of rock formation would be one foot in 996 years—say, roughly, 1,000 years. Now the result we obtained above was one foot in 6,000 years, so that our rate is six times slower than that which follows from Lord Kelvin's computation, and we venture to think that it would be more acceptable to geologists. One cannot help hoping that before long some attempts will be made to observe the rate of deposition in different seas. Would not observations of the amount of sediment suspended in sea water, taking samples fromvarious depths, be useful ? But it would be better still if some one would let down vessels (like rain gauges) on to the bed of the sea in various spots, leave them there for twenty years, and then take them up and measure the amount of solid matter contained in them. They could be attached to buoys by thin wire ropes; thus the sites would be indicated and they could be pulled up. Or again, perhaps in the future an international committee of scientific men may be formed to observe and measure the amounts of debris brought down to the Mediterranean by all the princi- Eal rivers flowing into it! It would take a long time, ut the work could be divided up, and when done we should have a fair idea of the amount of sediment settling down in that area of sea, and so could calculate the rate of rock formation that obtains there.— Knowledge.