If those great Secular variations of climate which we have been considering be indirectly the result of changes in the eccentricity of the earth’s orbit, then we have a means of determining, at least so far as regards recent epochs, when these variations took place. If the glacial epoch be due to the causes assigned, we have a means of ascertaining, with tolerable accuracy, not merely the date of its commencement, but the length of its duration. M. Leverrier has not only determined the superior limit of the eccentricity of the earth’s orbit, but has also given formulæ by means of which the extent of the eccentricity for any period, past or future, may be computed.

A well-known astronomer and mathematician, who has specially investigated the subject, is of opinion that these formulæ give results which may be depended upon as approximately correct for four millions of years past and future. An eminent physicist has, however, expressed to me his doubts as to whether the results can be depended on for a period so enormous. M. Leverrier in his Memoir has given a table of the eccentricity for 100,000 years before and after 1800 a.d., computed for intervals of 10,000 years. This table, no doubt, embraces a period sufficiently great for ordinary astronomical purposes, but it is by far too limited to afford information in regard to geological epochs.

With the view of ascertaining the probable date of the glacial epoch, as well as the character of the climate for a long course of ages, Table I. was computed from M. Leverrier’s formulæ.[194] It shows the eccentricity of the earth’s orbit and longitude of the perihelion for 3,000,000 of years back, and 1,000,000 of years to come, at periods 50,000 years apart.

On looking over the table it will be seen that there are three principal periods when the eccentricity rose to a very high value, with a few subordinate maxima between. It will be perceived also that during each of those periods the eccentricity does not remain at the same uniform value, but rises and falls, in one case twice, and in the other two cases three times. About 2,650,000 years back we have the eccentricity almost at its inferior limit. It then begins to increase, and fifty thousand years afterwards, namely at 2,600,000 years ago, it reaches ·0660; fifty thousand years after this period it has diminished to ·0167, which is about its present value. It then begins to increase, and in another fifty thousand years, namely at 2,500,000 years ago, it approaches to almost the superior limit, its value being then ·0721. It then begins to diminish, and at 2,450,000 years ago it has diminished to ·0252. These two maxima, separated by a minimum and extending over a period of 200,000 years, constitute the first great period of high eccentricity. We then pass onwards for upwards of a million and a half years, and we come to the second great period. It consists of three maxima separated by two minima. The first maximum occurred at 950,000 years ago, the second or middle one at 850,000 years ago, and the third and last at 750,000 years ago—the whole extending over a period of nearly 300,000 years. Passing onwards for another million and half years, or to about 800,000 years in the future, we come to the third great period. It also consists of three maxima one hundred thousand years apart. Those occur at the periods 800,000, 900,000, and 1,000,000 years to come, respectively, separated also by two minima. Those three great periods, two of them in the past and one of them in the future, included in the Table, are therefore separated from each other by an interval of upwards of 1,700,000 years.

In this Table there are seven periods when the earth’s orbit becomes nearly circular, four in the past and three in the future.

The Table shows also four or five subordinate periods of high eccentricity, the principal one occurring 200,000 years ago.

The variations of eccentricity during the four millions of years, are represented to the eye diagrammatically in Plate IV.

In order to determine with more accuracy the condition of the earth’s orbit during the three periods of great eccentricity included in Table I., I computed the values for periods of ten thousand years apart, and the results are embodied in Tables II., III., and IV.

There are still eminent astronomers and physicists who are of opinion that the climate of the globe never could have been seriously affected by changes in the eccentricity of its orbit. This opinion results, no doubt, from viewing the question as a purely astronomical one. Viewed from an astronomical standpoint, as has been already remarked, there is actually nothing from which any one could reasonably conclude with certainty whether a change of eccentricity would seriously affect climate or not. By means of astronomy we ascertain the extent of the eccentricity at any given period, how much the winter may exceed the summer in length (or the reverse), how much the sun’s heat is increased or decreased by a decrease or an increase of distance, and so forth; but we obtain no information whatever regarding how these will actually affect climate. This, as we have already seen, must be determined wholly from physical considerations, and it is an exceedingly complicated problem. An astronomer, unless he has given special attention to the physics of the question, is just as apt to come to a wrong conclusion as any one else. The question involves certain astronomical elements; but when these are determined everything then connected with the matter is purely physical. Nearly all the astronomical elements of the question are comprehended in the accompanying Tables.

In Tables II., III., and IV., column I. represents the dates of the periods, column II. the eccentricity, column III. the longitude of the perihelion. In Table IV. the eccentricity and the longitude of the perihelion of the six periods marked with an S are copied from a letter of Mr. Stone to Sir Charles Lyell, published in the Supplement of the Phil. Mag. for June, 1865; the eight periods marked L are copied from M. Leverrier’s Table, to which reference has been made. For the correctness of everything else, both in this Table and in the other three, I alone am responsible.

Column IV. gives the number of degrees passed over by the perihelion during each 10,000 years. From this column it will be seen how irregular is the motion of the perihelion. At four different periods it had a retrograde motion for 20,000 years. Column V. shows the number of days by which the winter exceeds the summer when the winter occurs in aphelion. Column VI. shows the intensity of the sun’s heat during midwinter, when the winter occurs in aphelion, the present midwinter intensity being taken at 1,000. These six columns comprehend all the astronomical part of the Tables. Regarding the correctness of the principles upon which these columns are constructed, there is no diversity of opinion. But these columns afford no direct information as to the character of the climate, or how much the temperature is increased or diminished. To find this we pass on to columns VII. and VIII., calculated on physical principles. Now, unless the physical principles upon which these three columns are calculated be wholly erroneous, change of eccentricity must undoubtedly very seriously affect climate. Column VII. shows how many degrees Fahrenheit the temperature is lowered by a decrease in the intensity of the sun’s heat corresponding to column VI. For example, 850,000 years ago, if the winters occurred then in aphelion, the direct heat of the sun during midwinter would be only 837/1000 of what it is at present at the same season of the year, and column VII. shows that this decrease in the intensity of the sun’s heat would lower the temperature 45°·3 F.

The principle upon which this result is arrived at is this:—The temperature of space, as determined by Sir John Herschel, is −239° F. M. Pouillet, by a different method, arrived at almost the same result. If we take the midwinter temperature of Great Britain at 39°, then 239° + 39° = 278° will represent the number of degrees of rise due to the sun’s heat at midwinter; in other words, it takes a quantity of sun-heat which we have represented by 1000 to maintain the temperature of the earth’s surface in Great Britain 278° above the temperature of space. Were the sun extinguished, the temperature of our island would sink 278° below its present midwinter temperature, or to the temperature of space. But 850,000 years ago, as will be seen from Table III., if the winters occurred in aphelion, the heat of the sun at midwinter would only equal 837 instead of 1000 as at present. Consequently, if it takes 1,000 parts of heat to maintain the temperature 278° above the temperature of space, 837 parts of heat will only be able to maintain the temperature 232°·7 above the temperature of space; for 232°·7 is to 278 as 837 is to 1,000. Therefore, if the temperature was then only 232°·7 above that of space, it would be 45°·3 below what it is at present. This is what the temperature would be on the supposition, of course, that it depended wholly on the sun’s intensity and was not modified by other causes. This method has already been discussed at some length in Chapter II. But whether these values be too high or too low, one thing is certain, that a very slight increase or a very slight decrease in the quantity of heat received from the sun must affect temperature to a considerable extent. The direct heat of the moon, for example, cannot be detected by the finest instruments which we possess; yet from 238,000 observations made at Prague during 1840−66, it would seem that the temperature is sensibly affected by the mere change in the lunar perigee and inclination of the moon’s orbit.[195]

Column VIII. gives the midwinter temperature. It is found by subtracting the numbers in column VII. from 39°, the present midwinter temperature.

I have not given a Table showing the temperature of the summers at the corresponding periods. This could not well be done; for there is no relation at the periods in question between the intensity of the sun’s heat and the temperature of the summers. One is apt to suppose, without due consideration, that the summers ought to be then as much warmer than they are at present, as the winters were then colder than now. Sir Charles Lyell, in his “Principles,” has given a column of summer temperatures calculated from my table upon this principle. Astronomically the principle is correct, but physically, as was shown in Chapter IV., it is totally erroneous, and calculated to convey a wrong impression regarding the whole subject of geological climate. The summers at those periods, instead of being much warmer than they are at present, would in reality be much colder, notwithstanding the great increase in the intensity of the sun’s heat resulting from the diminished distance of the sun.

What, then, is the date of the glacial epoch? It is perfectly obvious that if the glacial epoch resulted from a high state of eccentricity, it must be referred either to the period included in Table III. or to the one in Table IV. In Table III. we have a period extending from about 980,000 to about 720,000 years ago, and in Table IV. we have a period beginning about 240,000 years ago, and extending down to about 80,000 years ago. As the former period was of greater duration than the latter, and the eccentricity also attained to a higher value, I at first felt disposed to refer the glacial epoch proper (the time of the till and boulder clay) to the former period; and the latter period, I was inclined to believe, must have corresponded to the time of local glaciers towards the close of the glacial epoch, the evidence for which (moraines) is to be found in almost every one of our Highland glens. On this point I consulted several eminent geologists, and they all agreed in referring the glacial epoch to the former period; the reason assigned being that they considered the latter period to be much too recent and of too short duration to represent that epoch.

Pondering over the subject during the early part of 1866, reasons soon suggested themselves which convinced me that the glacial epoch must be referred to the latter and not to the former period. Those reasons I shall now proceed to state at some length, since they have a direct bearing, as will be seen, on the whole question of geological time.

It is the modern and philosophic doctrine of uniformity that has chiefly led geologists to over-estimate the length of geological periods. This philosophic school teaches, and that truly, that the great changes undergone by the earth’s crust must have been produced, not by convulsions and cataclysms of nature, but by those ordinary agencies that we see at work every day around us, such as rain, snow, frost, ice, and chemical action, &c. It teaches that the valleys were not produced by violent dislocations, nor the hills by sudden upheavals, but that they were actually carved out of the solid rock by the silent and gentle agency of chemical action, frost, rain, ice, and running water. It teaches, in short, that the rocky face of our globe has been carved into hill and dale, and ultimately worn down to the sea-level, by means of these apparently trifling agents, not only once or twice, but probably dozens of times over during past ages. Now, when we reflect that with such extreme slowness do these agents perform their work, that we might watch their operations from year to year, and from century to century, if we could, without being able to perceive that they make any very sensible advance, we are necessitated to conclude that geological periods must be enormous. And the conclusion at which we thus arrive is undoubtedly correct. It is, in fact, impossible to form an adequate conception of the length of geological time. It is something too vast to be fully grasped by our minds. But here we come to the point where the fundamental mistake arises; Geologists do not err in forming too great a conception of the extent of geological periods, but in the mode in which they represent the length of these periods in numbers. When we speak of units, tens, hundreds, thousands, we can form some notion of what these quantities represent; but when we come to millions, tens of millions, hundreds of millions, thousands of millions, the mind is then totally unable to follow, and we can only use these numbers as representations of quantities that turn up in calculation. We know, from the way in which they do turn up in our process of calculation, whether they are correct representations of things in actual nature or not; but we could not, from a mere comparison of these quantities with the thing represented by them, say whether they were actually too small or too great.

At present, geological estimates of time are little else than mere conjectures. Geological science has hitherto afforded no trustworthy means of estimating the positive length of geological epochs. Geological phenomena tell us most emphatically that these periods must be long; but how long they have hitherto failed to inform us. Geological phenomena represent time to the mind under a most striking and imposing form. They present to the eye, as it were, a sensuous representation of time; the mind thus becomes deeply impressed with a sense of immense duration; and when one under these feelings is called upon to put down in figures what he believes will represent that duration, he is very apt to be deceived. If, for example, a million of years as represented by geological phenomena and a million of years as represented by figures were placed before our eyes, we should certainly feel startled. We should probably feel that a unit with six ciphers after it was really something far more formidable than we had hitherto supposed it to be. Could we stand upon the edge of a gorge a mile and a half in depth that had been cut out of the solid rock by a tiny stream, scarcely visible at the bottom of this fearful abyss, and were we informed that this little streamlet was able to wear off annually only 1/10 of an inch from its rocky bed, what would our conceptions be of the prodigious length of time that this stream must have taken to excavate the gorge? We should certainly feel startled when, on making the necessary calculations, we found that the stream had performed this enormous amount of work in something less than a million of years.

If, for example, we could possibly form some adequate conception of a period so prodigious as one hundred millions of years, we should not then feel so dissatisfied with Sir W. Thomson’s estimate that the age of the earth’s crust is not greater than that.

Here is one way of conveying to the mind some idea of what a million of years really is. Take a narrow strip of paper an inch broad, or more, and 83 feet 4 inches in length, and stretch it along the wall of a large hall, or round the walls of an apartment somewhat over 20 feet square. Recall to memory the days of your boyhood, so as to get some adequate conception of what a period of a hundred years is. Then mark off from one of the ends of the strip 1/10 of an inch. The 1/10 of the inch will then represent one hundred years, and the entire length of the strip a million of years. It is well worth making the experiment, just in order to feel the striking impression that it produces on the mind.

The latter period, which we have concluded to be that of the glacial epoch, extended, as we have seen, over a period of 160,000 years. But as the glaciation was only on one hemisphere at a time, 80,000 years or so would represent the united length of the cold periods. In order to satisfy ourselves that this period is sufficiently long to account for all the amount of denudation effected during the glacial epoch, let us make some rough estimate of the probable rate at which the surface of the country would be ground down by the ice. Suppose the ice to grind off only one-tenth of an inch annually this would give upwards of 650 feet as the quantity of rock removed during the time. But it is probable that it did not amount to one-fourth part of that quantity. Whether one-tenth of an inch per annum be an over-estimate or an under-estimate of the rate of denudation by the ice, it is perfectly evident that the period in question is sufficiently long, so far as denudation is concerned, to account for the phenomena of the glacial epoch.

But admitting that the period under consideration is sufficiently long to account for all the denudation which took place during the glacial epoch, we have yet to satisfy ourselves that it is also sufficiently remote to account for all the denudation which has taken place since the glacial epoch. Are the facts of geology consistent with the idea that the close of the glacial epoch does not date back beyond 80,000 years?

This question could be answered if we knew the present rate of subaërial denudation, for the present rate evidently does not differ greatly from that which has obtained since the close of the glacial epoch.