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than all the known period of human history, aboriginal men, who possessed no arts, and left no monuments, and lived in the dark with no message of light from heaven, must have continued to wander, homeless and hopeless, in deserts and mountains, and in dens and caves of the earth.

The moral and religious difficulties of such a creed are plainly immense. I wish now to examine it simply on the side of physical science. Mr. Croll's theory is certainly elaborated with great pains and care, and includes a wide collection of materials, and a large amount of patient thought and ingenuity. It has received the highest praise from a writer in the Quarterly Review, as beautiful, simple, and complete. I need, therefore, to offer strong reasons for my own conviction, expressed before in the Annual Address, that it is based on a complete fallacy, and is wholly wanting in solidity and truth.

27. A first objection, made by Professor C. Martens, and more recently by Mr. Callard, is of a very simple and striking kind. The planet Mars is forty millions of miles further from the sun than our earth. Its excentricity is 0933 instead of 01678, or 5 times greater, and its absolute amount 26 millions of miles, or nine times greater than the present excentricity of the earth; three times greater than that at Mr. Croll's second, and twice as great as at his first, supposed glacial period. Yet the snows of this planet, while they increase in winter, and decrease in summer, are never seen to extend more than six or seven degrees from either pole. The spectroscope and telescope conspire to prove that Mars is not now suffering under an ice age. How, then, could the increase of the earth's excentricity from 3 to 10 millions of miles produce the glaciation of more than half the hemisphere, when one of 26 millions has no such effect in a planet half as far again from the sun

Mr. Croll observes that little is known of the climatic condition of Mars, and that its atmosphere may perhaps be wholly different from our own, and that other physical conditions, besides greater excentricity, may be needed to secure a glacial epoch. This may doubtless be true; but since we have only to guess at such causes of difference, the negative evidence, though not decisive, is strongly adverse to the notion that glaciation, in the case of our earth, is due mainly to a greater excentricity than now exists. For in Mars the aphelion distance is about 148 millions, while in Mr. Croll's ice era, our own would be 97 millions, and still the imaginary result from increased excentricity does not seem to follow.

28. A second objection has some weight. The total heat received by the earth in a year from the sun is inversely as

the minor axis, when the periodic time and the major axis are constant and do not change. This was stated by Sir J. Herschel in a paper read to the Geological Society in 1830. It admits of easy demonstration, and Mr. Croll quotes the paper in his Appendix, and admits the scientific truth. He thinks, however, the difference is so slight that it may be safely neglected, and treated as of no account. But this is not so plain. It would be very strange, if a period in which the earth receives the most heat from the sun were that in which, on the whole, it suffers the most from extreme cold. With an excentricity of 0575, or 10 millions excess of aphelion over perihelion distance, the excess above the present would be three-twentieths per cent., or 1 part in a thousand. Let us take 5,000 years on each side of Mr. Croll's date, or the interval from 205 to 215 thousand years ago. If a northern winter aphelion lay midway between, this would include half one whole circuit, in which the aphelion lies within the northern winter season. The excess of heat received from the sun in those 10,000 years above its mean amount will be, in Mr. Croll's mode of reckoning, about 27 billions of billions of foot pounds. This agrees ill with the hypothesis that the period is one marked by extreme and excessive cold.

29. A third and more decisive objection follows. The season which the theory singles out to account for extreme glaciation, is that in which the northern hemisphere receives the greatest excess of solar heat above the mean value.

The proof is simple. The total heat received by the earth. from the sun in its annual orbit is equal for equal angles. The swiftness and the nearness, the remoteness and the length of time, compensate each other, varying by the same law of the inverse square of the distance. But this is not true for the separate hemispheres. If the orbit were circular, each would receive more in the summer, and less in the winter half of the year. But from the excentricity, when the perihelion and aphelion are at the two solstices, the summer heat is increased and the winter heat diminished, or conversely, in the same ratio. But since the summer heat is greater than that of the winter, the total for the hemisphere whose summer is in the perihelion must exceed the other.

30. To make this plainer, let us take approximate values. Let the earth's distance from the sun be 90 millions, the excentricity, as in the supposed glacial epoch, one-ninth, or the greatest and least distances, 95 and 85 millions. The quantity of heat at perihelion and aphelion will vary in a duplicate ratio; or if 9 be taken for the mean quantity, 8 and 10. The ratios at midsummer and midwinter are as 1 + sin. to 1 sin. , nearly

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as 7 to 3, and for the whole half-year as 5 to 3. There is an excess or defect of about one-fourth of the mean value. Hence of 10 + 2 of 8 18.5, will be the total heat for the northern, and of 10 + 5 of 8 of 10 of 8 = 17.5, for the southern hemisphere, when the northern summer solstice is in the perihelion, and the northern winter solstice in the aphelion. Thus the northern half of our globe will receive from the sun one thirty-sixth, or nearly 3 per cent. of heat in excess of the mean value. Thus the period selected as the Ice Age is one in which the northern hemisphere receives from the sun an amount of heat exceeding by almost 3 per cent. its mean value, and greater than at any other period in the long course of 700,000 years.

31. Thus the result cannot depend on a lessened total amount of solar heat incident on the earth at the eras in question, for the total is increased. Sir J. Herschel, Arago, and other leading men of science, have failed to see that increase of excentricity within the actual limits could produce an ice age in either hemisphere. Mr. Croll admits that it could not, directly, be the cause of such a change; but he argues that, indirectly, it may be the cause, by bringing other causes into operation.

From the values of the

His reasoning, is as follows. excentricity at past periods he deduces the ratio of the direct solar heat at midwinter to its present amount. One column of his table gives the excentricity, from Leverrier's formulæ, at intervals of 50,000 years for three millions of years backwards, and one forward, and of 10,000 years for one million backward. Another column gives the ratio of the midwinter solar heat at each period to what it is now. The temperature of space is assumed to be 239° F. The excess above this limit is assumed to depend on the midwinter solar radiation, and to be strictly proportional to it. The midwinter heat of our country is taken at 39° F., or the excess as 278°. The ratios for the two selected eras, 850,000 and 210,000 years ago, are 837 and 864; hence the deficit at the two eras would be 45°.3, and 37°7, and the results -6°3 and +1°3 F. for the midwinter heat of our country at those two eras. With such a degree of cold, ice and snow would rapidly form. The heat of the summer, Mr. Croll argues, would be unable to melt the winter ice, and it would go on accumulating through many successive years, till the orbit and aphelion place were changed, and the main condition was thus reversed, after 10,000 years.

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Here Mr. Croll reverses his argument against Poisson's theory, that space is not a body, and can have no temperature,

No. 18, 1. 9. A temperature of space about two hundred and forty degrees below the zero of Fahrenheit is the basis of all his calculations.

In these calculations there are several serious defects, which disprove the conclusion, and require us to look further for an adequate explanation of the general prevalence of cold in the northern hemisphere during the Drift or Glacial period. The amount of the excentricity, the law of radiation, the proper point of the orbit for estimating the balance of solar heat, and loss by radiation, the law of midsummer heat, and the effect of aerial and oceanic currents, are all of them elements which seem to me to have been incorrectly assumed or left out of view. The combined result of the corrections thus required will be practically to set aside the whole theory.

32. First, the excentricity is calculated by M. Leverrier's formulæ. It might seem beforehand very doubtful whether these can be relied on for a date three millions of years ago, or even for 850,000, or 210,000 years. But there is here a special reason for distrust. The present excentricity is •0167836 (Hersch. Ast.), and those at the two eras in debate, 0747 and 0575. Now the maximum for the earth, according to Lagrange, is 07641, and according to Leverrier 077747, and the value at 850,000 years ago is thus very near the limit. But these calculations were made before the discovery of Neptune. Fresh calculations have been made by Mr. Stockwell, since that discovery, and the corrected maxima for the planets from Venus to Saturn are all diminished. Those of Leverrier are M. 225646, V. 086716, E. 077747, M. 142243, J. 061548, S. 081919, U. 064666. But the later values are M. 2317185, V. 0706329, E. ·0693888, M. 139655, J. 0608274, S. •0843289, U. ⚫0779652, N. 0145066. Thus the value accepted by Mr. Croll for his earlier date is one which exceeds the corrected maximum by 0053, or nearly a million miles. If Mr. Stockwell's calculation is correct, it is an impossible value.

An exact correction would, of course, involve a prodigious. amount of fresh labour; but a reasonable approach to it may be gained by diminishing the excess over the present excentricity in the ratio of the excesses of the two maxima. These are 0609634 and ・0526052. The values 0747 and 0575 will thus become 06676 and 05192, or about ninetenths of those on which the actual calculation has been based. This first correction will lessen the decrease of midwinter temperature three or four degrees.

33. But the method of deducing the midwinter heat from

the ratio of the heat received from the sun at the winter solstice is also defective. The excess of that winter temperature over the temperature of space is held to be strictly proportional to the amount of solstitial heat received. But this combines a mere hypothesis with a defective law of dispersion or loss by radiation. A simpler rule may be deduced, in a less hypothetical way, from the experiments of MM. Dulong and Petit. According to these, when heat radiates from a hotter to a cooler body, and the difference of their temperatures is constant, the radiation increases or diminishes. in the ratio of 1·165 to 1 for a rise or fall of 20° C. or 36° F. in their two temperatures. Of course, if the lower body has a fixed temperature, and the hotter alone varies, the ratio should be slightly greater. To establish an equilibrium

between the heat received from the sun and that radiated into space, the midwinter heat must thus be lowered till the radiation is lessened in the same proportion as the solar heat received.

Adopting this rule, and retaining Mr. Croll's values for the excentricity 0747 and 0575, and the answering ratios of midwinter heat, the lowering of temperature will not be 45°.3 and 37°.7 F., but 41°.94 and 34°34 only, a difference of more than three degrees. But with the corrected values •06676 and 05192 they will be 38°45 and 31°.84 only; or the winter heat at the later period, Mr. Croll's proper ice age, will be 70.2 F. instead of 1°.3, a difference of six degrees.

34. But a further correction is plainly required. The equilibrium between the heat received and lost is clearly not at the solstice itself. The greatest heat in summer and cold in winter is well known to be about a month later, that is, at a distance of about 30° from the solstice. Thus the distances, on which the solar heat, when the solstice is in the perihelion or aphelion, depends, will not be 1―e and 1+e, but 1—že√/3 and ‍1+1/3.

Introducing this correction, the lowering of the heat with the two uncorrected values of the excentricity will be 35°45 and 29° 81, but with the corrected or reduced values ⚫06676 and 05192, it will be 33°18 and 28°.73; so that, instead of -6°3 and +1°3 F. for the extreme or midwinter temperatures, the corrected values would be +5°8 and +10°3, or in the earlier period twelve, and in the later period nine degrees higher, than the value Mr. Croll has given.

35. The summer heat, in Mr. Croll's theory, is supposed to depend on wholly different principles from the winter cold. He speaks of it as follows.

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