APPENDIX.

1.

OPINIONS EXPRESSED PREVIOUS TO 1864 REGARDING THE INFLUENCE OF THE ECCENTRICITY OF THE EARTH'S ORBIT ON CLIMATE.*

M. DE MAIRAN.

M. de Mairan, in an article in the Memoirs of the Royal Academy of France "On the General Cause of Heat in Summer and Cold in Winter, in so far as depends on the internal and permanent Heat of the Earth," makes the following remarks on the influence of the difference of distance of the sun in apogee and perigee :

"Cet élément est constant pour les deux solstices; tandis que les autres (height of the sun and obliquity of his rays) y varient à raison des latitudes locales; et il y a encore cela de particulier, qu'il tend à diminuer la valeur de notre été, et à augmenter celle de notre hiver dans l'hémisphère boréal où nous sommes, et tout au contraire dans l'austral. Remarquons cependant que de ces mêmes distances, qui constituent co troisième élément, naît en partie un autre principe de chaleur tout opposé, et qui semble devoir tempérer les effets du précédent; sçavoir, la lenteur et la vitesse réciproques du mouvement annuel apparent, en vertu duquel et du réel qui s'y mêle, le soleil emploie 8 jours de plus à parcourir les signes septentrionaux. C'est-à-dire, que le soleil passe 186 jours dans notre hémisphère, et seulement 178 dans l'hémisphère opposé. Ce qui, en général, ne peut manquer de répandre un peu plus de chaleur sur l'été du premier, et un peu moins sur son hiver."

*See text, p. 10.

† Mathematical and Physical Series, vol. xxxvi. (1765).

MR. RICHARD KIRWAN.

Epinus,* reasoning on astronomical principles, attributes the inferior temperature of the southern hemisphere to the shorter abode of the sun in the southern tropic, shorter by seven days, which produces a difference of fourteen days in favour of the northern hemisphere, during which more heat is accumulated, and hence he infers that the temperature of the northern hemisphere is to that of the southern, as 189.5 to 175.5, or as 14 to 13."-Trans. of the Royal Irish Academy, vol. viii., p. 417. 1802.

SIR CHARLES LYELL.

"Before the amount of difference between the temperature of the two hemispheres was ascertained, it was referred by astronomers to the acceleration of the earth's motion in its perihelion; in consequence of which the spring and summer of the southern hemisphere are shorter by nearly eight days than those seasons north of the equator. A sensible effect is probably produced by this source of disturbance, but it is quite inadequate to explain the whole phenomena. It is, however, of importance to the geologist to bear in mind that in consequence of the precession of the equinoxes, the two hemispheres receive alternately, each for a period of upwards of 10,000 years, a greater share of solar light and heat. This cause may sometimes tend to counterbalance inequalities resulting from other circumstances of a far more influential nature; but, on the other hand, it must sometimes tend to increase the extreme of deviation, which certain combinations of causes produce at distant epochs."-Principles, First Edition, 1830, p. 110, vol. i.

SIR JOHN F. HERSCHEL, BART.

The following, in so far as it relates to the effects of eccentricity, is a copy of Sir John Herschel's memoir, "On the Astronomical Causes which may influence Geological Phenomena," read before the Geological Society, Dec. 15th, 1830.-Trans. Geol. Soc., vol. iii., p. 293, Second Series:

. . . . Let us next consider the changes arising in the orbit of the earth itself about the sun, from the disturbing action of the planets. In so doing it will be obviously unnecessary to consider the effect produced on the solar tides, to which the above reasoning applies much more forcibly than in the case of the lunar. It is,

"Memoirs of St. Petersburg Academy." 1761.

therefore, only the variations in the supply of light and heat received from the sun that we have now to consider.

"Geometers having demonstrated the absolute invariability of the mean distance of the earth from the sun, it would seem to follow that the mean annual supply of light and heat derived from that luminary would be alike invariable; but a closer consideration of the subject will show that this would not be a legitimate conclusion, but that, on the contrary, the mean amount of solar radiation is dependent on the eccentricity of the orbit, and therefore liable to variation. Without going at present into any geometrical investigations, it will be sufficient for the purpose here to state it as a theorem, of which any one may easily satisfy himself by no very abstruse geometrical reasoning, that the eccentricity of the orbit varying, the total quantity of heat received by the earth from the sun in one revolution is inversely proportional to the minor axis of the orbit? Now since the major axis is, as above observed, invariable, and therefore, of course, the absolute length of the year, it will follow that the mean annual average of heat will also be in the same inverse ratio of the minor axis; and thus we see that the very circumstance which on a cursory view we should have regarded as demonstrative of the constancy of our supply of solar heat, forms an essential link in the chain of strict reasoning by which its variability is proved.

"The eccentricity of the earth's orbits is actually diminishing, and has been so for ages, beyond the records of history. In consequence, the ellipse is in a state of approach to a circle, and its minor axis being, therefore, on the increase, the annual average of solar radiation is actually on the decrease.

"So far this is in accordance with the testimony of geological evidence, which indicates a general refrigeration of climate; but when we come to consider the amount of diminution which the eccentricity must be supposed to have undergone to render an account of the variation which has taken place, we have to consider that, in the first place, a great diminution of the eccentricity is required to produce any sensible increase of the minor axis. This is a purely geometrical conclusion, and is best shown by the following table:

By this it appears that a variation of the eccentricity of the orbit from the circular form to that of an ellipse, having an eccentricity of one-fourth of the major axis, would produce only a variation of 3 per cent. on the mean annual amount of solar radiation, and this variation takes in the whole range of the planetary eccentricities, from that of Pallas and Juno downwards.

"I am not aware that the limit of increase of the eccentricity of the earth's orbit has ever been determined. That it has a limit has been satisfactorily proved; but the celebrated theorem of Laplace, which is usually cited as demonstrating that none of the planetary orbits can ever deviate materially from the circular form, leads to no such conclusion, except in the case of the great preponderant planets Jupiter and Saturn, while for anything that theorem proves to the contrary, the orbit of the earth may become elliptic to any amount.

"In the absence of calculations which though practicable have, I believe, never been made,* and would be no slight undertaking, we may assume that eccentricities which exist in the orbits of planets, both interior and exterior to that of the earth, may possibly have been attained, and may be attained again by that of the earth itself. It is clear that such eccentricities existing they cannot be incompatible with the stability of the system generally, and that, therefore, the question of the possibility of such an amount in the particular case of the earth's orbit will depend on the particular data belonging to that case, and can only be determined by executing the calculations alluded to, having regard to the simultaneous effects of at least the four most influential planets, Venus,

* The calculations here referred to were made by Lagrange nearly half a century previous to the appearance of this paper, and published in the "Mémoires de l'Académie de Berlin," for 1782, p. 273. Lagrange's results differ but slightly from those afterwards obtained by Leverrier, as will be seen from the following table; but as he had assigned erroneous values to the masses of the smaller planets, particularly that of Venus, the mass of which he estimated at one-half more than its true value, full confidence could not be placed in his results. Superior limits of eccentricity as determined by Lagrange, Leverrier, and Mr. Stockwell:

Mars, Jupiter, and Saturn, not only on the orbit of the earth, but on those of each other. The principles of this calculation are detailed in the article of Laplace's work cited. But before entering on a work of so much labour, it is quite necessary to inquire what prospect of advantage there is to induce any one to undertake it.

"Now it certainly at first sight seems clear that a variation of 3 per cent. only in the mean annual amount of solar radiation, and that arising from an extreme supposition, does not hold out such a prospect. Yet it might be argued that the effects of the sun's heat is to maintain the temperature of the earth's surface at its actual mean height, not above the zero of Fahrenheit's or any other thermometer, but above the temperature of the celestial spaces, out of the reach of the sun's influence, and what that temperature is may be a matter of much discussion. M. Fourier has considered it as demonstrated that it is not greatly inferior to that of the polar regions of our own globe, but the grounds of this decision appear to me open to considerable objection.* If those regions be really void of matter, their temperature can only arise, according to M. Fourier's own view of the subject, from the radiation of the stars. It ought, therefore, to be as much inferior to that due to solar radiation, as the light of a starlight night is to that of the brightest noon day, in other words it should be very nearly a total privation of heat-almost the absolute zero respecting which so much difference of opinion exists, some placing it at 1,000°, some at 5,000° of Fahrenheit below the freezing-point, and some still lower, in which case a single unit per cent. in the mean annual amount of radiation would suffice to produce a change of climate fully commensurate to the demands of geologists.t

"Without attempting, however, to enter further into the perplexing difficulties in which this point is involved, which are far greater than appear on a cursory view, let us next consider, not the mean, but the extreme effects which a variation in the eccentricity of the earth's orbit may be expected to produce in the summer and winter climates in particular regions of its surface,

"Mém. de l'Acad. royale des Sciences." 1827. Tom. vii., p. 598.

+ Absolute zero is now considered to be only 493° Fah. below the freezingpoint, and Herschel himself has lately determined 271° below the freezingpoint to be the temperature of space. Consequently, a decrease, or an increase of one per cent. in the mean annual amount of radiation would not produce any thing like the effect which is here supposed. But the mean annual amount of heat received cannot vary much more than one-tenth part of one per cent. In short, the effect of eccentricity on the mean annual supply of heat received from the sun, in so far as geological climate is concerned, may be practically disregarded.-[J. C.]