“... 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, 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:—
| Eccentricity. | Minor Axis. | Reciprocal or Ratio of Heat received. |
|---|---|---|
| 0·00 | 1·000 | 1·000 |
| 0·05 | 0·999 | 1·002 |
| 0·10 | 0·995 | 1·005 |
| 0·15 | 0·989 | 1·011 |
| 0·20 | 0·980 | 1·021 |
| 0·25 | 0·968 | 1·032 |
| 0·30 | 0·954 | 1·048 |
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,[315] 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, 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.[316] 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.[317]
“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, and under the influence of circumstances favouring a difference of effect. And here, if I mistake not, it will appear that an amount of variation, which we need not hesitate to admit (at least, provisionally) as a possible one, may be productive of considerable diversity of climate, and may operate during great periods of time either to mitigate or to exaggerate the difference of winter and summer temperatures, so as to produce alternately, in the same latitude of either hemisphere, a perpetual spring, or the extreme vicissitudes of a burning summer and a rigorous winter.