2% Mr. Herschel on the Astronomical Causes 



the amount of diminution which the excentricity must be supposed to have 

 undergone^, to render an account of the variation w^hich has taken place, we 

 have to consider that, in the first place, a great diminution of the excentricity 

 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. 



Reciprocal, or Ratio 

 Excentricity. Minor axis. 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 LOU 



0.20 0.980 1.021 



0.25 0.9G8 1.032 



0.30 0.954 1.048 



By this it appears that a variation of the excentricity of the orbit, from the 

 circular form to that of an ellipse having an excentricity 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 excentricities, from that of Pallas and Juno downwards. 



I am not aware that the limit of increase of the excentricity 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 excentricities 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 excentricities 

 existing, they cannot be incompatible with the stability of the system gene- 

 rally ; 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 calcula- 

 tions alluded to, having regard to the simultaneous elfects of at least the four 

 most influential planets Venus, Mars, Jupiter, and Saturn, tiot only on the 

 orbit of the earth, but on those of each other. The principles of this calcula- 



* Mecanique Celeste^ Book II. No. 57. — Equation (u). ■- 



