On the Change of Eccentricity of the Earth's Orbit. 375 



but at the period 950,000 years ago it reached the high value 

 of 0*0517. Here we have three glacial epochs following each 

 other in close succession — or rather, we should say, one long 

 glacial epoch of about 250,000 years broken up by two mild 

 periods 100,000 years apart." 



The foregoing conclusions are irreconcileable with the opinion 

 commonly held by astronomers, that the quantity of heat received 

 from the sun annually increases with the increase of the eccen- 

 tricity; so that the periods selected as glacial epochs by Mr. 

 Croll are probably nearer the times of maximum heat, so far as 

 this is dependent on the eccentricity of the orbit. 



The following demonstration of the law, " That the quantity 

 of heat received per annum from the sun varies inversely as the 

 minor axis of the orbit" may be of use to some of your junior 

 readers : — 



By Kepler's law of areas 



rW = hdt, (1) 



Q (quantity of heat) oc ~§ = -7- 



dO _ s/~ade 



^//jLa(l — e 2 ) b\/~jJu 

 Therefore in one year 



Q27r\/a 1 , ON 



a V^ a * (2) 



If we expand j- in terms of e, we shall have 



Qajarl+i<*+g<«+jg<i»+&c. . . (3) 



From this expression, neglecting powers of e higher than its 

 square, we find that the minimum amount of heat is received 

 when the orbit is a circle, and that the excess above this mini- 

 mum varies as the square of the eccentricity. 



If the eccentricity of the earth's orbit have a real influence in 

 producing glacial epochs, it would appear from M. Leverrier's 

 calculations that it should be sought for in the future, and not 

 in the past; for at about 24,000 years after a.d. 1800, the 

 eccentricity of the earth's orbit will attain a smaller minimum 

 than usual, and the heat receivable from the sun will be less 

 than at any period within 100,000 years before the epoch. 



It may be useful here to reproduce M. Leverrier's Table. 

 2C2 



