Ball — Note on Astronomical Theory of Great Ice Age. 643 



"We have thus the following theorem : — 



Let 2E be the total sun-heat received in a year over the whole 

 earth ; then this is divided into shares as follows : — 



Northern hemisphere, summer, E 



winter, E 



27r 



TT - 2 sin e 



with identical expressions for the summer and winter in the southern 

 hemisphere. 



If we make e = 23° 27' we find that the heat received during the 

 summer (equinox to equinox) of each hemisphere is "627^, while the 

 heat during the winter of each hemisphere is •373^. More briefly 

 stiQ. If each hemisphere receives in the year a quantity of sun-heat 

 represented by 365 units, then 229 of these are during summer, and 

 136 during winter. These figures are independent of the eccentricity 

 of the earth's orbit. 



The length of the summer is defined to be the interval when the 

 sun's centre is above the equator. The length will of course vary 

 with the eccentricity and with the position of the equinoxes on the 

 orbit. We need only take the extreme case where the line of equi- 

 noxes is perpendicular to the major axis of the orbit. The maximum 

 difference between the length of summer and of winter is thus 



465 days x eccentricity. 



I take the maximum eccentricity of the earth's orbit to be 



0-0745, 



this being the mean of the values by Leverrier, Lagrange, and Stock- 

 well {see CroU, "Climate and Temp.," p. 531), and, therefore, the 

 greatest difference between summer and winter will be about 33 days, 

 i.e. one season is 199 days, and the other is 166 days. 



The total quantity of heat received during the year on each hemi- 

 sphere is practically independent of the eccentricity ; but the mode 

 in which that heat is received at the different seasons will vary, and 

 thus give rise to the following extreme cases : — 



Glacial. 



229. Heat units spread over 166 days. 

 136. Heat units spread over 199 days. 



Oe Inieeglacial. 



229. Heat units spread over 199 days. 

 136. Heat units spread over 166 days. 



