642 Proceedings of the Royal Irish Academy. 



XXXIX. — Note on the Astronomical Theoey of the Geeat Ice 

 Age. By Sm Eobeet Siawell Ball., LL.D., F.R.S. 



[Eead, May 24, 1886.] 



The following calculation has convinced me that Mr. Croll's theory- 

 affords an adequate explanation of the Ice age. I compute the total 

 quantity of heat received by each hemisphere of the earth during 

 summer and winter respectively as follows : — 



Let 211 ja^ be the quantity of sun-heat falling perpendicularly on an 

 area equal to the section of the earth at the mean distance a from the 

 sun in the unit of time. 



Let 8 be the sun's north declination. Then the share received by 

 the northern hemisphere will be 



— (1 + sinS), 

 and by the southern 



^(1 -sinS). 



At the distance r, and in the time dt, the heat received in the 

 northern hemisphere will be 



but we have 



r^ d6 = hdt, 



whence the expression becomes 



JT 



-(1 +sinS) .dd; 



but we have 



sin S = sin ^ . sin e, 



where e is the obliquity. 



The total heat received by the northern hemisphere from the vernal 

 to the autumnal equinox is 



{"^ H R 



— (1 + sm € sin 6) . dd = -j- {iv + 2 sin e). 



