646 EEPOET— 1891. 



The error was not perceived by Croll. lie, perhaps not unnaturally, accepted 

 Herschel's authority on such a matter, and consequently a thorough revision of 

 Croll's calculations and his doctrines based thereon becomes necessary. 



In a work now in the press, bearing the title of this paper, I have endeavoured 

 to develop the correct view of the subject, and to rewrite the astronomical theory 

 of the Ice Age. I may, however, here remark that the error into which Dr. Croll 

 unfortunately fell was very prejudicial to the conclusion he strove to prove. 

 Had he been acquainted with the accurate version of the mathematical facts, he 

 would have been able to show a much stronger case for the astronomical doctrine 

 of the Ice Age than that he actually presented. 



The essential point of the present communication lies in the announcement 

 that — 



If 100 represent the total number of heat units received on a hemisphere of 

 the earth in a year, then Go will be the share received during summer, and 37 

 during winter. 



A special importance attaches to these figures from the circumstance that they 

 are absolutely independent of the eccentricity of the earth's orbit, or of the position 

 of the equinoxes. They depend solely upon the obliquity of the ecliptic, and this 

 is a magnitude which, so far as our present purpose is concerned, maybe regarded 

 as constant during geological time. 



The distribution of the heat just stated is the point which I now desire to 

 emphasise. Herschel stated the uumbers to be 50 and 50. If his attention had 

 been sufficiently given to the matter, he would have seen that the numbers were 

 63 and 37. The correction is an important one. 



It is to be remembered that the units in which we are reckoning express the 

 total heat received from the sun. As the sun heat alone preserves the earth 

 from sinking to the temperatiu'e of space, it follows that the sun heat really main- 

 tains a temperature some hundreds of degrees greater than we would otherwise 

 have. A fluctuation in sun heat, which appeared small in comparison with the 

 total amount, might involve a vast change in climate. 



Owing to the perturbations of the planets, it will occasionally happen that the 

 eccentricity of the earth's orbit will become larger than it is at present. It seems 

 that the maximum eccentricity is sufficient to produce an inequality between the 

 duration of summer and winter amounting to 33 days. We have, therefore, the 

 following possible conditions in either northern or southern hemisphere : — 



Summer . . . .109 days. , Summer . . . .166 days. 

 ■Winter . . . .166 days. ^"^ Winter . . . .199 days. 



In each case it must be borne in mind that G3 heat-units arrive in summer 

 and 37 in winter. If the summer be the long one and the winter be short, then 

 the allotment of heat between the two seasons is fairly adjusted. The (J3 units 

 are distributed over the 199 days, and the 37 units over 166 days, and a milder 

 climate than our present one results. This is the genial inter-glacial state for that 

 hemisphere. If, however, a torrent of heat represented by 63 units is received 

 during a brief summer of 166 days, while the balance of '37 units is made to 

 stretch itself over 199 days, then a brief and intensely hot summer is followed by 

 a very long and cold winter. As this condition lasts for many centuries it seems 

 sufficient to produce a glacial epoch. 



I have only to add that on this view there must have been not only one but 

 several Glacial epochs throughout geological time, but they doubtless occurred at 

 very irregular intervals, and with wide differences in severity. It is, however, 

 noteworthy that the theory requires that when the northern hemisphere is glaciated 

 the southern hemisphere shall be in a genial state, and vice versa. It is also to 

 be observed that so long as the high eccentricity of the earth's orbit is maintained 

 the procession of the equinoxes will cause the glaciation to shift from one hemi- 

 sphere to another in a period of 10,500 (ten thousand five hundred) years. I do 

 not mean that this will always be the interval, but it does seem probable that 

 there may be clusters of two, three, or more ice ages, the individual members of 

 which are so divided. Each cluster is separated from the next by a vast period 



