NATURE 



289 



THE ASTRONOMICAL THEORY OF THE 

 GLACIAL PERIOD. 

 The Cause of an Ice Age. By Sir Robert Ball, Astro- 

 nomer-Royal for Ireland. Pp.180. (London: Kegan 

 I'aul and Co., 1891.) 



THIS book gives a popular account of the theory of 

 Adh^mar and CroU as to the causes of glacial 

 periods in geological history. 



The author's power as a popular expositor is well 

 known, and this little book shows him at his best. He 

 knows when to drive a point home, and yet is never 

 tedious in his reiteration But he has given here some- 

 thing more than a lucid explanation, for he makes a 

 valuable contribution to the subject, and the book may 

 be read with advantage by those who are already 

 acquainted with the literature bearing on the theory. 



The theory itself may be sketched in outline as 

 follows : — 



It is known that, under the perturbations of Venus and 

 Jupiter, the eccentricity of the earth's orbit varies within 

 certain limits. When the eccentricity is large, and when 

 the precession of the equinoxes brings the perihelion to 

 near the middle of, say, the northern winter, the annual 

 supply of solar heat is so distributed that there will be a 

 glacial period in the northern and a mild climate in the 

 southern hemisphere. Two or three maxima of glacia- 

 tion and mildness will usually succeed one another at 

 intervals of 10,500 years, because the eccentricity varies 

 with extreme slowness. When the eccentricity is small, 

 as at present, a moderate climate will prevail in both 

 hemispheres, whatever be the position of the perihelion. 



The keynote of Sir Robert Ball's presentation of this 

 theory is given in a short mathematical appendix. I am 

 disposed to dissent to some extent from the manner in 

 which this view is set forth, but the general argument 

 will, I think, do much to convince the scientific world of 

 the truth of the theory, even where Croll's more elaborate 

 discussions failed to do so. 



I will now give a paraphrase of the argument, and will 

 point out where it appears to me open to objection. 



The time taken by the earth to describe a degree of 

 longitude round the sun varies as the square of its dis- 

 tance from the sun, and the intensity of solar radiation 

 varies inversely as the square of the same distance. 

 Hence the amount of heat received by the whole earth 

 during the description of a degree of longitude is 

 constant. 



Let the year be divided into only two seasons, viz. the 

 northern summer or southern winter when the sun is 

 north of the line, and the northern winter or southern 

 summer when the sun is south of the line. Also let 

 similar days in summer and winter be defined as days on 

 which the sun sets (say at Greenwich) as much after 

 6 p.m. as before 6 p.m.; similar parts of summer and 

 winter will mean parts limited by similar days. 



Now consider the solar heat incident on any specified 

 area of one hemisphere, during any specified portion of 

 the summer and during the similar portion of the winter. 

 Suppose that the heat incident on the area in the portion I 

 NO. I 161, VOL. 45] 



of summer added to that incident on it during the 

 similar portion of winter be denoted by 2, and suppose 

 that the excess of the heat incident in the portion of 

 summer above that incident in the similar portion of 

 winter be denoted by 2a ; then it is clear that i + ^ is 

 proportional to the amount of heat received by the 

 specified area during the specified portion of its summer, 

 and I - « is proportional to the amount of heat received 

 by the area during the similar portion of winter.' Thus 

 we may say that the contrast between the summer and 

 winter supplies of heat (for given area and given 

 portions of summer and winter) is represented by the 

 fraction (i -(- a) ^ (i -a). 



This is, of course, equally true when the whole hemi- 

 sphere, and the whole of summer and winter, are con- 

 sidered, and Sir Robert Ball shows that a is then equal 

 to 2 sin 23 27' -Mr; (i -f «) -^ (i - o) is found to be 

 almost exactly as 5 to 3. Using percentages he gives 

 the ratio as 63 to 37, but the simple numbers 5 to 3 

 afford a closer approximation to accuracy. 



It is clear that if the specified portions of summer and 

 winter embrace the solstices, and if the specified area is 

 tropical, a will be small, and if it is polar it will be large. 

 The fraction (i -f «) -=- (i -a) continually increases as 

 we go northward, and it may be taken as a measure of 

 the severity of a climate. It is quite uncertain how far 

 the climate of any one place depends on the heat supplies 

 of the whole hemisphere on which it lies, and therefore it 

 is uncertain how large an area and how long a season 

 we ought to take into consideration in the present in- 

 vestigation. But I should have thought it legitimate, in 

 treating of the causes of glaciation, only to consider the 

 semi-annual heat supply of a polar cap, comprising, say, 

 all the area north of latitude 30° ; thus would have made 

 (i -\-a) -i- (i - rt) much greater than 5 to 3. It does not 

 seem to me, however, that we are bound to find an 

 answer to this almost insoluble problem. 



So far we have considered the supply of heat whilst 

 the earth describes so many degrees of longitude round 

 the sun, but climate depends on the supply of heat during 

 a given time. 



When the earth's orbit is circular, summer and winter 

 are of equal length, and so also are similar portions of 

 summer and winter ; thus the two ways of estimating 

 the heat supply coalesce, and the contrast between the 

 summer and winter daily supplies of heat is also repre- 

 sented by the fraction {\ -\- a) -r- {\ - a). The present 

 condition of affairs differs but little from this standard 

 case, and we know that the contrast between the summer 

 and winter daily supplies of heat is such as to produce 

 certain known climates, differing according to latitude. 



' If Jtt ±(^ be the sun's hour angle at sunset on any day in summer, and 

 on the corresponding day in winter, and if the sun's parallax on those days be 

 proportional to i ± K. *hen it is easy to show that the amount of heat 

 received by unit area in the course of the day is proportional to 



(i ± £)-[(* -I- cot (^) ± ijT] sin a sin A, 

 where ±5 is the sun's declination, -f- in summer and - in winter, and A is 

 the latitude of ihe place of observation. 



It follows that, what is called in the text, the contrast for unit area in 

 latitude A, for this pair of days is — 



Llf.(L±|V where. 

 I - « \i - E/ 



2(<fr -J- cot <<>) 

 The expression for the heat supply on unit area during any portion ot 



summer or winter involves elliptic integrals, which might be given if it 



were worth while. 



A triple integral is required to express the heat supply of any specified 



area during any specified portion of the year. 



