108 G. F. Becker — Certain Astronomical 



ferences in the inception or the cessation of glaciation in 

 various regions. It is not needful to assume that the glacia- 

 tion of the Sierra Nevada either began or ended synchronously 

 with the ice age in New England. 



The date at which a minimum of eccentricity last coincided 

 with a maximum of obliquity can almost certainly be deter- 

 mined. According to Stockwell the obliquity has been dimin- 

 ishing for the past 8000 years and was within 21 minutes of its 

 maximum value at the beginning of that time. According to 

 Leverrier the eccentricity passed through a minimum 40,000 

 years ago, the value being then about two-thirds of the pres- 

 ent one. So far as I know the obliquity has not been com- 

 puted beyond 8000. This can of course be done for StockwelPs 

 value of the masses of the planets, or for newer or better ones. 

 All the indications seem to be that within thirty or forty thou- 

 sand years conditions have occurred and have persisted for a 

 considerable number of thousand years which would favor 

 glaciation on the theory of this paper. It is conceivable that 

 very remote coincidences of high obliquity and low eccentricity 

 might be determined ; answering perhaps to glaciation in the 

 Paleozoic ; but until some simple law governing the periodi- 

 city of secular variations is discovered such a result is not to be 

 looked for ; it is at present practicable to formulate the varia- 

 tions only by omitting terms above a certain order and exter- 

 polation beyond a few score thousand years is consequently 

 untrustworthy. 



Calculation of Sunshine per unit area. 



The following note explains the method of finding the 

 amount of solar energy received per unit area of the earth's 

 surface in any latitude between equinoxes, the ellipticity of 

 the earth being ignored. Mr. L. W. Meech has already solved 

 the very similar problem of hnding the heat received per unit 

 area for the entire year, and it is possible to develop from his 

 formulas those applicable to the present purpose ; but this 

 would take nearly as much space as a fresh presentation. Mr. 

 Meech's method of dealing with the subject is also quite dif- 

 ferent from that here presented, which I worked out before 

 making acquaintance with his admirable memoir.* 



When the sun's declination is d, any parallel in latitude A 

 will be projected onto the circle of illumination as an ellipti- 

 cal arc dividing the circle into two unequal portions. If X and 

 o have opposite signs, the smaller of these areas will be a 

 crescent which I shall call W. To .find the area W shown in 

 diagram 1, let a be the earth's radius, a and b the semiaxes of 



* Smithsonian Contr. to Knowledge, vol. ix, 1857. 



