Conditions favorable to Glaciation. 113 



Substitution of these values in Z/2rca cos ?. gives the following 

 expressions for actual use : — 



At the equator the modulus is sin e and for either season 

 alike 



2E 1 



u = . 



7C 's/\ — e" 



From the equator to the polar circle the modulus is sin e/cos A 

 and the sunshine per unit area between equinoxes is 



sin A \ ,,, foot A 



u = 2 



vr 



| E I cos f [^ + F(90°- A)] 



- F 1 cos s I E (90° — A) — tan A tan e sin s I ± ^ sin £ !• . 



At the polar circle 



o cos £ ( 90° — £ n . ) 



w = 2 1 tan £ + cos £ In cot ± — sin £ \ 



n Vl - e 2 < 2^2 ) 



From the polar circle to the pole the modulus is cos A/ sin £ and 



sin A ( _. f„,, . tan e\ _, r , , 



u = 2 , J E 1 COS £ F £ + ^— - F 1 COS £ E(£) 



n^/\ _ e 2 ( L sin AJ [_ 



COS A 7T . / 



H ± - sin £ \ ; 



tan £ tan Aj 2 J ' 



and at the pole this reduces to 



1 j- . ) 



u = , -J sin £ ± sin £ Y 



Vl — e 2 ' > 



These formulas can be computed from known series or by 

 the help of Legendre's tables. For e = 23° 27' I have com- 

 puted the values tabulated in both ways with coincident results. 

 For e = 24° 36' I used the tables and checked by differences 

 with the other series. The radiant energy received during the 

 entire year is of course the sum of the energy received during 

 the two seasons. The quantities thus found and multiplied by 

 a constant coincide with Meech's values to four significant 

 figures. Meech took the apparent obliquity at 23° 28', and 

 the sine of this angle is 1-0007 the sine of 23° 27', so that a 

 closer correspondence could not be expected.* I have stated 

 my results to four decimals, though for the purposes of this 

 paper three would have been ample. 



It need scarcely be mentioned that the effect of the real 

 ellipticity of the meridian is to reduce the receipt of solar 

 energy towards the the poles by a trifling amount. 



Washington, D. C, June, 1894. 



* The obliquity was 23° 27' 30" in 1852, or after Meech had begun his investi- 

 gation. It is now about 23° 27' 11". 



