98 G. F. Becker — Certain Astronomical 



tion of the sun varies from zero at the equinoxes to 23° 27' at 

 the solstices. The next step is to find the average area ou the 

 circle of illumination representing the projection of the narrow 

 zone from equinox to equinox. When this is accomplished, 

 one has only to multiply the result by the time interval and 

 divide by the length of the parallel of latitude to obtain the 

 area on the circle of illumination representing the solar radia- 

 tion received per unit area of the earth's surface between the 

 autumnal and the vernal equinoxes. The unit in which radia- 

 tion is measured may be arbitrarily chosen and as arbitrarily 

 changed, provided that it is employed for all latitudes. I have 

 chosen one which is convenient. It and the formulas for 

 computation are explained in a note appended to this paper. 



The heat received per unit area between equinoxes is inde- 

 pendent of the length, of the season being proportional to the 

 change of the earth's longitude in its orbit.* The average rate 

 at which heat is received during one of the great seasons is 

 therefore merely the total heat per unit area divided by the 

 length of the season. 



The radiant energy per unit area depends to a slight extent 

 upon the eccentricity of the orbit. If u a is the energy per 

 unit area for zero eccentricity, and u the energy for eccentri- 

 city e, then 



Vi—e" 



Though the difference is small, it is perfectly easy to take it 

 into consideration, and this I have done. 



At the present time the warm season in the northern 

 hemisphere is approximately 186 days 10 hours longf or 

 1*0208 times half the year. The eccentricity of the orbit 

 is 0*01677, so that if P is the present mean rate at which 

 sunshine is received per unit area in summer in the northern 

 hemisphere and L the length of the summer;}: 



P = %=■ = 0*97978 u a . 



Wl-e 2 



So too if p is the present winter rate I find 

 p = 1*02138 u . 



* The heat received on the area when the earth is in a given position is directly 

 as the time and inversely as the square of the distance, r, from the sun. Id an 

 instant therefore it is proportional to dt/f 2 . By Kepler's first law this is equal 

 to 'd&/h where # is longitude and h a constant. 



f See Nautical Almanac for 1895. 



\ The coefficients are stated to five figures not because they are of themselves 

 of interest to this degree of accuracy, but because in checking the tabulated 

 values the numbers really used should be known. 



