428 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51 



always represented by the area of the portion bounded by the corre- 

 sponding portion of the curve, the initial and final ordinates and the 

 intermediate portion of the axis of abscissae. 



Similarly the whole of the surface that lies below the curve for 

 any given day is proportional to the sum total of the insolation 

 that the whole earth receives on that date and inversely proportional 

 to the square of the distance of the earth from the sun. 



If now by means of a planimeter or by means of mechanical 

 quadratures, using the tables in which the argument is the sine, 

 we convert these areas into rectangles, then the vertical sides of 

 these rectangles represent the average sum total of insolation for 

 the whole earth, and of course similar results may be obtained for 

 all elements that can be plotted in corresponding manner. 



By the application of this method to the numbers under D in 

 table 1 we obtain 299.3 or m round numbers 300 thermal days 

 as the mean amount of insolation received annually. 



If now we imagine the energy given by the sun annually to the 

 whole earth's surface as distributed uniformly over this surface, 

 then on the average every element of the surface would receive 

 as much as an equal surface element at the equator receives in 

 300 average equatorial days. 



We can thus also determine with great ease the latitudes that 

 receive annually this average sum total of insolation. We have 

 only to seek in the preceding tables the places at which D = 300. 

 This value we find at sin <p = 0.6 or if we interpolate more accur- 

 ately sine <p = 0.604 which corresponds to <p = ±37° 9'. Hence 

 those points on the earth's surface (or the upper limit of the atmos- 

 phere) lying between the parallels of 37 9' north and south receive 

 more than the average insolation and those lying poleward of 

 them receive less. 



For this reason Ave may appropriately designate these two paral- 

 lels as the insolation normals or the "Median lines of insolation." 



Since the sines are proportional to the surfaces of the corre- 

 sponding zones, it follows directly that 0.604 or 6/10 or 3/5 of the 

 earth's surface receives more and 2/5 receives less than the aver- 

 age quantity of radiation coming annually from the sun. 



In similar manner we can take from these same tables the "tem- 

 perature-normal" or the "median line of the temperatures" by 

 seeking that circle of latitude whose temperature is the same as 

 the average temperature of the whole earth's surface, which is 

 i 5 °C. 



In the northern hemisphere we find this latitude at sin <p =■ 0.62 



