XX 



ON CLIMATOLOGICAL AVERAGES FOR COMPLETE SMALL 

 CIRCLES OF LATITUDE 



BY PROF. DR. W. VON BEZOLD 



[Sitzungs Berichte der Berliner Akademie fur igoi, pp. ij^o-i^^. Translated 

 from Gesammclte Abhandlungen, Berlin, igo6, pp. S57~37 ^ 



In a previous memoir 1 I have referred to the fact that in the 

 tabular or graphic presentation of average values for the complete 

 parallel-circles it is not advantageous to choose the geographical 

 latitude as argument or as abscissa. By this method of presenta- 

 tion which has hitherto been exclusively employed we obtain a 

 picture in which the polar regions are relatively too prominent. 



It is well known that the zones included between small circles 

 having the same difference of latitude correspond to very different 

 areas according as they lie in high or low latitudes. 



In a table progressing by equal angular differences the numbers 

 between the equator and latitude 30 occupy only one-half as much 

 space as those relating to the higher latitudes 30- 90 , whereas 

 that part of the earth's surface between thirty degrees and the pole 

 is not larger than the zone between the equator and 30 . 



A table arranged in steps of io° gives to the zone from o° to io° 

 only the same space as that given to the polar cap between 8o° 

 and 90 , whereas the former occupies more than eleven times the 

 area of the latter. 



Similarly a graphical presentation in which the geographic lati- 

 tudes are chosen as abscissae produces a wholly distorted image 

 from which one can obtain a correct idea only after careful medi- 

 tation. But the matter is entirely changed when we introduce the 

 sine of the geographic latitude as argument or as abscissa. When 

 this is done then the same tabular differences, i.e., equal differences, 

 of the arguments or equal distances on the axis of abscissas, 

 correspond to zones of equal areas on the surface of the earth and 

 the separate values or ordinates appear to have the weight that 



1 No. XIII of this collection of translations. 



416 



