72 Trans. Acad. Sci. of St. Louis. 



lines divided the maps into zones or sections, one zone 

 comprising, let us say, the territory whose mean annual 

 temperature lay between 50** and 55**, the next 55° to 60°, 

 etc. 



It was intended at first to find the areas included in 

 these several zones by the planimeter. Then, knowing 

 the area over which the mean temperature was 50°, an- 

 other over which it was 55°, etc., the average of the whole 

 might easily be computed. 



This integration by means of the planimeter was aban- 

 doned, however, for it was found by Professor Nipher 

 that the areas of different sections of the map as shown 

 by the instrument were not proportional to the actual 

 areas of those sections. It was also difficult to properly 

 weight the values with respect to areas, unless the areas 

 between the lines of equal value were subdivided into 

 smaller areas. 



The method actually adopted by Professor Nipher was 

 to take each state by itself, and for each year average all 

 the observations recorded, also filling in values by inter- 

 polation methods, where the reports were thinly scattered 

 in some portions of the state as compared with other por- 

 tions, so as to make the observations as evenly distributed 

 as possible. These interpolated values were estimated by 

 means of the values on each side of the deficient areas. 



As an illustration, Minnesota has naturally a great 

 many more stations to report from the southern and 

 southeastern parts of the state than from the northern; 

 perhaps the lower half of the state would have three- 

 fourths of the observations. It would be manifestly un- 

 fair to give the northern half of the state only one-third 

 the weight of the southern half in determining the rain- 

 fall or average temperature. In some states no inter- 

 polation was necessary, in others a great many were 

 added. Enough observations were on the maps original- 

 ly, however, so that these interpolations could be made 

 with a tolerable degree of accuracy. 



In Missouri in the year 1896 the number of observa- 



