PAPERS ON GEOLOGY AND GEOGRAPHY 199 



third, five; the fourth, seven; etc., in arithmetrical progres- 

 sion. Thus an approximately correct average may be ob- 

 tained. 



There are certain types of topography for which a state- 

 ment of the average inclination has little meaning from the 

 geographer's standpoint, though it still retains its value to the 

 engineer. Such are the types in which large and distinct units 

 of area possess markedly different degrees of inclination, while 

 each by itself is relatively uniform. The till plains of central 

 Illinois are examples. Broad, flat uplands are cut by narrow, 

 steep-sided valleys. A statement of the average inclination of 

 such a surface has small geographical value. What is needed is 

 a distinction of the two areas, and a statement of the average 

 inclination of each, together with an indication of its area. 



For the determination of the average inclination of each 

 division of such a region, the graphic method is admirably 

 suited, while Finsterwalder's method of measuring the lengths 

 of contour lines is, depending on the specific conditions, either 

 inapplicable or very complicated. 



SUMMARY 



In connection with several lines of investigation a statement 

 of the average inclination of a land surface is desirable. The 

 best method formerly used is, in many instances, slow and ex- 

 tremely laborious, and is subject to considerable errors of 

 measurement. The graphical method here proposed is simple 

 and easily and quickly applied. Its accuracy depends some- 

 what on the character of the topography, and is, to a large 

 degree, proportional to the number of measurements taken. 



It, therefore, serves either for quick, rough determinations, 

 or for those in which the maximum accuracy is required. By 

 the use of a close network of small squares the method may be 

 made to compare favorably in accuracy with its competitors at 

 a considerably lower labor cost. 



