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. 
