196 ILLINOIS ACADEMY OF SCIENCE 



to the true value of the average inclination as can be obtained. 

 The accuracy of the result depends on the contour interval, on 

 the faithfulness with which the topography is represented on 

 the map, and on the accuracy of the measurements of the 

 lengths of the contours and of the area. 



Finsterwalder's method is doubtless the best that can be 

 devised for maps on which the contours are few, far apart, 

 and moderately smooth, but it is very laborious and subject 

 to considerable inaccuracy of measurement when applied to 

 maps on which the contours are closely spaced. 8 There are 

 many occasions when a less laborious method, even if less 

 accurate, is desirable, and when the graphic method here pro- 

 posed should prove useful. 



The graphic method is based upon the principle, demon- 

 strated by Finsterwalder 4 that the tangent of the angle of the 

 weighted average inclination of a profile line is the 

 arithmetrical sum of its acclivities and declivities divided by 

 its projected length. 



In accordance with this principle, the tangent of the angle of 

 average (weighted) inclination of a meandering profile drawn 

 across a map would be equal to the sum of all the acclivities 

 and declivities divided by the projected length of the profile. 

 Such a profile, if drawn across a map in such a way as to be at 

 all points at right angles to the strike of the surface, (crossing 

 all contours at right angles) would permit the determination 

 of the actual average inclination of the land surface along the 

 line of the profile. A network of these meandering profiles, 

 all drawn at right angles to the strike of the surface at every 

 point, furnishes a means of determining the average inclination 

 of the surface of the region with a degree of accuracy which, 

 as will be shown in the following paragraphs, depends on the 

 nature of the topography and on the number and locations of 

 the profiles. 



In practice it is not necessary actually to draw the profiles. 

 The operation is carried out graphically as follows : with a 

 straight edge of paper and a sharp, hard pencil, begin at some 

 point chosen at random in the area to be measured. Lay the 



•A map-measure, a self-recording toothed wheel so constructed as to turn freely 

 on a pivot, is on the market and will be found very useful for making linear 

 measurements of meandering lines such as contours. 



4 Loc. cit. 



