CYCLOGRAM ANALYSIS 



19 



mediates. In rare cases two more intermediates have been taken ; the formula 

 then becomes 



Y // _ Y n - 2 + 4Y n -i + 6Y n + 4Y n+ i + Y D+2 

 n ~ 16 



The Hann is especially useful in a very rapid graphic application, giving 

 a result very close to the exact numerical value. Any difficult case may be 

 solved quickly by slight additional care. If in an ordinary plot each three 

 points in succession be taken as a triangle, and the distance from the middle 

 of the base (connecting terms 1 and 3) to the central term be considered, 

 then the point § from base to the central term is the running mean of 3 and 

 the point \ from base to the central term is the Hanned value or second 

 intermediate, giving double weight to the middle term. After trifling prac- 

 tise, this is quickly done by hand on a plot and any doubtful case may very 

 easily be measured. Figure 7 shows the original data (solid line) and the 



1820 



1825 



1830 



1835 



184-0 



1.50 

 1.25 

 1.00 

 0.75 

 0.50 

 0.25 



Fig. 7 — Smoothing methods compared. 



same smoothed by second intermediates (broken line) which is practically the 

 same as the "graphic Hann," and also smoothed by a running mean of three 

 (dotted line). The figure shows that the weighted mean introduces less 

 distortion into the original data. Very long running means have been 

 abandoned in favor of a general treatment of long curves that will be described 

 below. 



Mass diagrams and residual mass diagrams are secondary curves much 

 used by hydraulic engineers because they show totals and trends (fig. 8). 

 A mass diagram sums up in a single ordinate the totals contained in the pre- 

 ceding data. For example, it may be the continued sum of the intake of a 

 reservoir and shows easily the total amount entering since any given date. 

 The curve inclines rapidly upward. For water use it is convenient, but for 

 climatic studies in which causes are sought, it is not well adapted, since the 

 latter requires the knowledge of the ratio of any one year to any other year 

 and that is not easily obtained from a mass diagram. The residual mass 

 diagram is the same thing as the mass diagram, except that departures from 

 the mean are used each year in place of the full values. The curve therefore 



