In Fig. 139 the method is nearly identical with that used in Fig. 138, except that in Fig. 139 we are determining the greatest possible rate of uniform consumption from a fiuctuating supply, instead of determining the smallest possible rate of uniform supply for a fluctuating consumption. In Fig. 139, the lines beginning at the hump in 1870 are drawn at different angles to touch the different humps and show various rates of possible consumption. These flow lines are also continued in the other sections of the curve just as if the curve had been shown continuously in one line instead of in three separate sections. The scale for Fig. 139 is selected to show "million

CUMULATIVE CURVES 163

gallons per square mile." The scale could just as well have been made to show the total gallons of rainfall in the whole watershed, but it was more convenient to put the scale on a square-mile basis, dividing the total rainfall by the number of square miles in the watershed.

Cumulative or mass curves are very frequently used for the study of quantities in earth work, especially in railroad construction. Cumulative curves showing the total quantities of earth removed from cuts and the total amount used in fills can be kept to give the whole information in the most convenient form for quick reference and accurate study.

Chapter X FREQUENCY CURVES. CORRELATION

MANY business problems can be studied most rapidly and conveniently if the data are put in the form of frequency curves. Though engineers have used curves for many years to represent data relating to the laws of physics, the engineer has made practically no use of frequency curves such as are used by the biologist. This is probably due to the fact that the engineer can determine the laws of physics from mathematical computations based on a relatively small number of observations, while the biologist must deal with statistical averages based upon observations and measurements in thousands of different cases.