For example, in a bacteriological examination of a pond at varying depths, distance below the surface would be the independent, and number of bacteria per cubic centimeter the dependent variable. In a seasonal gauging of a stream the dates of observation would be the independent and cubic feet per second of flow the dependent variable. Sometimes we consider more than two variables simultaneously, and we then have two or more independent variables from which to consider a dependent variable.

It is difficult to make a general rule for determining in any case which is the independent variable and which is the dependent variable. The decision depends entirely on how any set of data is approached and on the habits of mind of tlie investigator. When time is one of the variables it is usually, but not always, the independent variable. If we consider values or quantities at different dates, as in Fig. 80, time is very obviously the independent variable. If, however, we are interested in the length of time required to do different operations, as in Fig. 85, Fig. 86, and Fig. 87, our data are expressed in length of time and time is the dependent variable. This example is an exceptional case and it is named here only to show that, although time is

CURVE PLOTTING 85

ordinarily the independent variable when it enters into curve plotting, nevertheless there may be occasions when time is the dependent variable, and charts should be plotted accordingly. It is important that the person drawing a chart should in each case distinguish between the independent varial)le and the dependent variable, for this distinction affects the whole arrangement of the chart.