two curves will be as nearly as possible at equal distances from the zero line. It is difficult to prove a "lag" unless the scales are selected so that the peaks and valleys in the two curves are at the same height above zero. After the two curves have been plotted separately to carefully selected scales, they may be superimposed and read through both sheets of paper held in front of a bright light. As the horizontal scales for the two curves are the same, it will be found, if the curves depend upon each other without the element of "lag," that the peaks and valleys will almost coincide. If there is "lag," it will be found necessary, in order to make the peaks and valleys coincide, to shift one sheet horizontally over the other so that the horizontal scales disagree. When the paper has been shifted back and forth until the nearest possible coincidence of the two curves has been obtained, the extent of the "lag" may be determined by seeing how far the two horizontal scales are out of agreement. "Lag" is an important feature of many different sets of curves and must be kept constantly in mind when curves are being compared.
In Fig. 137 the growth in the importance of the loan department can readily be seen by considering the twelve-months progressive moving average showing the average total monthly loans. Though there is, in January, 1912, a very high peak which overshadows all other peaks, the general tendency of the curve is still rapidly upward, because of the fact that a number of high points follow each other in close succession, each nearly as high as the peak of January, 1913, which stands out alone with low points on either side.
The number of separate loan accounts opened and the number of accounts closed is shown in Fig. 137 by means of cumulative curves. The fact that the cumulative curve for the number of accounts closed follows so nearly the angle of the cumulative curve for the number of accounts opened, shows that the number of accounts outstanding has not greatly increased. It also shows that since numerous accounts are being closed, the loans are being made to other employees rather than being repeated continually to the same employees.
Fig. 138 is a study made to determine the size of tank necessary to supply sufficient boiler-feed water for a number of locomotives and tugboats. The average amount of water used each day by all the locomotives combined is given in the lower cumulative curve. The shape of the curve shows that locomotives fill their tanks chiefly between six and nine o'clock in the morning and between five and
