PLOTTING.
So many curves have been made in connection with this study that a practically uniform system throughout has been adopted. The paper used is a cross-section paper with the smallest divisions 2 mm. in extent and with heavy lines at every centimeter. The smallest divisions are uniformly used for one year unless in some special study. For the illustrations, these plots are traced and drawings made from which the engravings are reproduced. For use in the periodograph, the plot is made on the same scale and continued in length to any amount up to about 40 inches. The space between the base-line and the curve has then been cut through with a sharp knife, usually a razor blade, and the curves have been mounted in long strips some 4 inches wide and 50 inches long, and the backs painted with opaque paint. In this way they are mounted for analysis. A mirror behind reflects light of the sky overhead through the curve and supplies the necessary illumination for photography.
Problems in plotting. — In connection with the plotting of the curves used in this study, certain problems have arisen which seem worthy of consideration. The ordinary plot and the ordinary averaging seem extremely good and appropriate when the variations are small in comparison with the mean values, but when the variations are large in comparison with the mean values it does not seem to the writer certain that the usual plotting conveys an accurate idea or gives a suitable basis for further work. This may be illustrated by the plotting of rainfall. If the rainfall doubles in some unusual year, it produces an immensely greater change in the area of the curve than when it goes to one-half of the mean. Doubling the mean produces the same changes as going down to zero, though in proportion the latter is infinitely greater.
The enormous exaggeration, therefore, of excessive rain values was felt to introduce misleading material in the ordinary form of a plot. In order to overcome this at least one experiment has been made with what is called a bilateral plot. In this the quantities from 0 to 100 per cent of the mean are plotted as before, but the quantities over 100 per cent of the mean are inverted in percentage and plotted above the mean line on an inverted scale. It is recognized that this is not the perfect way of making a plot of this sort, for by this plan the mean value of the new curve will not be at the same point as before, but will be somewhat below it. However, the matter is only in the experimental stage and it has not been thought necessary to work out a correct procedure.
