64 CLIMATIC CYCLES AND TREE-GROWTH. 
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 illumi- 
nation 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 com- 
parison 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 experi- 
mental stage and it has not been thought necessary to work out a 
correct procedure. 
