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 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. 



