Ill] OF THE SECULAR GROWTH OF TREES 239 



In the case of trees, the seasonal periodicity of growth and the 

 direct influence of weather are both so well marked that we are 

 entitled to make use of the phenomenon in a converse way, and to 

 draw deductions (as Leonardo da Vinci did*) as to climate during 

 past years from the varying rates of growth which the tree has 

 recorded for us by the thickness of its annual rings. Mr A. E. 

 Douglass, of the University .of California, has made a careful study 

 of this question, and I received from him (through Professor H. H. 

 Turner) some measurements of the average width of the annual 

 rings in Californian redwood, five hundred yfears old, in which trees 

 the rings are very clearly shewn. For the first hundred years the 

 mean of two trees was used, for the next four hundred years the 

 mean of five; and the means of these (and sometimes of larger 

 numbers) were found to be very concordant. A correction was 

 appHed by drawing a nearly straight fine through the curve for the 

 whole period, which line was assumed to represent the slowly 

 diminishing mean width of annual ring accompanying the increasing 

 size, or age, of the tree; and the actual growth as measured was 

 equated with this diminishing mean. The figures used give, then, 

 the ratio of the actual growth in each year to the mean growth 

 of the tree at that epoch. 



It was at once manifest that the growth-rate so determined 

 shewed a tendency to fluctuate in a long period of between 100 and 

 200 years. I then smoothed the yearly values in groups of 100 

 (by Gauss's method of "moving averages"),, so that each number 

 thus found represented the mean annual increase during a century: 

 that is to say, the value ascribed to the year 1500 represented the 

 average annual growth during the whole period between 1450 and 

 1550, and so on. These values, so simply obtained, give us a curve 

 of beautiful and surprising smoothness, from which we draw the 

 direct conclusion that the climate of Arizona, during the last five 

 hundred years, has fluctuated with a regular periodicity of almost 

 precisely 150 years. I have drawn, more recently, and also from 

 Mr Douglass's data, a similar curve for a group of pine trees in 

 Calaveras County |. These trees are about 300 years old, and the 



* Cf. J. Playfair McMurrich, Leonardo da Vinci, 1930, p. 247. 

 t When this was first written I had not seen Mr Douglass's paper On a method 

 of estimating rainfall by the growth of trees. Bull. Amer. Geograph. Soc. XLVI, 



