CYCLES 119 



each tree marked in some way to represent its resemblance. The best 

 four (D^4, 16, 20, and 21) were then taken by themselves, having a 

 regard both to this resemblance and to their wide distribution in 

 California, and the average record of the 4 trees plotted for 2,000 years. 

 These plots were slightly smoothed and duplicated so that each one 

 overlapped its neighbor half-way, and nearly every part of each tree's 

 record appeared twice. In exactly the same manner two other com- 

 plete sequoia records were prepared; one was an average of D-3, 12, 

 20, and 23, preferred for showing the sunspot cycle, and the second was 

 the "best selected" sequoias, with good consistent records. All these 

 were prepared by an assistant and marked by him with a reference 

 letter, so that I had no idea of the date or identity of any curve. The 

 assistant then selected 250 years of Flagstaff tree-records whose exact 

 dating was also unknown to me. Comparison was made by cycles 

 between the Flagstaff record and the unknown sequoia records. After 

 they were completed, all dates of resemblance were looked up, and it 

 proved that instead of the six possible correct coincidences, there were 

 a dozen apparent agreements, of which six, or 50 per cent, were correct 

 and the other six scattering. Thus it appeared that in group averages 

 there is a 50 per cent resemblance between the cycles in tree-growth 

 in Arizona and those in tree-growth in California, and that a fair 

 assurance in cross-dating between these two regions can be reached, 

 if one uses, as in this method, enough data from which to obtain a 

 convergence of results. 



Advantages of the cyclograph — This instrument, which converts 

 mathematical integration into a photometric process, has been used 

 almost exclusively in the analyses about to be described. Its extra- 

 ordinary advantage is its rapidity of analysis and its flexibility in 

 showing the analysis of every part of the curve at the same time in the 

 cyclogram or differential pattern, and also in its independence of 

 fixed periods, for it shows many periods at once, whether fixed, variable, 

 or broken. 



Disadvantages of the cyclograph — The chief disadvantage is that 

 in its present form one can not assign quantitative amplitudes. This 

 could be done by passing the photographic negative of the cyclogram 

 under a recording photometer, of which there are several types suffi- 

 ciently accurate. The amplitudes could be derived easily from the 

 galvanometer curve. 



PERIODOCRITE 



Professor C. F. Marvin, chief of the United States Weather Bureau, 



has suggested (1921) the use of a process which he names the period- 



ocrite. It simply solves the question : does the application of a given 



cycle reduce the probable error? If so, the use of the cycle is justified. 



9 



