148 



CLIMATIC CYCLES AND TREE GROWTH 



smallest interval recognized being one-tenth unit. It is then easy to sum up 

 the columns, mentally transforming symbols into numbers, and obtain a set 

 of periodogram numbers. These when plotted form a weighted frequency 

 periodogram. 



It is evident from the optical nature of the cyclogram method of cycle 

 analysis that there is a logarithmically decreasing exactness in assigning a 

 cycle value with increasing length of the cycle. Hence, the abscissae of 

 the periodogram are taken to represent a logarithmically increasing range 

 from 5 to 42 ; in practise a range of 5 per cent is used, successive intervals over- 

 lapping by one-half the range. 



It is often of value to plot the individual cycle lengths in other ways than 

 the one described above and called a cycle diagram. For instance, a long 

 sequence of data may be segmented into several equal time intervals for each 



Fig. 57 — Construction of a frequency periodogram from ten groups 

 in the Central Pueblo area. 



of which a cycleplot is prepared; if the sets of cycle lengths obtained by 

 analysis are plotted in suitable symbols with the ordinates corresponding to 

 the successive time segments equally spaced, then slant alignments from one 

 segment to another may become evidence of cycle flow, i.e. gradual change of 

 cycle lengths. Again, by using time on a vertical scale and cycle lengths as 

 abscissae (or the reverse), it is possible to represent graphically the exact range 

 of occurrence of the cycles in any data. An example of this may be found in 

 figure 3 Id where it is called a chrono-periodogram. 



ERRORS OF THE INSTRUMENT 



The errors of the instrument fall into two classes, those involved in the 

 building of the cycleplot and those due to manipulation of the optical ele- 

 ments of the cyclograph. 



