50 CLIMATIC CYCLES AND TREE GROWTH 



0.3; then it was reduced to 0.25, and now for some years it has been close 

 to 5 per cent of the constant spacing of the lines. This opening may be said 

 to smooth the data by a running mean of its equivalent percentage of the 

 cycle length. The smallness of the opening reaches a practical limit when the 

 cyclogram becomes too faint to be properly seen or conveniently photographed. 



Lag Analysis — This refers to two prisms so arranged close to the main 

 cylindrical lens of the cyclograph that the beam of light from that lens to 

 the analyzing plate divides into three parts, two of them making displace- 

 ments of the cylindrical pattern on each side of the normal by an amount 

 equal to the space between the analyzing lines. In this way analysis is made 

 of the data in normal position and with lags of one and two cycle lengths all 

 at the same time. This is the equivalent of averaging overlapping cycles, 

 which has been found very efficient. 



A small pantograph is being arranged by which to sketch at once any 

 pattern on an enlarged scale. A photographic attachment has long been 

 used for similar purpose but it is less rapid, though more accurate. A number 

 of moving pictures have been taken of the changing cyclogram as the mirror 

 moved outward, each one built of about 650 separate exposures. The attach- 

 ment for the purpose was built by Dr. V. A. Brown and the pictures were 

 taken in 1929 in our laboratory. The pictures show well on the screen but 

 improved projection devices and other features are needed to make these 

 pictures a practical aid in analysis. 1 



CYCLOGRAM READING 



Attention is called to Plate 16C which gives an analysis of 500 years of 

 tree-ring record near Flagstaff. A cyclogram from these data was illustrated 

 in Volume I, Plate 12f, and this cyclogram is taken from Volume II, ibid., 

 plate 9, figure 7 and figure 19, number 7. Our plate includes the explanatory- 

 diagram, showing the cycle lengths indicated in the various alignments. The 

 setting is made at cycle length of 14 years. One has a choice here between 

 a slightly varying line that passes horizontally through all the data at an 

 average value of close to 14 and a straighter line at 14.2, with a 180° phase 

 reversal at 1820. There are often some signs of double crests in the 14-year 

 cycle and such a phase reversal is not an impossibility. 



From the beginning at about 1400 to about 1635, an 11.3-year cycle (or 

 close to that) is evident if one looks at a low angle across this cyclogram. 

 During the early part, and even to 1520 or so, this 11.3-year cycle shows two 

 crests and thus becomes a Hellmann cycle. The 57-year beats of inter- 

 ference between 11 years and 14 years are conspicuous. From 1650 more 

 or less to perhaps 1800 one can see the sharply inclined lines of a 10-year 

 cycle, or coarser lines slanting the other way that read near a 21-year cycle. 

 This cyclogram was made from an early plot that did not carry quite the 

 technique used today but it approximated closely enough to give a good 

 illustration. (Another cyclogram reading is given on pages 122, 123.) 



1 Construction of a modified form of cyclograph with a much shortened track, is 

 now in progress. 



