146 CLIMATIC CYCLES AND TREE GROWTH 



regularity of period, number of maxima, regularity of amplitude, strength of 

 amplitude, kind of fractionization if any, and freedom from ambiguous 

 maxima and alternative settings. 



CYCLOGRAM FORMULAE 



A cyclogram pattern may show harmonics arising from two fundamentally 

 different causes. In one case the harmonic is only apparent and arises from 

 a fractionization of the pattern due to a fractional setting ; in the second case 

 the harmonic actually exists in the data under analysis. 



Harmonics Due to the Cyclograph — The following criterion may be used for 

 judging the fractionization of a setting. If the movable mirrors are set at a 

 point on the scale, i/j of a cycle length existing in data plotted at normal scale, 

 i/j being a simple ratio, then there will be i times the normal number of 

 horizontal rows in the pattern, every row consisting of a series of light dots 

 located one to every j successive lines of the analyzing plate. 



It has been found in practise that with the exception of settings at \, 

 \, \, and rarely \ and ?, the effect of harmonics and multiples is negligible, 

 and these when they occur can easily be recognized. It is possible that 

 the less simple harmonics determine to some extent, however, the apparent 

 presence in real data of subordinate, weak cycles which may not be real. 



Harmonics in the Data — Consider an arrangement, with a 12.0 unit stand- 

 ard cycleplot in the window, the mirrors set at 12.0 ; then the pattern consists 

 of five horizontal rows of light dots. 



Suppose we replace the 12-unit standard with any other cycleplot, which 

 also contains a 12-unit cycle and, in addition, a set of secondary maxima of 

 smaller amplitude spaced half-way between the major maxima. We now 

 find double the number of rows of light images in the cyclogram, every other 

 row being relatively faint. Two secondary maxima will give two fainter 

 companion rows of images. The departure from a straight alignment of 

 the rows of dots of course measures the departure of the cycle from a per- 

 fect cycle or periodicity. 



It is important to note that the secondary maxima will not be of as great 

 a mean amplitude as the fundamental. They may exactly divide the space 

 between the fundamental crests into 2, 3, 4, ... n parts depending on the 

 number 1, 2, 3, . . .(n-1) of secondary maxima, in which case there will be 5n 

 equally spaced rows in the pattern, or they may directly follow or precede 

 the fundamental, in which case there will be 5 similar sets of rows, the arrange- 

 ment of rows within the set depending on the positions of the secondary 

 maxima. Again, departure from straight alignment will depend upon de- 

 parture of the maxima from exact spacing. 



Alignment Formulae — Since cyclograms may be observed at all scale set- 

 tings between 5 and 42 units, the inclinations of cycle alignments in the pattern 

 change with the setting. Let origin of coordinates be at intersection of a 

 sweep line, analyzing line, and a horizontal cross-hair. Consider the rec- 

 tangular coordinates of the adjacent light dot in any alignment with reference 



