APPENDIX 155 



non-symmetrical but often not widely different in height. It is evident that 

 if one should force these curves into such artificial form as a sine curve with one 

 crest, the position of maximum might be changed somewhat. It was felt 

 that there was not sufficient justification for this final smoothing, and the 

 summation curves were simply Hanned (Chapter II). 



Rows — As stated above, usually only an integral number of rows or repe- 

 titions of the cycle were considered for amplitude. In a few cases of longer 

 cycle lengths, half-rows were also permitted in order to make full use of the 

 data. 



Per cent Amplitude — The block method of summation for amplitudes, 

 using for fractional periods rows not all containing exactly the same number 

 of elements, has been discussed on pages 30 and 97. The difference between 

 maximum and minimum of the Hanned summation curve is the total range of 

 amplitude. Half this quantity, divided by the mean ordinate for the summa- 

 tion interval, is the per cent amplitude given. Here also, as in the case of the 

 position of first maximum, further smoothing, and elimination of the effect of 

 interfering cycles, might alter the results. It should be remembered that the 

 summation method will yield the true amplitude only with an indefinitely 

 large number of sets; the value obtained from the limited number of sets is an 

 approximation. 



A. D. Ratio — This test for cycle reality is discussed on pages 58 and 98. 

 The values, while significant statistically, are not in themselves decisive for 

 any individual case. 



Vertical Scale — This refers to the summation curves: See discussion 

 following. 



CYCLE SUMMATION CURVES 



The accompanying curves show the mean cycle forms derived in comput- 

 ing the amplitudes given in the tables of Chapter V. These curves become 

 part of the reduction process and should be made clear to the reader, because 

 the cycles may take forms quite different from the easy flow of the sine curve. 



Identity of the curves will be recognized by the number attached to each 

 curve which refers to a corresponding number given in the tables of Chapter V, 



Exactly one cycle length is plotted and, if necessary, the curve is slightly 

 smoothed by the usual Hanning process. In most curves the left end repre- 

 sents the date of beginning as indicated in the "duration" in the tables (the 

 phase may be checked by referring to date of first maximum), and the hori- 

 zontal scale is two years to the division. In the 5-year means it is, of course, 

 10 years per division. In laying out the curve for its repetitions the frac- 

 tional year at its end, if any, must be taken into account. 



