CYCLOGRAM ANALYSIS 49 



Limits of Range — The track as first introduced in 1918 carried the analyz- 

 ing box toward or away from the cycleplot placed in a window for sky illumi- 

 nation. In 1920 the reconstructed instrument had for a time a stationary 

 analyzing box and a single movable mirror. This gave a range from 6 out 

 to about 25 units. Two more mirrors introduced into the light path extended 

 the range to about 35 units. For some years now the range has been extended 

 to 42 units by lengthening the track. 



One finds from experience that the mirrors must be very firm and not 

 allowed to move in their mountings; the track must be exceedingly straight 

 and without irregularities that might change the alignment of the mirrors; 

 and that the scale along the track should be tested occasionally to make sure 

 that some little vibration has not altered it, or to check for any slight error 

 in adjustment of the automatic focusing device. 



Cycle lengths less than the minimum setting of the instrument are rather 

 difficult to determine and are best reached by replotting at enlarged hori- 

 zontal scale. An attempt was made to use finer analyzing plates with more 

 lines to the inch. But that was found to change the scale readings of the 

 instrument and the pattern looked unfamiliar; so we resorted to replotting. 

 A scale of x4 is used more often than any other. It works well in testing the 

 "2-year" cycle (Chapter V). Of course, plots at odd sizes of scale are sent 

 to us for analysis and corrections are readily applied to the readings. Tests 

 of cycle values at "unknown scale" need only a change of plus or minus 10 

 to 50 per cent; a pantograph will do this quickly and accurately. 



Resolving Power — One might class under the resolving power both the 

 lower limit of the cycles that can be seen with the instrument and the accuracy 

 with which a setting is made on a cycle. The former is a question of range 

 but it is not so much a mechanical limitation as a mathematical or statistical 

 one. It takes 3 or 4 points in the data to locate a cycle. Our smallest read- 

 ing is 5.0, which seems quite safe. But the Hanned curve is used in 90 per 

 cent of our work and this process enlarges the independent terms and so 

 there are less than 5 in our 5.0 cycle. A running mean of 3 gathers 3 together 

 in one point, reducing the number of original data to one-third, and one 

 could not rely on settings at 5.0. But the Hann has a statistical "conserva- 

 tion" 1 of less than 3; it may be as little as 2, for it does not remove entirely 

 the effect of strong individual departures. At any rate, in a Hanned sequence 

 we readily see cycles at 4 and even sometimes cycles at 3. This is not by 

 direct setting at these figures but by harmonics that are more easily reached. 



The accuracy of making a setting on a row or alignment of maxima de- 

 pends on the length of the sequence of maxima, the precision in periodic 

 occurrence of the maxima, on the number of repetitions of the cycle and on 

 the percentage duration of the maxima in terms of the cycle length. This 

 last is usually a quality in the data, but it also depends on the size of the 

 opening in the analyzing lines expressed in per cent of the width between 

 the centers of the lines. This then becomes in some cases a limiting factor 

 in the accuracy of setting. In early forms of the cyclograph this ratio was 



1 See page 58. 



