ANALYSIS OF SOLAR RECORDS 71 



Analysis of Monthly Sunspot Numbers — In our analysis of the monthly 

 numbers, 1750 to 1934, instrumental limitations lead us to consider cycles of 

 5 months to 30 or 40 in length. The monthly changes are strong and easily 

 analyzed within each spot cycle while the spots are relatively numerous, 

 but the changes become very weak at the minima. It is difficult to adjust 

 the small changing values during minima in order to place them on a level 

 with the large changes at maxima on a scale suitable for continued analysis 

 over long intervals including both maxima and minima. Nicholson's pro- 

 posal is excellent: to study each cycle from minimum to minimum. In 

 cyclogram analysis this is done automatically, for the overlapping of two 

 sunspot cycles at the minimum is very slight and can easily be marked on 

 the plot that is analyzed. 



For purposes of longer analysis, the changes at minima have to be "stand- 

 ardized." Other students of cycle analysis will recognize this need and the 

 dangers of its application. In our rapid cyclogram analysis it has been 

 possible to try several processes. In the first attempt, the smoothed annual 

 values were subtracted from the monthly values. This was not satisfactory 

 because it left the fluctuations near sunspot minima practically invisible. 

 In the second attempt the monthly values were divided by the smoothed 

 annual means, thus "standardizing" the curve into monthly percentage 

 departures from annual smoothed means taken as unity. But this raised 

 the changes at minima to enormous size, obviously a serious exaggeration. 

 So since we merely wish to make the minimal changes large enough to have 

 an importance of their own but not an equality with the changes at maximum, 

 we have used a process in between the two described; we have taken the 

 monthly values in their original form, added 10 spot number units to each 

 one, and then divided by the mean smoothed line, also with 10 units added, 

 and have plotted the results. This has been found to keep the minima sub- 

 ordinated without concealing their changes. 



The results obtained represent my own analysis made about 1918, further 

 examined in 1922 and repeated recently, and Mr. Schulman's independent 

 results obtained recently. Plate 18 gives the data in cyclogram form. 

 From the analyses we discover several things. Some cycles do pass 

 unchanged through the minima but cycles also seem to start and stop with 

 a slight preference for maxima and minima. A crude analysis was made of 

 the times of starting and stopping (crude because these times are not well 

 defined) and many beginnings and endings seemed to occur in a 10-year 

 cycle with occasional cutting to five years. Caution is needed in attaching 

 significance to this result. 



Cycles found in the monthly sunspot numbers may be condensed into a 

 frequency periodogram as in figure 31c, where the various monthly values are 

 brought together for comparison with radiation and other changes studied 

 below. The following table gives the data regarding them. 



