14 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 98 



The monthly means of solar radiation and the monthly sunspot 

 numbers were next multiplied hy a cosine series of five waves each 

 of eight terms ; the resulting means, when plotted, give curves like 

 those shown in figure n. Both curves show a period of about 8 

 months during the years 1920- 1929. The maxima in the two curves 

 differ slightly in time, the solar radiation maxima being occasionally 

 slightly behind and at other times slightly ahead of the spot maxima ; 

 but in the average the two are simultaneous, the greater amount of 

 solar radiation coming at the same time as the maxima of spots. 



These periods of about 11 months and 8 months are the same as 

 those found by Dr. C. G. Abbot in the monthly means of solar radia- 

 tion. In addition figures 10 and 11 show that there exist similar 

 periods in the monthly sunspot numbers coinciding in phase with the 

 solar radiation. 



These periods are not exactly 11 months, and 8 months in length. 

 They appear to be about one-twelfth and one-sixteenth respectively of 

 the sunspot period of 11. 17 years or 134 months. 



The analogy nearest to the process described is found in the 

 phenomena of sound. Certain physical objects, as for example, a taut 

 wire, respond only to sound waves of one rate of vibration or to waves 

 near that length. If waves of increasing length or rates of vibration 

 are sounded, the object will begin to respond with vibrations when 

 the key note of the object is approached and will show strong response 

 when the key note is reached. Changes in physical state may thus be 

 studied ; a glass tumbler will emit one key note when it is empty 

 and a different note when it is partially filled with water. 



In a similar manner changes in atmospheric conditions may be 

 studied by a succession of cosine waves, such for example as the 

 diurnal waves of temperature which have a large amplitude when the 

 sky is clear and a lesser amplitude when it is cloudy. 



The method of computation described here in the search for hidden 

 periodicities is slow and tedious, but efforts are in progress to perfect 

 a machine which will do the work more rapidly and more accurately. 

 The machinery consists of a Coradi harmonic analyzer, and a Fergus- 

 son universal pantograph which permits changing the horizontal time 

 scale to fit the analyzer without changing the vertical scale of quantity. 

 In this manner any series of harmonic waves of whatever length may 

 be mechanically integrated and the plot advanced step by step until 

 the entire curve is covered. 



Observed data are analyzed with this mechanism and the results, 

 when plotted, disclose any hidden periodicity near the length of the 



