26 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. Jl 



lation is 0.60 and in the second 0.64; see table VIII, column p and 

 columns one to two. This analysis appears to prove that there exist 

 simultaneously periods of different length in solar radiation. 



Study of Periodic Changes in the Temperature at Buenos 

 Aires by Means of the Harmonic Formulas 



In order to try every available method of attack on this complex 

 problem, it was decided to try an analysis of the data by the harmonic 

 formulas. 



The points to be considered in such an analysis were that the 

 periodic terms are very variable and the periods apparently reverse 

 in phase from time to time. 



After much consideration and many experimental efforts, it was 

 decided to compute the harmonic terms for each individual period 

 and assume successive trial periods differing by one-half day begin- 

 ning with three and running to 12, and afterwards assuming suc- 

 cessive periods differing by one day up to 16 days, and by two days 

 from 16 to 30 days (omitting only the period of 28 days). 



The formulas used were as follows : Let l^, l^,U. . . . ln_x t>e observed 

 values which are associated with equidistant values of some argument 

 (say time) ; then the single periodic terms ; namely, coefficients of a 

 sine curve passing through the observations, may be represented by 

 the formulas : 



L = A^-\-A^ cos <i> + B^ sin </>,, (4) 

 in which 



4i.= tan^, (8) a= VAJ+B? or a= 4^, (g) <t^=^^-'^. (10) 

 i) J sm (7 11 



^ wangle of epoch; namely, the angular distance from zero to the 

 part of the sine curve at the time of the first observation. The quad- 

 rant of 6 is determined by the signs of A-^ and 5^, being in the first 

 quadrant when the signs are +/ + , in the second when they are 

 + / — , in the third when they are — / — , and in the fourth when they 

 are —/+ ; a = amplitude. 



Diagrammatically A.^ and B-^ may be represented as the sides of a 

 triangle as in figure 7. 



The angle 6 is not the angle derived by dividing the sum of the 

 sines by the sum of the cosines, but is the complement of that angle 

 and measures the angular distance from O to E. 



