30 



SMITHSONIAN MISCELLANEOUS COLLECTIONS 



VOL. 71 



by dots. Small triangles indicate the values of 6 corresponding with 

 maxima in the amplitudes ; larger triangles indicate the largest ampli- 

 tudes. At the bottom of figure 10 is shown a plot of the amplitudes 

 for 20 successive periods of four days. The plot of the successive 

 values of 6 may be called a phasograin and of a an ampligram. Plots 



Table IX. — Examples of Computation of Phase Angles and Amplitudes in 

 Periods of Four and Four and Five-tenths Days 



T 

 (I) 



2.3 

 7-7 

 3-9 

 2.9 



8 hialf-days 



(0 



0=298 



:3-7i 



(2) 



T 

 (2) 



3-3 

 3-9 

 2.3 



4.2 



Dif. 



-1.0 

 3-8 

 1.6 



-1-3 



Sin 

 values 



0.0 

 0.7 

 1.0 

 0.7 



Cos 



values 



1.0 

 0.7 

 0.0 



-0.7 



Products 



Sin 



0.00 



2.66 



1.60 



- -91 



Cos 



— 1. 00 



2.66 

 .00 

 .91 



Sums 



+3-35 +2.57 



6 = 37' 



0=1.05 



9 half-days 



(I) 



1.9 



4-0 



4.0 



9.2 



7 



6.0 



1.9 



0.1 



2-3 



Sin 

 values 



0.0 



0.6 

 1.0 

 0.9 

 0-3 

 -0-3 

 -1.0 

 -0.9 

 —0.6 



Cos 



values 



1.0 



0.8 

 0.2 



o-S 



—0.9 



-0.9 



-0-5 

 0.2 

 0.8 



Products 



Sin 



0.00 



2.40 



4.00 



8.28 



2.16 



—1.80 



— I .90 



— 0.09 



—1.38 



Cos 



1.90 

 3-20 



0.80 



— 4.60 



—6.48 



5-40 

 0-95 

 0.02 

 1.84 



Sums j-l-ii.67 



—9-67 



1 = 320" 



■3-37 



of this kind were made for each period computed. It is seen that the 

 plot of the amplitudes shows irregular variations. The interpretation 

 of this is that the maxima indicate times when the phase of two or 

 more periods come together. The secondary maxima were inter- 

 preted as indicating that two periods were beating together, that is, 

 were in the same phase, while the larger maxima indicate that three 



