NO. 3 SOLAR RADIATION AND THE WEATHER— CLAYTON 3I 



or more periods were near the same phase. With these points in 

 mind the following rules were drawn up for determining the true 

 periods from the plots. 



1. Mark the epoch angles on the plot by some especial symbol 

 where the amplitudes showed maxima. (In the plot, figure lo, these 

 points are indicated by triangles.) 



2. Wherever a number of dots on the plot appear to lie in straight 

 lines, draw lines through them (see line 3.57 in figure 10). 



3. These lines should pass through or near the points where the 

 epoch angles coincide with maximum altitudes or beats (indicated by 

 the triangles in the plot) . Two lines at different angles to the hori- 

 zontal should pass through or near the angles coinciding with sec- 

 ondary maxima in the amplitude and three or more through or near 

 the angles coinciding with the larger maxima (see figure 10). 



4. When a line drawn through the points as indicated above slopes 

 downward from the horizontal the length of the true period, p, will be 



P=^, (17) 



and when it slopes upward, it will be 



w — I 

 in which p' indicates the length of the period used in the calculations 

 and n equals the number of periods and fraction needed for the line 

 to cross the abscissas differing by 360°, as for example, from 0° to 

 360°. The three lines drawn in accordance with these rules, in 

 figure 10, gave by these formulas estimated lengths of 3.57, 4.96, 

 and 5.98; while the true periods were 3.60, 4.80, and 6.10. 



5. To obtain the true epoch angle 6, at any time, read the angle 

 indicated by abscissas cutting the line at the selected point of the time 

 and correct it by the formula : 



'=«'+f^(^-/) 



The correction is plus when the line slopes upward and minus when 

 it slopes downward. 



With these rules and without any clue to the number or length of 

 the true periods entering into the plot, Mr. Rankin undertook to find 

 the true periods and submitted the following result given in the first, 

 second and third columns of table X ; the true periods and the ampli- 

 tudes used in forming the combined sums are given in the fourth 

 column. 



