POOR, THE FIGURE OF THE SUN 419 



The corresponding s}Tiodic periods are 26.92 and 33.35 days respectively. 

 Sun-spot observations give 27.25 days for the synodic period. This un- 

 certainty in the period prevents us from using the method of equations of 

 condition, similar to that used in investigating the fluctuations corresponding 

 in period to the sun-spot cycle. But Newcomb ^ has lately developed a 

 method, which he calls the "method of time-correlation," by which the 

 fluctuations in any measured quantity can be investigated and the existence 

 of or tendency towards periodic variations detected. This method may be 

 briefly outlined as follows. 



Suppose we have a series of values of a measured quantity for equi- 

 distant intervals of time, 



t, 2t, 3t, etc. 



and let 



be the departures of these values from the general mean. Now multiply 

 each one of these residuals in turn by the first residual, a^, so that we have 

 the products 



RaS^h* lin*!!* ^n^a 



If these residuals be purely periodic, having for a period some multiple of 

 t greater than 2, then these products will fall into a rh\i;hmical series. The 

 first product and the product corresponding to the end of the period wull 

 both be positive; the intermediate products, positive or negative. If we 

 form a similar series of products by multiplying the second and each suc- 

 ceeding one by the second residual, then these products will again fall into 

 a similar rhythmical series. Continuing the process we should have the 

 following: 



aoSo agaj apa, a^a^ 



ajSii ajaj ajaj ajaj 



a^S-Z ^2^3 ^"^i ^2^(i 



I I ■ I I 



Sums [aoao] [aoaj [agaj [a^aj 



If, now, the period in which the residuab repeat be 4t, then the first 

 and fifth products will in every series be positive, and therefore the sums 

 of these products, [a^ a^] and [ao aj, will be positive. The intermediate 



1 A Search for Fluctuations in the Sun's Thermal Radiation through their Influence on 

 Terrestrial Temperature (American Phil. Society, N. S., Vol. XXI, Part V). 



