CHAPTER V. 



Correlation between the Longitude and Latitude Motions 

 of the Sun-spots. 



In the preceding cliapters we have investigated the motions in longitude and 

 latitude respectively. Now we shall examine whether any connection exists 

 between these motions. When the material of observation was first divided according 

 to AX cos ß (= x) and Aß (= y), this distribution was given in the form of correla- 

 tion-tables between x and y. Such tables were obtained for each latitude-zone, 2,5 

 degrees broad, during each year of both periods. Tiiese original tables, amounting 

 to 438, I have given on pages 60 — 71, properly combined. In order to obtain 

 a better survey of the distribution, I have used a class-breadth of l.'o also in the 

 case of latitude motion. 



Even a cursory examination of these correlation-tables shows that the line of 

 symmetry of the frequency-surface of the motions within all zones in tlie northern 

 hemispliere has a different position from the line of symmetry in the southern 

 zones. From the tables it appears that in the former case, the greater of the prin- 

 cipal axes passes through the second and fourth quadrants, but through the first 

 and third in the latter. 



Hence we see that a connection does exist between the longitude and latitude 

 motions. The degree of such a connection is usually expressed by a number, the 

 coefficient of correlation r, the value of whieli cannot exeed ±1. If ?' = 0, the 

 variables x and y are independent, but if r=±l, a certain value of y corresponds 

 to a certain value of x, and vice versa. For further information, the reader is 

 referred to works on mathematical statistics ^ 



Designating the relative moments about the mean by 



1 For example G. Udny Yulk: An Iiitrod notion to the Theory of Stntisticf . I>onilon 1912. 



we have 



(38) 



Lunds Uni 



rsitets Årsskrift. N. F. 



Afd. 2. Bd 



9 



