64 



O. A. Åkesson 



from the equation (34). It would, however, involve very long an.d arduous work to 

 obtain a result in this way. 



Another method, which if practicable, would more easily give a result, is the 

 following. We assume a probable hypothesis ol the connection between and 

 on one side, and the spot area on the other, and afterwards we try to determine 

 the constants. Thus, by way of trial, I have assumed the dispersion arising from 

 he proper motion of the spots to follow a law of the form 



(35) '^ = 7^' 



analogous to Maxwell's law of the distribution of the velocities of molecules, where 

 /»G- = a constant, 



m being the mass of a molecule. The dispersion arising from errors in the measure- 

 ments I suppose to be proportional to the section of the spot, thus 



36) = Ä-.,10^"' . 



Hence it follows, that the observed dispersion a might be expressed by 

 (37) G' = ^^k,no"\ 



0) 



Now the above, as well as other similar hypotheses, do not exoctly agree with 

 the graphical representation, given in fig. 7, for which reason I do not here~state 

 the calculations made. That it does not seem quite possible to give as a simple 

 function of the spot-area is evident from the fact of the large spots often consistmg 

 of a great number of small components. Since, however, owing to reasons previously 

 stated, it would seem as if the portion of the dispersion arising from errors in the 

 measurements, forms a fairly inconsiderable part of the observed dispersion, I do 

 not enter into any determination of and g.^ . Besides, the equation (35) gives an 

 approximate representation of the dispersion as a function of the spot-area. The 

 curves given in fig. 7 are thus drawn through the observed values of dispersion, 

 without the aid of analytical expressions. 



That this intimate connection existing between the dispersion and the spot-area 

 has a simple mechanical explanation seems most probable. 



