152 DE. C. CHEEE: AN ENQUIRY INTO THE NATURE OF THE RELATIONSHIP 



Assuming the relation between any magnetic quantity R such as the daily range 

 of declination and sun-spot frequency S to be of the simplest type, 



E = a + 6S . 



(1), 



I determined the values of the constants a and 6 in a number of cases. The chief 

 results were as follows : 



Supposing each month of the year treated separately, it was found that both 

 a and b were conspicuously lower in "winter" (the four months November to 

 February) than at the " equinoxes " or in " summer " (May to August) ; but b/a was 

 larger in " winter " than at the " equinoxes," and larger at the " equinoxes " than in 

 "summer." The b constants were generally fully larger at the "equinoxes" than in 

 " summer," but to this there were exceptions. 



The values of b/a were distinctly larger in the case of inclination and horizontal 

 force than in the case of declination and vertical force ; generally they were larger for 

 inclination than for horizontal force, and larger for declination than for vertical force. 



In all the elements b/a was larger when R represented the sum of the 24 hourly 

 differences from the mean value for the day than when it represented the range in 

 the diurnal inequality. 



In (A) the letters D, I, II, V were used for declination, inclination, horizontal force 

 and vertical force respectively. This practice is continued here when it tends to 

 brevity. 



2. The first question now to be considered is as to the dependence of a and b on 

 the particular period to which the magnetic and sun-spot data refer. 



This is not so simple as might appear at first sight. Very few observatories have 

 magnetic records extending over any large number of years, and in the few cases 

 where such long records exist their homogeneousness is seldom, if ever, beyond 

 dispute. There lias usually been change both in the' apparatus and its environment, 

 and it is difficult even for those in immediate charge of an old observatory to know 

 what allowance ought to be made to put old and new records on a common footing. 

 This is especially true of V and I. The element where least uncertainty should 

 prevail is D, but even here there is usually cause for doubt. 



Milan Declination Ranges. 



3. RAJNA'" has recently considered a long series of data representing the mean 

 value for each year of the diurnal range of D at Milan. Since 1871 the range seems 

 to have been determined from regular daily observations at 8 A.M. and 2 P.M. ; but 

 previous to that date there seems to have been some lack of strict uniformity. 

 RAJNA has calculated values for a and b in the formula (1) from the data for the 

 59 years 1836 to 1894, and independently for the 24 years 1871 to 1894, employing 



* 'Rendiconti del R. 1st. Lomb.,' Series II., vol. 35, 1902. 



