154 DR. C. CHBEE: AN ENQUIEY INTO THE NATURE OF THE RELATIONSHIP 



The values found in the several cases for a, b and b/a, with the corresponding 

 values from RAJNA'S formula (I.), appear in Table I. 



TABLE I. Milan Declination Ranges. 



4. It is certainly satisfactory that the values of a and b for the period 1890 to 

 1900 differ so little from RAJNA'S values for the long period 1836 to 1894. The 

 probable error, employing my values of and b, is only some 4 or 5 per cent, less 

 than that found when employing KAJNA'S values for the long period. 



In considering the results for the two earlier periods, we must remember the want 

 of homogeneousness referred to above. The mere existence of KAJNA'S formula (I.) 

 seems, however, evidence that, in his opinion, the want of homogeneousness is not 

 serious, and the similarity of formula? (I.) and (11.) to a certain extent supports this 

 view. 



The period 1837 to 1850 gives a very high value for a and a distinctly low value 

 for b. The outstanding features of this period were the high mean sun-spot 

 frequency, and the largeness of the declination range in the years of sun-spot 

 minimum. Unless the results are very sensibly affected by heterogeneousness in the 

 data, we must conclude that values calculated for a and b from a period as long as 

 14 years may depart somewhat widely from those calculated from a different equal or 

 longer period. The range of variability would seem least in b and (naturally) 

 greatest in b/a. 



The value calculated for b from the period 1854 to 1867 agrees well with RAJNA'S, 

 but the value found for a is distinctly lower than his. The sun-spot frequency 

 during this period presented similar features to those occurring in the 11 years 1890 

 to 1900. 



Greenwich Declination and Horizontal Force Ranges. 



5. A second long series of data is that employed by Mr. ELLIS in two papers,* in 

 which he compares D and H ranges at Greenwich with sun-spot frequency. 

 Mr. ELLIS gives the observed D and H ranges from the diurnal inequalities for each 

 month of the period 1841 to 1896. These are based on all days, excluding those of 



* ' Phil. Trans.,' vol. 171, for 1880, p. 541 ; ' Proc. Roy. Soc.,' vol. 63, 1898, p. 64. 



