16 



AMPLITUDE OF THE SOLAR-DIURNAL VARIATION 



In determining the least square coefficients in these equations, allowance has 

 been made for the different weights due to the readings at the even and odd hours. 

 is reckoned from midnight at the rate of 15 an hour. To compare the numerical 

 quantities of the angles C l} C 2 , C s , C t , in the general expression 



A d = S l sin (0 + Ci) + A *in (20 + CJ + B 3 sin (30 + Q + B, sin (40 + C7 4 ), 

 with the same quantities in the formula of the diurnal variation (pp. 8 and 9 of 

 Part I), 180 must first be added or subtracted from each angle given there; since, 

 in the discussion of Part I, increasing numbers correspond to a decrease of western 

 declination, the scale being thus graduated, whereas, in the present case, increasing 

 positive numbers correspond to an increase of western declination, as stated above. 



The following table exhibits the close correspondence of the computed and ob- 

 served mean annual value of the regular solar-diurnal variation : 



The maximum difference at anyone hour is less than 11", and the probable error 

 of "any single hourly result is + 0'.05. The probable error of any single computed 

 value from a monthly expression is +OM9. 



By means of the preceding equations, the hourly values of the diurnal variation 

 for each month of the year have been computed ; and the results, projected in 

 curves, are given in Diagrams D and E. The first contains the curves for the 

 six months of the summer half-year, and the second those of the winter half-year. 

 Positive ordinates correspond to a westerly movement, and negative ordinates to 

 an easterly movement, of the north end of the magnet. The diagram following 

 (F) contains the type curves for summer, winter, and the whole year, all being 

 upon the same scale. 



by Mr. Karl Kreil from his discussion of declinometer observations at Prague, extending over ten con- 

 secutive years (1840-'49), and selected from a thirteen years' series, in order to obtain mean results 

 unaffected by the smaller inequality of the teor eleven year period with which our results are still 

 affected. Part I of the present discussion, however, affords ready means of changing slightly the numeri- 

 cal values of the coefficients B t , B s , B.,, B t , in our equations, in order to obtain the values we would have 

 obtained, had we discussed a consecutive eleven year series of observations or one extending over a series 

 of years corresponding to the actual length of the solar period then observed. Mr. Kreil's discussion 

 will be found in Vol. VIII of the proceedings of the mathematical and physical section of the Imperial 

 Academy of Sciences at Vienna (1854). 



