14 



REPORJ." — 1872. 



The solution of the equations (6), when these groups of numbers were 

 successively substituted, gave then the two sought-for sets of results as 

 follows : — 



called 



The increment 



pertains to 

 the constants. 



"2 



"3 



"4 

 a. 



a- 



,1'0 



.2-0 



-.2 1 



'J 

 o 







2-2 



9 



Column of ?n, 



or values of 



annual increments 



for 1811. 



—0-916 

 —0-303 

 -0-388 

 -0-301 

 -0-795 

 + 0-966 

 -0-314 

 4-0-027 



Column of §,„.., or 



values of annual 



increments 



for 1843-5. 



+ 1-.339 

 -0-465 

 + 0-280 

 -0-829 

 -0-621 

 -0-290 

 — 0-255 

 -0-242 



Now, with the help of this Table, the rule for the reduction of any magnetic 

 element that had been observed in the year 1829 + 7 (with r for any positive 

 or negative number) to what it must be stated to have been in 1829, proved 

 to be : — 



1. That to the observed value must be added the number which hereto- 



fore has been uniformly designated by n ; 



2. That this n has to be calculated 



by the schedule (1) (under "I when a d or a declination is to 

 " A. On the equations" &c.) J bo reduced ; 



by the schedule (2) (under "I when an i or an inclination is 

 the same) J to be reduced ; 



by the schedule (3) (under 

 " B. On the equations" &c.) 



by the schedule (4) (under 

 the same) 



when X or the northern hori- 

 zontal component is to be 

 reduced ; 



when Y or the western hori- 

 zontal component is to be 

 reduced ; 



by the schedule (5) (under! wli en Z or the vertical com- 

 the same). J ponent is to be reduced ; and 



3. That, independently of the nature of the observed element, when 

 calculating its reduction n, there must be substituted, in the 

 formula employed, for a^ (with ^ for the integers successively from 

 1 to 8), a 5^ which corresponds to the following expression, when 



