18 REPORT 1872. 



their turn gave the final equations for the most probable twenty-four values 

 of Gaussian constants. 



It appears that by so doing we have given to the data of observation, 

 first, the requisite symmetrical repartition over the earth, and then, secondly, 

 to all its parts the nearest possible equality of weight. Indeed, when selected 

 as just said, there followed one another quite casually, on each parallel, 

 observations that were instituted in 1829 and those which had been 

 reduced to this year, now from the earlier date of their direct validity, 

 now from the later one. These data became therefore affected by the stiU 

 remaining defects of reduction to a different extent and in alternate directions, 

 just as by those inevitable errors of observation which the usual formation of 

 final equations supposes to exist in their numerical material. 



But then, lastly, as to the reduction of elements from the spots of direct 

 observation to the neighbouring predetermined points, we have avoided its pre- 

 judicial influence by alwaj's using a merely mechanical interpolation, relating 

 to points which in latitude as well as in longitude differed in alternate 

 directions from those points to which we were to reduce them. 



The following Table contains, according to the hitherto used notation 

 of X:=/cosi cosd, Y=/costsinrf, and Z=/ sin?', those values of 270 magnetic 

 elements for 1829 on which our new values of the Gaussian constants have 

 exclusively been foimded. To these fundamental numbers are added under 

 AX, AY, and AZ, their respective excesses on the values which a computa- 

 tion with the old assumed constants assigned to them. These latter numbers 

 show thus to what extent the hitherto existing theory of terrestrial magnetism 

 still wanted correction in different paits of the earth's surface. 



It is still worth mentioning that, for the determination of our following 

 normal values of X, T, and Z, we have employed out of the vicinity of the 

 parallels 



to M= 23°, 39 observed elements. 



or altogether 303 direct measurements for 7 parallels with 189 normal 

 values. 



As for the remaining three parallels, to m = 130°, m=150°, and « = 165°, we 

 have directly (though always after reduction to 1829) assumed the 81 elements 

 which General E. Sabine, in his ' Report on Magnetic Observations in the 

 Antarctic Ocean,' assigns to the intersections of these circles with the 

 meridians to X = 40°r, where v denotes the integers from to 8. He has of 

 course deduced these values from a larger number of observations at neigh- 

 bouring points ; and by assuming this number to be 97 or from 32 to 33 for 

 each parallel, we finally obtain 400 for the number of direct measurements 

 that have been used for the estimation of the following 270 normal values. 



