TERRESTRIAL MAGNETISM. 211 



and we can only fill these up with the greatest uncertainty. It 

 was soon found that the calculation must be pushed at least as 

 far as magnitudes of the fourth order, making the number of 

 co-efficients to be determined amount to twenty-four. In all 

 probabiUty, members of the fifth order will also be found in- 

 fluential ; but, in a first attempt, the values of h, m, k', &c. must 

 be stiU too much charged with errors, arising from the uncer- 

 tainty of many of the data (and which from their nature these 

 values involve), to permit the introduction of a still greater 

 number of unknown values in the process of elimination. 



It should be remarked that the intensities in Sabine's map are 

 expressed according to the arbitrary unity in common use, by 

 which the total intensity in London = 1-372. In these calcula- 

 tions, and in the tables given in the sequel, this unity has been 

 altered so as to make all the numbers a thousand times greater, 

 the intensity in London on which they rest being made = 1372. 

 It is obvious that a unity for the intensity may be taken at plea- 

 sure, since the unity for fi may be considered as arbitrary, and 

 made to accord therewith. If further deductions are desired re- 

 quiring fx. to be reduced to absolute measure, it will only be ne- 

 cessary to multiply aU the co-efficients by the factor which re- 

 duces to an absolute measure the intensities expressed according 

 to the arbitrary unity. 



26. 



The numerical values of the 24 co-efficients obtained by the 

 first calculation, the longitude X, being reckoned east from Green- 

 wich, are as follows : 



These numbers, which may be considered as the elements of 



