Prof. W. A. Norton on Terrestrial Magnetism. 221 



as remarkably small, when it is considered that these are first 

 determinations in which the nicest attention to accuracy would 

 have been misplaced. The same may be said of the determina- 

 tions of horizontal intensity and declination. The differences in 

 Tables IX and X, might be made still smaller by making the cal- 

 culations from a greater number of observed intensities. 



An elaborate discussion can alone decide the question of the 

 origin of the small differences (not due to errors of observation) 

 that exist between the computations of vertical and horizontal 

 intensities and declinations, and the observed values of the same : 

 —determine whether they are not attributable (partially or en- 

 tirely) to thermal differences between the magnetic crust of the 

 earth and the air, variations in the constitution of this crust in 

 passing from one point to another, &c, or are referable to small 

 deviations of the theory from the truth. 



Dip and Total Intensity. 



The total intensity, or directive force of the needle, may be 

 obtained by taking the square root of the sum of the squares of 

 the horizontal and vertical intensities ; and the dip by dividing 

 the vertical by the horizontal intensity. The quotient will be 

 the tangent of the dip. The error of total intensity will be in 

 ^l instances less than the sum of the errors of the horizontal and 

 vertical intensities. Denoting by E the error of vertical intensity 

 and by d the dip of the needle, the error (e) entailed upon the 

 total intensity by this, will be e= E sin d. The error e? entailed 

 by that of the horizontal intensity will be e l = E' cos d. The total 

 e ^or will then be nearly E sin d + E' cos d. This error, except in 

 ve ry low latitudes where the formula for the vertical intensity is 

 theoretically inaccurate, is every where less than 0-1, and gener- 

 % only a few hundredths. Denoting the total intensity by 

 M E cos d, 



M > we have, tangent of error of dip due to E= ~"|ji~~ J and > tan " 



E' sin d 

 gent of error of dip due to E' = — g— . Hence, tangent of total 



«n:or of dip * E^osrf -E^sm^ (nearly .) Without going into a 



detailed calculation, it may be seen that the error of the dip can- 

 not exceed 4°, (except near the equator on the western continent, 

 ^here the formula for the vertical intensity is theoretically mac- 

 CUf ate ;) and is generally very much less than this. 



tensity i 



.. ascertained, from a discussion of the observations 

 been made upon the intensity and dip, that the m- 



- ■■ " that the intensity is not 



This fact 



tensity is not a function of the dip ; or t 

 necessarily the same, though the dip i 

 sn °w s that the horizontal and vertical c 



same 



