GAUSS AND WEBER ON TERRESTRIAL, MAGNETISM. /" 



" One main difficulty in the application of this method con- 

 sists in the fact, that the above-mentioned law holds good, 

 namely, that the action of a magnetic needle is inversely as the 

 cube of the distance, with sufficient accuracy only for veiy great 

 distances, and where the effects are too small to be determined 

 with precision by direct observation. At moderate distances 

 the variations from the law become veiy perceptible ; but theory 

 teaches that these very differences are subject to rule ; and ma- 

 thematics afford us the means of recognising, and almost wholly 

 eliminating them, by the combination of experiments made at 

 various moderate distances." 



For the purpose of showing the application of the small mea- 

 suring apparatus to the above-mentioned observations, we shall 

 give lastly, in a few words, the necessaiy process of coiTection. 

 This is threefold : 



1. Instead of the values given hj direct observation for the 

 deflexions Vq, v^, v^, etc., of the needle by the magnet bar acting 

 at various distances, Bq, jRj, R^, etc., the following combined values 

 are to be taken : 



Vo = i («'o - «o' + «'o" - «o"') 



^1 = 4 (^'l ~ «l' + ^l" ~ ^l'") 



M 



2. To the approximate values of — , which were obtained by 



equation (IV.) 



M _B? tang v 



f ~ 2 

 the following corrections are added : 



M 



Approximate value of — . Correction. 



Rq^ tang Vq L 



_ 2 - R^ 

 R{^ tang V, L 



. 2 ~ 'R^ 



^2' tang v^ L 



2 "''• - -R^ ^^''' 



3. As the number of the measured dimensions i?Q, i?j, R^, etc. 



and Vq, Vj, ^2, etc., is greater than is required for the determina- 



M 



tion of the unknown quantities L and -=, , the rules of the calculus 



of probabilities are employed in order to obtain from them the 



