74 GAUSS AND WEBER OX TERRESTRIAL MAGNETISM. 



If we represent, according to this established unity, the mag- 

 netism of the needle by m, that of the bar by M, the distance 

 (supposed considerable) between them by R, and the moment 

 of rotation exerted by the bar on the needle by f, the reduced 

 moment of rotation is 



The position of the bar relatively to the ^ \ 



needle, assumed in this case, did not in fact P 



exist in the Gottingen experiments, but a 



different jjosition represented in the annexed ^ 



figure. However, the same thing is true of 



the two positions, with this single difference, 



that f has a different value, which we shall 



designate by F. In the Memoir '' Intensitas" 



&c., it is proved that 



F=2f 



•so that, 



FW 

 mM=i^ (II.) 



It is to this second case that the formulae, hereafter to be men- 

 tioned, will refer, as apphcable to the Gottingen observations. 



" In this way therefore we have a complete and precise idea 

 of the measm'c of the magnetic force of a magnetized needle. A 

 needle of twofold power will impart to one equally magnetized 

 a reduced moment of rotation = 4 ; and generally, when we 

 know the number for the reduced moment of rotation which a 

 needle imparts to another needle equally magnetized, we have 

 the absolute measure of the power of magnetism in each needle ; 

 it being the square root of that number. 



" There only remains then, in order to be able to reduce the 

 force of terrestrial magnetism to absolute measures, to give some 

 method by which the moment of rotation which a needle pro- 

 duces in a similar one at considerable distance, (and in the posi- 

 tion represented in the figure) may be determined with preci- 

 sion. A great difficulty might at first appear, from a circum- 

 stance purposely omitted in what has been akeady said, viz. 

 the impossibility of observing this very weak action of the needle 

 N S upon the needle n s, (which we will for a time suppose to 

 be magnetized exactly as strongly as N.S) ; since it cannot be 

 withchawn from the omnipresent, and much more powerful ac- 



