GAUSS AND WEBER ON TERRESTRIAL MAGNETISM. 77 



The ratio which the force of the bar on the needle (at the 

 given distance R) bears to that of the earth's magnetism is ex- 

 pressed by the quotient 



F 

 niT 

 and accoi'ding to equation (III.) 



m 1 = , or — — = tang v. 



tang V ml 



But according to equation (II.) 



,^ FB? F 2M 



m M = , or — — = -=^-7^ J 



and, 2M ,--^ C . 



^^.Mr=^.tang., 



makes known to us the maximum moment of rotation which the 



bar A^ ith the magnetism M would exert on a similar bar at the 



distance R ; for this maximum, according to the fundamental 



2 M^ 

 laws of magnetism, must be " ; and the above equation, 



2M^ C ^ 

 gives —^3— = -^. tang v. 



This result, multipUed by the cube of the distance R, gives 

 double the moment of rotation ; and the square root of the half 

 gives the force of the bar in absolute measure ; or 



M= ly/^^'-J^"g^ (V.) 



If, finally, we divide by the moment of rotation exerted by the 

 earth on the needle, calculated according to equation (I.) we 

 obtain 1 / 2C „ 



^=T\/ RHangv' (^^-^ 



and this number expresses the absolute measui'c of the earth^s 

 magnetism. 



" This appears the most easily understood exposition which 

 can be given, without the use of mathematical signs, of the 

 possibility of expressing the force of the earth's magnetism by 

 a number which shall be perfectly independent of the individu- 

 ality of the magnetic bars employed. In the actual application 

 some points will appear in a somewhat different form, without, 

 however, affecting in the least the nature of the method; and 

 it will, besides, be necessary to take into consideration several 

 collateral circumstances." 



