WITH MAGNETISM AND ELECTRICITY. 187 



the bismuth had been several times regularly changed at the end 

 of each oscillation, and the limit of the arc of oscillation nearly 

 attained, an interruption was effected by permitting the bismuth 

 to remain unmoved during two oscillations, and then again regu- 

 larly changed as before. The negative arc of oscillation was 

 thereby suddenly converted into a positive one, which, however, 

 soon diminished to zero, and very soon afterwards passed over 

 into a negative ; the deflection caused by the bismuth (in its 

 upper and lower positions) was here most clearly exhibited. 

 When the arcs of oscillation are counted from that which is 

 nearest to zero, the arc nearest to the limit may, by means of 

 the known decrementum logarithmicum, be easily reduced to the 

 limit-value, and thus a more accurate mean value for the latter 

 may be found. For this purpose we have only to divide the ob- 

 served value of the riih. arc of oscillation in the above experiments, 



3 



where the decrementum logarithmicum was nearly = log. - by 



ji 



( 1 — (-] ). We thus obtain the reduced values exhibited in 



the fifth column, and the mean values derived from the latter 

 in the sixth column. From all the observations taken together, 

 we find the limit-value to be 



x=- 58-4. 

 From this limit-value of the arc of oscillation, the deflection E 

 corresponding to the needle's position of equilibrium can be 

 deduced, namely E = — 5*93 ; or taking the mean of several 

 series of experiments made by different observers, 



E=-5-l7, 

 while for a bar of iron of 59200 times less weight, the same 

 value, determined by similar experiments, was found to be 



E^=-f 128-4. 

 From this we learn, by reduction to the same weight, that the 

 diamagnetism of the bismuth is 1470000 times less than the 

 magnetism of the iron. The result, however, is only true for a 

 particular form of the iron bar and for a definite strength of the 

 magnetizing force, namely X = 629*9, a number obtained from 

 the measured strength of current and from the coils of the elec- 

 tro-magnetic spiral. 



