M. F. Reich on Diamagnetic Action. 251 



The repulsions, therefore, exerted by the respective magnets were 

 as follows : — 



mm 



No. 4. 3-2875 divisions of the scale = 0-3840 = 1 



... 4&5. 9-9375 ... =1-1608 = 3-0228 



... 4,5&6. 15-9250 ... =1-8601=4-8441 



The ratio of these repulsions shows decidedly that they increase 

 more speedily than in the simple ratio of the magnetic forces ; 

 but the ratio is still far from that of the squares of the forces. 

 The principal cause of this divergence is, that the distance of the 

 sphere of bismuth from the magnetic pole increased with the repul- 

 sion; and this augmentation of distance must exert a considerable 

 influence, both because the total distance was but small, and also 

 because, supposing diamagnetic polarity to exist, the repulsion 

 must be in the inverse ratio of the fourth power of the distance. 

 Denoting, therefore, by C the distance of the centre of repulsion 

 in the bismuth sphere in its position of equilibrium without the 

 magnet, from the place occupied by the magnetic pole, then in 

 the case of No. 4 we have the distance equal C + 0-3840; with 

 Nos. 4 and 5, C + 1-1608 ; and with Nos. 4, 5 and 6, C + 1-8601 : 

 the repulsive forces, therefore, are to each other in the ratio 



1 3-7917 6-6508 



(C + 0-3840)4* (C + 1-1608)4 ' (C + 1-8601)4- 



By setting these ratios equal to the repulsions found by experi- 

 ment, the quantity C, which is not to be found by direct mea- 

 surement, might be determined ; for this purpose, however, the 

 experiments are not sufficiently exact. On account of the small- 

 ness of the distance from the sphere of bismuth, the lateral 

 position, and consequently oblique action of the magnets, must 

 make itself felt when three of them are employed. 



Second experiment. — It is plain from the foregoing experi- 

 ments, that it is more advantageous to permit the magnets to act 

 from a greater distance upon the sphere. To obtain a sufficient 

 repulsion under these conditions, the intensity of the magnets 

 must be considerably increased. For this purpose thirty-two 

 bar-magnets, quite similar to those described, were made use of. 

 They were characterized by successive numbers, aud lay, when 

 they all acted together, in four horizontal series, each embracing 

 eight bars ; so that from Nos. 1 to 8 formed the first quarter, 

 from Nos. 2 to 16 the second quarter, &c. of the surface formed 

 by the cuds of the bars : the centre of this surface was in the 

 horizontal line passing through the centre of the sphere at right 

 angles to the arm of the torsion balance, and at a distance of 50 

 millims. from the chamber. I determined the respective inten- 



S2 



