Intelligence and Miscellaneous Articles, 227 



gives 



dx^dy 2 ' 



For a circular plate it follows that when one electrode of the 

 primary current is in the centre, and the entire periphery is the 

 second electrode : 



p=— Alognatr, u=JcA(x— hy) |r 2 , v = Jc A(y + hx) | r 2 , p = JcA\r; 

 the stream-lines are logarithmic spirals with the equation 

 $ = h log nat r -j- const. ; 



r and $ are the polar coordinates, p the components of the current 

 in the direction of r. Similarly found stream-lines were observed 

 in Greissler's and Hittorf's tubes under the influence of magnets. 

 The flow in an infinite plate with two or more point-shaped 

 electrodes is obtained by superposition. The equation of the 

 stream-lines is then 



h log nat (r | r') = $— & + const. 



for two electrodes to which the polar coordinates r, §, ?*', $' refer. 

 Leduc (Journal de Physique, 2nd series, vol. iii. p. 366) has sug- 

 gested the hypothesis that the changes of resistance which mag- 

 netism produces in bismuth are merely apparent, and caused 

 by the fact that the currents are forced into longer paths by Hall's 

 phenomenon. In this case, from what has been above said, no 

 changes in resistance are to be expected in a rectangular strip 

 in the entire extent of which the currents flow parallel to two 

 sides which lie opposite. For the circular plate the strength of 

 the current i=27rrpd = 2irJcA^, the resistance s is therefore 

 log nat (r Q : r ) 1 + h 2 , , r 



2irK6 2tvck r 1 



in which r 2 is the radius of the plate, r x that of the central electrode. 

 Hence it would be increased in the ratio 1 -f h? : 1 by the mag- 

 netism. If JE is the electromotive force of the battery, jo the 

 difference of potentials of the electrodes of the plate, then 



S IV S-\- XV 



in which w is the resistance of the rest of the circuit. Prof. Ettings- 

 hausen found for a bismuth disk corresponding to these conditions, in 

 two experiments with the magnetic fields 6364 and 481 0, the values 

 1-257 and 1-180, which agree tolerably with the formula, since 

 with bismuth from another source it is true R varied from 8 to 10, 

 On the other hand, it seems difficult to explain the great difference 

 in resistance which was found with rectangular bismuth strips as 

 arising from want of homogeneity, or from the fact that the 

 current was led, and taken away from individual points, and 

 not at the entire breadth. The integral p= — ax + cy corresponds 

 to a rectangular strip of thickness 3, at whose shorter sides b the 

 primary current enters and leaves, while the longer sides I are 



