Intelligence and Miscellaneous Articles. 319 



Consider the curve itself; its first polar or emanant, viz. 



its second, third polars, and so on. Form the Hessians of each of 

 these curves, H, Hj, H„, &c., which will contain XYZ in the degrees 

 0, 3, 6, &c. I suppose them to have been so multiplied by nume- 

 rical factors that the substitution of x, y, z for X, Y, Z shall make 

 all identical. Form now the emanants of the (w — 2)nd degree, or 

 the polars of that degree of H, H„ Ho, &c. with respect to XYZ : 

 these will all be of the same degree in XYZ, viz. 2(w — 2), and by a 

 syzygetic combination of these can be formed the curve of the 

 (n — 2)nd degree required. For instance, for a curve of the fourth 

 degree it is D^H-SD'^H, ; 



for a curve of the fifth degree, 

 and so on. D3H-4D3H. + 6D3H,, 



September 10, 1858. . 



ON THE ELECTRO-MAGNETIC ROTATION OF LIQUIDS. 

 BY A. BERTIN. 

 Experiments upon electro-magnetic rotations are usually made by 

 employing, as moveable conductors, copper wires turning round a 

 central pivot. By this method, however, none but slightly varied 

 phsenomena can be observed ; and in this manner the electro-dynamic 

 theories can only be submitted to a small number of verifications. 

 It is otherwise when a liquid is taken as the moveable conductor. 

 The experiment is also very easy : it is sufficient to cause a current 

 to pass into a liquid, taking as electrodes two concentric circles of 

 copper, and to submit it at the same time to the action of a magnet, 

 an electro-magnet, or an electro-dynamic coil. The liquid is imme- 

 diately seen to turn rapidly round the common centre of the two 

 electrodes, even when the pile employed consists only of a small 

 number of elements. On changing its place, the rapidity and the 

 direction of the rotation are varied, according to the position given 

 to the moveable current. These changes are subject to the fol- • 

 lowing laws : — 



1. The centrifugal and centripetal currents turn in opposite direc- 

 tions, other things remaining the same. 



2. There is a series of points in the space where the rotation is 

 null : their totality constitutes a neutral surface, on each side of 

 which the rotation changes its direction. 



3. For a vertical magnet, the neutral surface has for generator 

 a curve with two branches passing through the poles, and resembling 

 a hyperbola mounted upon the axis of the magnet. Between the 

 two branches of this neutral line the rotation of the centrifugal cur- 

 rent is positive, or in the same direction as the circulation of the 

 current which would produce magnetization ; outside the neutral 

 line this rotation is in the opposite direction, or negative. 



Theory explains these phaenomcna in their smallest details. The 

 action of the magnet upon the horizontal current which traverses 

 the liquid in the nearest part is a horizontal force perpendicular to 

 the moveable current, and has for its expression 



