: '} 



430 Action of Magnetism on a Permanent Electric Current. 



properly protected. There are many cases where the pinnacles 

 of the same turret of a church have been struck where one has 

 had a rod attached to it; but it is clear that the other pinnacles 

 were outside the cone; and therefore, for protection, each pin- 

 nacle should have had its own rod. It is evident also that 

 every prominent point of a building should have its rod, and 

 that the higher the rod the greater is the space protected. 



XLIX. Note on Mr. E. H. Hall's* Experiments on the u Action 

 of Magnetism on a permanent Electric Current." By J. 

 Hopkinson, F.E.S.t 



IF X, Y, Z be the components of electromotive force, and 

 u, v, w the components of current at any point, in any 

 body conducting electricity, we have the equations 



X = 'R 1 u + S 3 v + S 2 w — Tv, 



Y = S 3 w + R 2 v + SiW? + Tw, 



Z = S 2 w + SiV + R 3 ty, 



where R^ R 2 , ^3? Si, S 2 , S 3 , T are constants for the substance 

 under its then circumstances (vide Maxwell's ' Electricity,' 

 vol. L p. 349). 



After obtaining these equations, Maxwell goes on to say: — 

 " It appears from these equations that we may consider the 

 electromotive force as the resultant of two forces, one of them 

 depending on the coefficients E and S, and the other depend- 

 ing on T alone. The part depending on R and S is related 

 to the current in the same way that the perpendicular on the 

 tangent plane of an ellipsoid is related to the radius vector. 

 The other part, depending on T, is equal to the product of T 

 into the resolved part of the current perpendicular to the axis 

 of T; and its direction is perpendicular to T and to the current, 

 being always in the direction in which the resolved part of 

 the current would lie if turned 90° in the positive direction 

 round T. 



" Considering the current and T as vectors, the part of the 

 electromotive force due to T is the vector part of the product 

 T x current. 



" The coefficient T may be called the rotatory coefficient. 

 We have reason to believe that it does not exist in any known 

 substance. It should be found, if any where, in magnets 

 which have a polarization in one direction, probably due to 

 a rotational phenomenon in the substance." 



* Phil. Mag. March and November 1880. 

 t Communicated by the Author. 



