on a Piece of Iron carrying an Electric Current. L55 



are the components of the intensity of magnetization at a 



place x, y,z\ a, j3, y the components of the magnetic force ; 



and u, v, w the component of the current : then X, the x 



component of the mechanical force on unit volume at x, //, :. 



is given by the equation 



. da ,-„ da , r . dot /i\ 



X = A^- +B -y- + C -r +vy-wp, • • (1) 

 dx ay dz 



with similar expressions for the forces parallel to y and ;. 

 This expression may be transformed by the relations 



da dy . d^ da „ 



dz dx dx dy 



into 



X=A ( i? +B^+0^+i<7 + 4*0)-»GB + 4 1 rB); 



dx dx ax 



or 



dx clx dx 



where a, l>, c are the components of the magnetic induction. 



It follows from this that if we take the force on a mag- 

 netized element as equal to A-r + B— +C^-, and this 

 1 dx dy dz 



seems at once to follow from the conception of a magnetic 

 element, we must take the force on the current to be equal 

 to the product of the current and the magnetic force : if, how- 

 ever, we take the force on the element tobeA-^-4-B — + C -7- 



dx dx dx 



(and this is what Maxwell did, see Art. 631*, Electricity and 

 Magnetism), we must take the force on the current to be the 

 product of the current and magnetic induction. 



In the problem of the pressure exerted by a plane electro- 

 magnetic wave on a plate of iron placed parallel to the wave- 

 front tbe force at right angles to the plate due to the mag- 

 netization calculated on the first supposition is zero, since the 

 magnetic force perpendicular to the plate is everywhere zero. 

 The pressure calculated by the forces on the current is /3 2 /87r, 

 the result which, as Lord Rayleigh points out, is required by 

 the radiation theory. On the second supposition the pressure 



due to the magnetization is | B — dz or — -—7 — - ft 2 ; but the 



pressure due to the forces on the current is now /^/3 2 /87r, so 

 that the total pressure is again /3 2 /8vr. 



Yours very truly, 

 Cambridge, June 6, 1898. J. J. THOMSON. 



