(93) If we com<s>pare<\s>bine the equations of Magnetic Force (B) with those of Electric currents (C) and put for brevity dF/dx + dG/dy + dH/dz = J and d<sup>2<\sup>/dx<sup>2<\sup> + d<sup>2<\sup>/dy<sup>2<\sup> + d<sup>2<\sup>dz<sup>2<\sup> = [del operator] <sup>2<\sup> (63) 4[pi][mu]p' = dJ/dx  <s>d<sup>2<\sup>[mu]<sup>2<\sup>/dx<sup>2<\sup><\s> [del operator]<sup>2<\sup>F 4[pi][mu]q' = dJ/dy  [del operator]<sup>2<\sup>G 4[pi][mu]r' = dJ/dz  [del operator]<sup>2<\sup>H } (64) If the medium in the field is a perfect dielectric there is no true conduction and the currents p' q' r' are only variations in the dielectric displacement or, by the equations of Total Currents (A) p'=df/dt q'=dg/dt r'=dh/dt (65) But these electric displacements are caused by electromotive forces and by the equations of Eectric Elasticity (E) P=kf Q=kg R=kh (66) These electromotive forces are due to the variations either of the electromagnetic or the electrostatic functions as there is no motion of conductors in the field, so that the equations of electromotive force (D) are P= dF/dt  d[psi]/dx Q= dG/dt  d[psi]dy R = dH/dt  d[psi]/dz } (67) (94) Combining these equations we obtain the following k(dJ/dx)  [del operator]<sup>2<\sup>F) + 4[pi][mu](d<sup>2<\sup>F/dt<sup>2<\sup> + d<sup>2<\sup>[psi]/dxdt) = 0 k(dJ/dy)  [del operator]<sup>2<\sup>G) + 4[pi][mu](d<sup>2<\sup>G/dt<sup>2<\sup> + d<sup>2<\sup>[psi]/dydt) = 0 k(dJ/dz)  [del operator]<sup>2<\sup>H) + 4[pi][mu](d<sup>2<\sup>H/dt<sup>2<\sup> + d<sup>2<\sup>[psi]/dzdt) = 0 } (68) If we differentiate the third of these equations with respect to y and the second with respect to y[sic, z?] and subtract J & 4[H?] disappear and be remembering the equations (B) of magnetic force the results may be written
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Manuscript details
 Author
 James Clerk Maxwell
 Reference
 PT/72/7
 Series
 PT
 Date
 1864
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Cite as
J. C. Maxwell’s, ‘Dynamical theory of the electromagnetic field’, 1864. From The Royal Society, PT/72/7
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