It has been shown by Larmor, Kottler and others that the classical method of calculating diffraction from the Kirchhoff formula in terms of a scalar light function cannot be applied directly to the electromagnetic field since it takes into account neither the vector character of the field nor the effect of charges along the contour of the opening. The field equations are integrated directly by means of a vector analog of Green's theorem. The results are applied to the calculation of diffraction of electromagnetic waves from a rectangular slit in a screen of infinite conductivity. The results are compared with an exact solution obtained recently by Morse and Rubenstein.