The present theory of magnetism, in which it is treated as a phenomenon of current electricity, suffers from objections which are pointed out. The meanings of B and H on an atomic scale are considered, and a method of picturing B and H, inside a ferromagnetic body, without mentioning magnetic poles or dipoles, is developed. It is shown that this method satisfactorily accounts for the demagnetizing field in certain simple cases and that it also makes clear why H occurs in the circuital theorem while B is used in Laplace's equation. Rigorous definitions of B and H at any point in a magnetic medium are then developed. In the concluding section the advantages of the suggested method are summarized.