Maxwell notes thatIn the larger treatise I sometimes made use of methods which I do not think the best in themselves, but without which the student cannot follow the investigations of the founders of the Mathematical Theory of Electricity.

For this reason, and owing to the less technical presentation of the Elementary Treatise, the latter has been called "the final, unfinished expression of the understanding [Maxwell] achieved by studying and extending Faraday’s work".

[2] Maxwell's relationship with Michael Faraday's work was foundational: as a young man, embarking on his study of electricity, Maxwell decided "to read no mathematics on the subject till I had first read through Faraday's Experimental Researches.

As so often with Maxwell's work, even popular presentations such as the Elementary Treatise contain subtle insights, and these were recognised by his immediate followers.

Lewis Fry Richardson, for example, developed a trial and error method of solving two-dimensional flow nets, using a comment in Chapter VI:Maxwell in §92 of his Elementary Treatise on Electricity and Magnetism speaks of tentative methods of altering known solutions of the Laplacian equation by drawing diagrams on paper and selecting the least improbable.

The object of the present thesis is to point out that this method can do far more than merely alter known results, and that it may be so far from tentative as to yield an accuracy of one per cent of the range.

Joseph Turner, for example, discussed the Elementary Treatise in his 1955 paper 'Maxwell on the Method of Physical Analogy'.