curl of a vector field. (The term 'curl' was first used by James Clerk Maxwell in 1870.) MacCullagh first showed that the curl is a covariant vector in the sense that its components are transformed in the appropriate manner under coordinate rotation. Taking his cue from George Green, he set out to develop a potential function for a dynamical theory for the transmission of light. MacCullagh found that a conventional potential function proportional to the squared norm of the displacement field was incompatible with known properties of light waves. In order to support only transverse waves, he found that the potential function must be proportional to the squared norm of the curl of the displacement field. It was accepted that his radical choice ruled out any hope for a mechanical model for the ethereal medium. Nevertheless, the field equations stemming from this purely gyrostatic medium were shown to be in accord with all known laws, including those of Snell and Augustin-Jean Fresnel. At several points, MacCullagh addresses the physical nature of an ethereal medium having such properties. Not surprisingly, he argues against a mechanical interpretation of the luminiferous aether because he readily admits that no known physical medium could have such a potential function resisting only rotation of its elements. "Concerning the peculiar constitution of the ether, we know nothing and shall suppose nothing, except what is involved in the foregoing assumptions [rectilinear vibrations in a medium of constant density]... Having arrived at the value of [the potential function], we may now take it for the starting point of our theory, and dismiss the assumptions by which we were conducted to it." Despite the success of the theory, physicists and mathematicians were not receptive to the idea of reducing physics to a set of abstract field equations divorced from a mechanical model. The notion of the ether as a compressible fluid or similar physical entity was too deeply ingrained in nineteenth century physical thinking, even for decades after the publication of Maxwell's electromagnetic theory in 1864. MacCullagh's ideas were largely abandoned and forgotten until 1880, when George Francis FitzGerald re-discovered and re-interpreted his findings in the light of Maxwell's work. William Thomson, 1st Baron Kelvin succeeded in developing a physically realizable model of MacCullagh's rotationally elastic but translationally insensitive ether, consisting of gyrostats mounted on a framework of telescoping rods, described in his paper On a Gyrostatic Adynamic Constitution for