This equation can be recast in several ways, and it has been studied in various forms by authors including Kaluza, Pauli, Gross & Perry, Gegenberg & Kunstatter, and Wesson & Ponce de Leon, but it is instructive to convert it back to the usual 4-dimensional length element c 2 d τ τ 2 ≡ ≡ g μ μ ν ν d x μ μ d x ν ν , which is related to the 5-dimensional length element d s as given above: