Andrew Odlyzko finds the earliest use of gravity models for travel demand and spatial interaction in his new working paper “The forgotten discovery of gravity models and the inefficiency of early railway networks“, moving the clock a few years earlier.

Abstract. The routes of early railways around the world were generally inefficient because the prevailing doctrine of the time called for concentrating on provision of fast service between major cities and neglect of local traffic. Modern planners rely on methods such as the “gravity models of spatial interaction,” which show the costs of such faulty assumptions. Such models were not used in the 19th century.
The first formulation of gravity models is usually attributed to Henry Carey in 1858. This paper shows that a Belgian civil engineer, Henri-Guillaume Desart, discovered them earlier, in 1846, based on the study of a unique and extensive data set on passenger travel in his country. His work was published during the great Railway Mania in Britain. Had the validity and value of this contri- bution been recognized properly, the investment losses of that gigantic bubble could have been lessened, and more efficient rail systems in Britain and many other countries would almost surely have been built. This incident shows society’s early encounter with the “Big Data” of the day and the slow diffusion of economically significant information. The methods used in the study point to ways to apply methods of modern network science to analyze information dissemination in the 19th century.