On the early history of Bessel functions

Communicated by Curtis Wilson     

On the history of the principle of least squares

Communicated by C. Truesdell     

On the history of the Euclidean Steiner tree problem

The history of the Euclidean Steiner tree problem, which is the problem of constructing a shortest possible network interconnecting a set of given points in the Euclidean plane, goes back to Gergonne in the early nineteenth century. We present a detailed account of the mathematical contributions of some of the earliest papers on the Euclidean Steiner tree problem. Furthermore, we link these initial contributions with results from the recent literature on the problem.     

The early history of the factorial function

Communicated by U. Bottazzini     

William Stukeley and the early history of the Orrery

Relations between J. A. C. Chaptal, pioneer of heavy chemical industry in France, and A. L. Lavoisier, reformer of chemical theory, are examined in the light of unpublished correspondence they exchanged in the period 1784–1790. The letters, together with Chaptal's early publications, allow a reconstruction of his conversion to Lavoisier's antiphlogistic chemistry. They also reveal a series of petitions that Chaptal made to Lavoisier, in the latter's official capacity as a director of the Régie des poudres et salpêtres, for relief from the controlled price of saltpetre for his acid works in Languedoc. Finally, the relationship is explored as a window on the interplay between chemical theory and industrial practice during the period of the Industrial Revolution.     

Bartolomeo Telioux and the early history of the thermometer

In the late 1810s and 1820s the Edinburgh phrenologists were largely concerned with trying to establish phrenology as the true science of mind. They challenged the accepted theories about the nature of mind and the brain; in turn, phrenology was attacked by the proponents of Scottish common-sense philosophy and by some medical men. The ensuing debate, which is discussed as an example of conflict between incommensurable world-views, involved a wide range of contentious theological, philosophical, scientific and methodological issues.