This paper aims, on the one hand, to determine the valid span of the diagram of unequal hours and, on the other, to find a mathematical expression for the error. It is found that the diagram is valid for the two days of the equinoxes and for the times when the sun is on the horizon or on the meridian. This subject has previously been treated by Delambre in 1819 and Drecker in 1925, but not comprehensively.

Summary The first attempt at a classification of sundials appeared only in 1953, in the catalogue established by Henri Michel for the Museum of Liège. It was immediately followed, in the same year, by the article by Kathleen Higgins, exclusively dedicated to this topic. The influence of this second study has spread out throughout the numerous articles on sundials that have been subsequently published. The aim of the present paper is to bring some order to these two old classifications, which (...) are in fact quite similar and were sufficiently valid at the time, and to propose a new approach to the problem based, for the first time, on principles directly linked to astronomy and geometry. Moreover, this latter approach has the advantage of a flexibility in its application to all kinds of sundial collections. (shrink)

Résumé Le cadran solaire analemmatique est présenté pour la première fois par un mathématicien français, appelé Vaulezard, dans un petit fascicule publié en 1640. Suit un deuxième ouvrage, plus complet, en 1644. Dernier venu, ce cadran attire l'attention d'importants savants tels que Foster et Lalande. Parfait dès le départ, il a néanmoins la singulière particularité d'inspirer diverses tentatives d'amélioration, plutôt infructueuses, et d'être à l'origine de quelques variétés de cadrans analemmatiques qui, elles, connaissent un franc succès. Nous apportons la preuve (...) trigonométrique et, pour la première fois semble‐t‐il, la preuve géométrique de sa validité astronomique en suivant fidèlement la méthode de construction indiquée par Vaulezard. Nous effectuons, en outre, un survol aussi exhaustif que possible des différents modèles dérivés de ce cadran ainsi que de la littérature les concernant. Summary The analemmatic sundial was briefly presented for the first time in 1640 by the French mathematician Vaulezard and was described in more detail by him in 1644. The analemmatic dial is the last genuine sundial to be invented and it has attracted the attention of some important scholars such as Foster and Lalande. Although perfect from the very beginning, it had the unusual particularity of inspiring several unfortunate attempts at its improvement as well as being at the origin of a few other types of analemmatic dials, which met with a certain success. We provide here the trigonometric proof and for the first time, the geometric proof of its astronomical validity by closely following the construction method of Vaulezard. We also make a comprehensive survey of the different kinds of analemmatic sundials and of their literature. (shrink)

Le cadran solaire analemmatique est présenté pour la première fois par un mathématicien français, appelé Vaulezard, dans un petit fascicule publié en 1640. Suit un deuxième ouvrage, plus complet, en 1644. Dernier venu, ce cadran attire l'attention d'importants savants tels que Foster et Lalande. Parfait dès le départ, il a néanmoins la singulière particularité d'inspirer diverses tentatives d'amélioration, plutôt infructueuses, et d'être à l'origine de quelques variétés de cadrans analemmatiques qui, elles, connaissent un franc succès. Nous apportons la preuve trigonométrique (...) et, pour la première fois semble‐t‐il, la preuve géométrique de sa validité astronomique en suivant fidèlement la méthode de construction indiquée par Vaulezard. Nous effectuons, en outre, un survol aussi exhaustif que possible des différents modèles dérivés de ce cadran ainsi que de la littérature les concernant.SummaryThe analemmatic sundial was briefly presented for the first time in 1640 by the French mathematician Vaulezard and was described in more detail by him in 1644. The analemmatic dial is the last genuine sundial to be invented and it has attracted the attention of some important scholars such as Foster and Lalande. Although perfect from the very beginning, it had the unusual particularity of inspiring several unfortunate attempts at its improvement as well as being at the origin of a few other types of analemmatic dials, which met with a certain success. We provide here the trigonometric proof and for the first time, the geometric proof of its astronomical validity by closely following the construction method of Vaulezard. We also make a comprehensive survey of the different kinds of analemmatic sundials and of their literature. (shrink)

Summary The first attempt at a classification of sundials appeared only in 1953, in the catalogue established by Henri Michel for the Museum of Liège. It was immediately followed, in the same year, by the article by Kathleen Higgins, exclusively dedicated to this topic. The influence of this second study has spread out throughout the numerous articles on sundials that have been subsequently published. The aim of the present paper is to bring some order to these two old classifications, which (...) are in fact quite similar and were sufficiently valid at the time, and to propose a new approach to the problem based, for the first time, on principles directly linked to astronomy and geometry. Moreover, this latter approach has the advantage of a flexibility in its application to all kinds of sundial collections. (shrink)