^The 46° halo was first explained as being caused by refractions through ice crystals in 1679 by the French physicist Edmé Mariotte (1620–1684). See: Mariotte, Quatrieme Essay. De la Nature des Couleur (Paris, France: Estienne Michallet, 1681). Sun dogs as well as the 22° and 46° halos are explained in terms of refractions from ice crystals on pages 466 - 524 (页面存档备份,存于互联网档案馆).