The main object of this article is to suggest that John Napier took the word “ logarithm ”, though not the idea, directly from the Psammites (Arenarius, Sand-Reckoner) of Archimedes. Incidentally it will contain the results of new research into Napier's life, together with an examination of the history of some of the texts of the editio princeps of Archimedes (Basel, 1544) which exist at present in this country.