In any collection of the principal vigesimal number systems of the world, one would naturally begin with those possessed by the Celtic races of Europe. These races, the earliest European peoples of whom we have any exact knowledge, show a preference for counting by twenties, which is almost as decided as that manifested by Teutonic races for counting by tens. It has been conjectured by some writers that the explanation for this was to be found in the ancient commercial intercourse which existed between the Britons and the Carthaginians and Phoenicians, whose number systems showed traces of a vigesimal tendency. Considering the fact that the use of vigesimal counting was universal among Celtic races, this explanation is quite gratuitous. The reason why the Celts used this method is entirely unknown, and need not concern investigators in the least. But the fact that they did use it is important, and commands attention. The five Celtic languages, Breton, Irish, Welsh, Manx, and Gaelic, contain the following well-defined vigesimal scales. Only the principal or characteristic numerals are given, those being sufficient to enable the reader to follow intelligently the growth of the systems. Each contains the decimal element also, and is, therefore, to be regarded as a mixed decimal-vigesimal system. IRISH.[329] 10. deic. 20. fice. 30. triocad = 3-10 40. da ficid = 2-20. 50. caogad = 5-10. 60. tri ficid = 3-20. 70. reactmoga = 7-10. 80. ceitqe ficid = 4-20. 90. nocad = 9-10. 100. cead. 1000. mile. GAELIC.[330] 10. deich. 20. fichead. 30. deich ar fichead = 10 + 20. 40. da fhichead = 2-20. 50. da fhichead is deich = 40 + 10. 60. tri fichead = 3-20. 70. tri fichead is deich = 60 + 10. 80. ceithir fichead = 4-20. 90. ceithir fichead is deich = 80 + 10. 100. ceud. 1000. mile. WELSH.[331] 10. deg. 20. ugain. 30. deg ar hugain = 10 + 20. 40. deugain = 2-20. 50. deg a deugain = 10 + 40. 60. trigain = 3-20. 70. deg a thrigain = 10 + 60. 80. pedwar ugain = 4-20. 90. deg a pedwar ugain = 80 + 10. 100. cant. MANX.[332] 10. jeih. 20. feed. 30. yn jeih as feed = 10 + 20. 40. daeed = 2-20. 50. jeih as daeed = 10 + 40. 60. three-feed = 3-20. 70. three-feed as jeih = 60 + 10. 80. kiare-feed = 4-20. 100. keead. 1000. thousane, or jeih cheead. BRETON.[333]