232 Prof. De Morgan 07i Fernel's Measure of a Degree. 

 4 barley-corns are 1 digit. I 10 feet are 1 perch. 



125 paces 1 Italic stadium. 



1000 paces 1 Italic mile. 



iOOO paces 1 German mile. 



5000 paces 1 Swiss mile. 



4 digits 1 palm' 



4 palms 1 foot. 



U foot 1 cubit. 



10 palms (2,^ feet) 1 step. 

 20 palms (5 feet) 1 pace. 



This system is found in manuscripts, but was particularly 

 conspicuous from the invention of printing up to A.D. 1570. 

 It sank gradually, as actual measurement began to prevail, 

 and was hardly understood by the middle of the seventeenth 

 century. This table appears also in the Cosmography of Gem- 

 ma Frisius (1548); in that of Apian (printed at various times 

 from 1529 up to 1570), in which the measures are illustrated 

 by drawings from the human body ; in Stofler's Commentary 

 on Proclus (1534); and in many other works which I have 

 seen. From its constant occurrence, always accompanied by 

 reference to the human body, and never by division of the 

 foot into twelve inches, it may be considered as highly pro- 

 bable that the geometrical writers found a reference to the 

 parts of the human body more convenient and less liable to 

 error than an attempt to write in the measures of one country 

 for the readers of all. In our own day few authors think of 

 more than their own countrymen : it was otherwise when a 

 learned language was in use. The vernacular writers soon 

 made the confusion of not distinguishing the feet of their own 

 country from the geometrical foot. Their predecessors made 

 the distinction ; their only connexion with the actual measures 

 of the world being their belief that the geometrical Italian mile 

 was the old Roman mile, in which they were not far wrong; 

 and that their geometrical German mile was a representative 

 of some one mile used in Germany, nearly. 



I had formed the preceding opinion from such circum- 

 stances as I have referred to, and many others; being certain 

 of this much, that an " Italian mile," believed to be the an- 

 cient Roman mile, was universal. I lately found a strong con- 

 firmation of my opinion, in all its details, namely, that the 

 same thing is asserted by Clavius (who died in 1612 at the age 

 of 75) in his Commentary on Sacrobosco (I quote the edi- 

 tion of 1618). His words are, " ... enumerandae sunt men- 

 surae quibus mathematici, maxime geometricc, ulunhir. Ma- 

 thematici enim, ne confusio oriretur ob diversitatem niensu- 

 rarum in variis regionibus (nuaslibet namque regio proprias 

 habet propemodum mensuras) utiliter excogitarunt quasdavi 



• It appears from the drawings that the palm was measured across the 

 iriddle joint of the fingers. 



