in Reply to Mr. Galloway's Remarks. 231 



of 1528 is to be assumed as agreeing with that of 1668, to 

 within its twentieth part. In the tract of John Buteo of Dau- 

 phiny on Noah's Ark (1559), he has given a semipes regms 

 printed from a line of metal. This agrees so nearly with the 

 French measure of our own day, that it may be considered as 

 probable that no important change took place from 1528 to 

 1559, seeing that none has taken place from that time to our 

 own day. I have another semipes regius in the work of one 

 Glareanus (1572) agreeing with the former to the thirtieth of 

 an inch. Both should be lengthened to allow for the shrinking 

 of the paper. 



In my first communication, I mentioned the " famous Italian 

 mile, the universal standard of the middle ages," taking it for 

 granted that no dispute could arise on the subject. Mr. Gal- 

 loway has taken me to mean by " Italian mile," a mile used 

 by the Italians, of which he asserts, and correctly, that there 

 were many. He requires it to be shown that there was only 

 one Italian mile in use in the days of Fernel, and that Fernel 

 knew its precise value. The first I shall endeavour to do, 

 namely, to show that the mathematicians of the sixteenth cen- 

 tury had a mile among themselves, or believed they had such 

 a mile, which they called Italian ; and also that there could 

 have been no very great difference between the (so-called) 

 Italian mile of one writer and another. As to the second 

 point, namely, that Fernel knew its precise value, though I 

 believe he did know it as well as others, yet it is only neces- 

 sary for me to establish a common usage: I do not see how 

 I can be required to show that Fernel was cognizant of notions 

 prevailing in his day and country. 



There was among the writers of the fifteenth and preceding 

 centuries a system of measures derived most expressly from 

 the human body, founded on ihe Jin ger-hr end th, which was 

 assumed to represent four grains of barley placed side by 

 side (not end to end as in the English inch). In this system 

 mathematicians expressed lengths, always using the Italian mile, 

 frequently the German mile, sometimes others. The Italian 

 mile was believed to be the old Roman mile, the German 

 mile was mostly used by writers of that country, and so on : but 

 to avoid the diversity of measures which actually existed even 

 in each country, and the inconveniences arising from want of 

 compared standards, the mathematical writers of all countries 

 settled their miles by convention founded on an appeal to the 

 finger-breadth, palm and foot, which, if their own expressions 

 are to be trusted, were actually considered as represented by 

 the lengths bearing their names. Fernel, as well as others 

 whom I shall cite, gives a complete table, as follows : — 



