94 Mr. Galloway's Remarks on Fernel's Measure of a Degree. 



nendi ac metandi, turn in quantitate." {Geographice et Hy- 

 drographicc Rcformatcc, lib. xii. 1661, p. 48.) It is obvious, 

 therefore, that the expression Italian mile, unless accompanied 

 with some explanation, or reference to some other standard, 

 conveys no precise information. Fernel's statement, taken 

 altogether, seems to suggest the idea that he used the expres- 

 sion, not for the purpose of defining the foot which was the ori- 

 ginal measure, but as a popular term, familiar to the writers of 

 that age, and therefore likely to give a clearer notion of a large 

 magnitude than would be conveyed by expressing it in feet. 



The geometrical j)(ice participates in all the vagueness of the 

 Italian mile. Riccioli makes frequent mention of the Rornan 

 geometrical pace as distinguished from that of the moderns. 

 The true solution of the greater part of the difficulties attend- 

 ing this subject will probably be found in the supposition that 

 the terms geometrical pace and geovietrical foot were used more 

 frequently to denote a particular mode of division than abso- 

 lute measures. Five geometrical feet make a geometrical 

 pace, and 1000 paces a mile; while the writers of each coun- 

 try tacitly assume the foot to be taken according to their own 

 standards. It would be easy to accumulate quotations in 

 support of this view, but the following may suffice. 



Norwood, in the " Epistle Dedicatory" prefixed to his Sea- 

 ?na7i's Practice (1678), says " the way of finding distances at 

 sea is rather opinionative and conjectural than certain, being 

 founded upon this supposition, that the compass of the world 

 in any great circle is '21,600 Italian miles (as they call them), 

 and that such an Italian mile contains 1000 paces, and every 

 of those paces five English feet." Thus the common practice 

 in England, according to Norwood, was to call 5000 English 

 feet an Italian mile. 



Paucton {Metrologie, p. 179) cites the followiiig passage 

 from an old treatise on itinerary measures by the Sieur Sam- 

 son of Abbeville : — " Le pas commun de I'homme est de deux 

 pieds et demi. Le pas des Allemands, qu'on appelle pas geo- 

 metriqtie est de cinq pieds de Roi. Ainsi quand on dit : le 

 mille d'ltalie a niille pas, la lieue de France a trois milles pas, 

 on entend des pas geometriques." Here the geometrical 

 pace is expressly stated to be five French feet, and conse- 

 quently the Italian mile to contain 5000 French feet. 



I may observe, in passing, that the sentence last quoted fur- 

 nishes, at least, one evidence that the " curious fiction which 

 the geometers of the 16th century called a geometrical pace" 

 was sometimes regarded as longer than five English feet. 



In order to make good the assertion that Fernel " certainly 

 used the Italian mile of his day," it would be necessary to 



