Mr. Galloway's Remarks on Fernel's Measure of a Degree, 93 



also in his Astr07iomie (2638). In adopting the correction of 

 Lalande, Delambre probably did not think it worth while to 

 verify the numbers. 



Lalande refers to the Memoires for \1\^ as the authority 

 for his correction. The volume indicated contains a paper 

 by La Hire, in which the reduction of the toise is simply men- 

 tioned with a reference to a former volume, but a circumstan- 

 tial account of the matter is given by Paucton {Metrologie, 

 p. 18). 



But to return to the subject in hand. The case as respects 

 Montucla and Delambre stands thus : — (I quote the dates, as 

 Mr. De Morgan says the confusion is older than Delambre 

 and Lalande.) 



1. Fernel, in 1528, declares the length of a degree of any 

 great circle of the earth to be 68,095^ paces of five feet each. 



2. Picard, in 1671, assumes that the foot used by Fernel 

 was the ordinary Paris foot of six to the toise, and accord- 

 ingly states the result to be 56,74-6 toises, which is the num- 

 ber given by Montucla. 



3. Lalande, in 1787, shows that in consequence of the al- 

 teration of the toise in 1668, which Picard had overlooked or 

 not thought it worth while to notice, the result obtained by 

 Fernel was 57,070 toises, which is the number given by De- 

 lambre in his Astronomie*. 



Tims it appears that Montucla and Delambre, instead of 

 stating " a very different result" from Fernel, state precisely 

 the same result but in different terms ; on the assumption, how- 

 ever, that Fernel gives the diameter of his wheel in Paris feet. 



It is now necessary to advert to the passage in which Fernel 

 states the result of his measure to be 68 Italian miles and 96 

 paces. This point has been discussed by Lalande {Mem., 1787), 

 who remarks that Fernel's Italian mile of 68 to the degree is 

 in fact a measure used in some parts of Italy, but that the 

 mile differs widely in different parts of the country, varying 

 from 48 to 81 in the degree ; and from this circumstance and 

 the manner in which Fernel compares his result with that 

 of the Arabians, he concludes that what he says about Italian 

 miles must be abandoned; in other words, has no definite 

 meaning apart from the expression of the measure in feet. 

 Riccioli, who lived nearer the time of Fernel, and will be ad- 

 mitted to be an unexceptionable authority, confirms this de- 

 scription of the vagueness of the Italian mile. " Italica mil- 

 liaria incredibilem habent varietatem, turn in modo ea compo- 



* Delambre has given a detailed account of Fernel's measure in the Hi- 

 iluirc dc C AUronomie du Moyen yigu. 



