Mr. Galloway's Remarks on Fernel's Measure of a Degree. 91 



important to the right understanding of Fernel's operation, and 

 to the discussion of the point at issue. The passage is as fol- 

 lows : — After describing the manner in which he ascertained, 

 by observations of the sun's altitude, that he was exactly one 

 degree to the north of Paris, and stating that, according to the 

 report of the country people, the distance of the place from 

 Paris was twenty-five leagues, Fernel adds (I quote from 

 Snellius, Eratosthenes Batamis, p. 1 1 5), 



" Nee tamen vulgi supputatione satiatus, veJiiculum quod 

 Parrhisios recta via petebat conscendi ; in eoqiie residens tota 

 via \1 ,02^ fere rotce circumvoliitiones collegia vallibus et mon- 

 tibus ad cequalitatem quoad facidtas nostra fercbat, redactis. 

 Erat atitem rotcB illius diameter 6 pedum, sexqiie paido niagis 

 digitortim gcometricorum ; ob idque ejus ambitus pedum erat 

 20, seu passuum 4 ,- Ids ergo revolutionibus per 4 ductis, repperi 

 passus 68,096 ; qui miliaria sunt Italica 68, cum passibus 96, 

 malui tamen hos passus in passus 95 cum quarto convertere, 

 ne qucepiam fractio foret in terrce diametro prcefigenda." 



Here, then, is a perfectly clear and explicit account of the 

 wholeof the geodetical part of the operation. Aftermaking adis- 

 cretionary allowance for the inequalities of the road, the wheel 

 of the vehicle in which he travelled was found to have made 

 17,024 revolutions. The diameter of the wheel was measured 

 and found to be six geometrical feet and six digits (the digit 

 is one-sixteenth of a foot), and a little over ; whence the cir- 

 cumference of the wheel was twenty feet, or four paces, 

 and the whole distance 17,024 x 4 = 68,096 paces of five 

 feet each, that is to say, 340,480 feet. The primary mea- 

 sure is therefore in feet, and the question to be decided re- 

 solves itself into this, — What is the equivalent of the measure 

 which Fernel calls a geometrical foot ? 



Now the most obvious and probable supposition is, that the 

 foot used by Fernel in measuring the diameter of his wheel 

 was the ordinary Paris foot in use at the time. This is the sup- 

 position of Picard, Cassini, Montucla, Lalande, and Delam- 

 bre ; and although, perhaps, it cannot be formally proved to be 

 correct, there is nothing in the statement of Fernel (notwith- 

 standing the use of the word geometi-icorion) to furnish the 

 slightest reason for suspecting that in measuring the diameter 

 of the wheel he used a rule or scale different from what would 

 have been applied to any common purpose of mensuration ; 

 or that, having used an ordinary scale, he reduced the actual 

 measure to any other standard. But before discussing this 

 point it will be proper to explain the ovigin of the numbers 

 given by Montucla and Delambre. 



Fernel reduces his 68,096 paces to 68,095^ in order to have 



