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



pitis), that 80 grains of barley are contained exactly in the 

 ancient Roman foot of the time of Vespasian, and conse- 

 quently that a Roman mile, or 5000 Roman feet, must con- 

 tain 400,000 such grains. Supposing, therefore, grains of 

 barley grown in Lombardy to be of the same size as those of 

 barley grown in Arabia, the ancient Roman mile is to the 

 Arabian mile in the ratio of 400,000 to 576,000, or of 1000 

 to 1440, so that an Arabian mile contains 1440 Roman paces ; 

 whence the Arabian degree is 56f x 1440 = 81,600 Ro- 

 man paces (p. 44). Riccioli also found the Bologna foot to 

 be to the ancient Roman foot in the ratio of 1520 to 1200 

 (p. 46), that is, of 19 to 15. Multiplying, therefore, 81,600 

 by i|, the length of the Arabian degree is found expressed 

 in Bologna paces, namely, 64,421 paces. The numbers 81,600 

 and 64,421 are given by Riccioli in the table at the end of 

 his fifth book (p. 176) as the length of the degree in Roman 

 paces and Bologna paces respectively, with the marginal in- 

 dication, " Ex Campano et Fernelio," from which indeed 

 an incautious reader might think Fernel's French degree was 

 meant. 



The method by which Fernel connects his measure with 

 that of the Arabians is not quite of so refined a nature as that 

 of Riccioli, but probably about as accurate. He conjectures, 

 from the statements of Campanus, that the Arabian mile con- 

 tained 1000 commo?i paces (meaning double paces, or two steps) 

 of a man of the average size, and that 1000 common paces are 

 exactly equal to 1200 geometrical paces of five feet, which he 

 found, upon trial, to be the case with respect to his own paces. 

 Hence the Arabian degree must contain 56f x 1200 = 68,000 

 geometrical paces, or 68 Italian miles, the foot, which is not 

 defined, being always the unit of the measure. 



Now, even if all the other assumptions were admitted, it 

 would still be necessary, in order to connect Fernel's result 

 with Riccioli's Bologna paces, to suppose that 576,000 grains 

 of barley are exactly of the same length as 6000 feet of the 

 scale in terms of which Fernel has given the diameter of his 

 wheel. Riccioli makes no such supposition ; in fact he sets 

 aside altogether Fernel's measure of the French degree, and 

 gives his conjectural value of the Arabian degree in Roman 

 feet and Bologna paces. Lalande says Riccioli was deceived 

 by Fernel's mention of the Italian mile. The party deceived 

 appears to have been M. Lalande himself 



There is still a consideration which may be suggested as 

 favouring the presumption of the correctness of Picard's 

 supposition. Is it at all pi'obable that Fernel was aware of the 

 difference between the Paris foot and the foot used in different 

 parts of Italy, or even the ancient Roman foot ? The treatise 



