Mr. Galloway's Remarks on Fernel's Measure of a Degree. 95 



show, — 1st, that there was only one Italian mile in use in the 

 days of Fernel ; and 2nd, that Fernel knew its precise value 

 — not merely knew that so many repetitions of it made a de- 

 gree (which was the usual definition), but had a material re- 

 presentative of some aliquot part of it which he could apply 

 to the measurement of his wheel. Neither of these points will 

 be easily established. The only thing certain in the relation 

 of Fernel, is 17,024- revolutions of a wheel 20 feet in circum- 

 ference; and the whole question, as has been already re- 

 marked, is whether he meant Paris feet {Pieds de lloi)^ or feet 

 of some other denomination. Picard and all the French au- 

 thors assume that he meant Paris feet. Norwood evidently 

 makes the same assumption when he represents Fernel's pace 

 as being " more than five English feet," the French foot ex- 

 ceeding the English foot, according to Snellius (from whom, 

 probably, Norwood took his idea of the French foot), in the 

 ratio of 1055 to 968. 



In stating his reasons for assigning a different value to 

 Fernel's measure from that of Montucla and Delambre, Mr. 

 De Morgan quotes Riccioli as giving " a true account." 

 Lalande, on the other hand, asserts that Riccioli seized upon 

 the expression Italian miles as a means of making Fernel's 

 result, as well as that of the Arabians, agree with his own, 

 which was much less accurate; and he says, " it would be 

 unjust to admit the valuation of Riccioli, who makes Fernel's 

 degree equal to 64,421 Bologna paces, which are equal to 

 62,726 toises" {Mem., 1787, p. 220). Now it will probably 

 be considered not the least remarkable circumstance con- 

 nected with this history, that Riccioli gives no reduction of 

 Fernel's result whatever, nor states its value in any other terms 

 than those used by Fernel himself. He gives, it is true, the 

 value of the Ay-ahian measure as being 64,421 Bologna paces, 

 and as Fernel states his result to differ from that of the Ara- 

 bians only by 96 geometrical paces, it may be presumed that 

 Riccioli considered the above as a sufficiently near expression 

 of its value. But however this may be, the measure reduced 

 by Riccioli is the Arabian measure and not Fernel's, and the 

 64,421 Bologna paces are found by a process wholly and abso- 

 lutely independent of Fernel's operation. The reduction 

 which is given in Riccioli's work above cited is as follows : — 



The Arabian degree is stated by Campanus and others to 

 be 56 1 miles. In order to define the length of the mile, the 

 Arabian authors say it contained 4000 cubits ; that a cubit 

 contained 24 digits ; and that a digit was equal in length to 

 six grains of barley. Hence the Arabian mile is equivalent to 

 4000 X 24 X G = 576,000 barleycorns. Now Riccioli and 

 Grimaldi found by trials repeated frequently {iterum ac sce^ 



