Mr. Galloway's Remarks on Fernel's Measure of a Degree. 23 



of their proper length, than there is for supposing that the 

 drawings from the human body with which some of the old 

 authors illustrated their measures, were intended to be of the 

 natural size, which they manifestly are not. The figure is a 

 line marked on the margin of the page, extending as high as 

 the head-line at the top, and a little below the letter-press at 

 the foot ; and suggests the idea of its having been adapted 

 by the printer to the length of the page, or made as long as 

 possible for the purpose of showing the small divisions. 



It should be kept in mind that the work in which the dia- 

 gram is found is not that in which Fernel's operation for mea- 

 suring the degree is described, nor does it contain any allusion 

 to that operation, which was probably not executed when the 

 work was printed. Neither is there in the Cosmotheoria any 

 allusion to this figure. 



Supposing, however, the fact to be as Mr. De Morgan assumes, 

 how are we to reconcile the result with the reasoning in his 

 previous papers respecting the geometrical pace and the Italian 

 mile? In his first letter he stated the Italian mile to be 1628 

 English yards, or, according to Dr. Bernard, 1667 yards, the 

 former statementgiving Fernel's degree equal to about 63 statute 

 miles, and the latter to 641 ; an d in his second letter he con- 

 firms this result by arguments which he considers to be deci- 

 sive of die question. But when the actual measure, or what 

 is assumed to be such, is produced, it turns out that the true 

 length is only 53 miles and three quarters. The error was 

 therefore between a fifth and a sixth of the whole quantity. 

 Mr. De Morgan himself appears to feel this difficulty, and 

 observes that the difference cannot be easily explained unless 

 we adopt a surmise of Paucton, that the geometrical pace was 

 4^ Roman feet. What weight may be due to this surmise 

 I cannot pretend to say, but the discrepancy seems to afford 

 a pretty conclusive proof of the accuracy of the position main- 

 tained in my former letter, namely, that the Italian mile and 

 geometrical pace were vague and indefinite terms, having no 

 certain meaning unless defined with reference to some standard 

 foot, and that therefore the use of them by Fernel afforded 

 no presumption against the supposition of Pi card, that his 

 measure was given in Paris feet. If Paucton surmises that 

 the geometrical pace was 4£ Roman feet, he also surmises that 

 it was greater than 5 Roman feet (p. 179); but he likewise 

 tells us that the idea of the geometrical pace has been lost for 

 ages. 



According to Mr. De Morgan's hypothesis Fernel's 68*096 

 Italian miles contained 3,404,800 English inches, and conse- 

 quently a single mile was equivalent to 1389 English yards, 



