Prof. De Morgan on Fernel's Measure of a Degree. 409 



Fernel himself, published at Paris in 1526, two years before 

 the Cosmotheoria : it is likely enough that he corrected the 

 proofs of the former about the time when he made the measure 

 of a degree which is described in the latter. In this Monalo- 

 sphcerium (leaf 25, page 2) 1 found Fernel's own geometrical 

 foot, marked on a line extending down the page, divided into 

 four palms, one of which is divided into four digits, one of 

 which is divided into four grains. Fernel's words on it are, 

 " Caeterura virga queedam mensoria omni molimine nobis de- 

 ligenda est," mensurarum diversitate locupletata*. " Hac 

 quippe duce faciliore negotio in omnes provehemur opera- 

 tiones ; magnoque usui futura, si quintupedalem quantitatem 

 toti concesseris." The title of the line is Figuratio pedis geo- 

 metrici. Fernel's geometrical foot is then the line thus figured 

 plus an allowance for the shrinking of the paper. 



Before I give the measure, I point out what it ought to be 

 nearly, from Fernel's own description of his step. The ave- 

 rage step of a man is 30 English inches, or very near to it : 

 Fernel says that five of his paces make six geometrical paces. 

 At 60 inches to a pace, 300 inches make six geometrical paces, 

 whence the geometrical pace should be 50 inches, and the 

 geometrical foot ten inches (English). 



On measuring the geometrical foot in the Monalosp/iccrium 

 (that is, in the copy of it at the Museum), I find it to be within 

 a sixtieth of an inch of ni?ie inches and two thirds. 



On examining the plate of Dr. Bernard's work on Ancient 

 Weights and Measures (1687), 1 find that in my copy, the 

 length described as 7 inches has shrunk to 6*^ inches. Having 

 no better means of forming a correction for Fernel's paper foot, 

 I adopt this one, and increase 9§ inches in the ratio of 41 to 

 42, which gives nine inches and nine tenths, for the foot of 

 Fernel's paper f before shrinking; say ten inches, as in all pro- 

 bability the above allowance may be a little too small, on ac- 

 count of the greater age of Fernel's work. 



What then was Fernel's degree, which the historians, one 

 and all, think to have been so near the truth that they exclaim 

 at his luck? His geometrical pace is 50 English inches, his 

 Italian mile 50,000 inches, and his degree of 68*096 Italian 

 miles is therefore 340,4800 English inches, ox Jifty-three miles 

 and three quarters, instead of more than sixty-nine miles. And 

 the fact turns out to be, that whereas I was unable to allow 

 Fernel a longer than the Roman foot, and the French historians 



• I am obliged to (jiiotc these three words from niemory, having for- 

 gotten to write them down. 



'; I believe it is the opinion of jjrinlcrs that much the greater part of the 

 bhrinking of paper takes place in the drijing. 



