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



the diameter of the earth expressed by a whole number. From 

 the numbers which he gives it is easy to see that he proceeded 

 in this manner : observing that his value of the degree would 

 give the diameter nearly equal to 7800 miles of 1000 paces 

 each, he assumes it to be 7800 miles exactly ; whence, taking 

 the ratio of the circumference to the diameter to be as 22 to 

 7, he finds the circumference = 24,514 miles and 285^ paces, 

 and consequently one degree = 68,095^ paces nearly^ that is, 

 equal to 340,476 feet, omitting a fraction. 



The value assigned to Fernel's degree by Montucla, namely, 

 56,746 toises, was first given by Picard in his Mesure de la 

 Terre, published in 1671. Picard merely observes that 68,096 

 paces (of five feet) make 56,746 toises and four feet (the toise 

 being six feet), " selon nostre fa9on de mesurer" (p. 2) . Taking 

 Fernel's reduced value, or 340,476 feet, we get 56,746 toises. 

 Ozanam [Dictiomiaire Mathematique^ 1691) and Cassini 

 {Grandmr et Fig. de la Terre, 1720) give this value; and 

 Montucla, writing in 1758, quotes it without suggesting any 

 doubt of its accuracy. 



Delambre's value, namely 57,070 toises, is due to the inge- 

 nuity of Lalande, by whom it was given, in the Mem. de VAcad. 

 des Sciences, 1787, as a correction of Picard's reduction. After 

 remarking that Fernel's result as stated by Picard, namely, 

 56,746 toises, differs only by 323 toises from 57,069 toises, 

 the length assigned to the degree by a then recent determina- 

 tion, he adds, " But this exactness, already so singular, be- 

 comes much more astonishing when we take into account the 

 change made in the Paris foot since the time of Fernel. We 

 know positively, from the testimony of Picard, of Azout, and 

 De la Hire {Mem., 1714), that the toise of Paris was short- 

 ened by Jive lines in 1668 ; therefore, on computing according 

 to the toise now in use, it is necessary to add 323 toises to 

 the measure of Fernel, which thus becomes 57,070 toises, that 

 is to say, the same withiusa single toise as the value found at 

 the present time," p. 219. 



In this passage there is manifestly some inaccuracy, for on 

 adding 323 to 56,746, we find not 57,070 but 57,069, as La- 

 lande himself had remarked in a previous sentence. From 

 the whole statement we might be inclined to suspect 323 to be 

 a misprint for 324 ; but it is curious enough that neither of 

 those numbers is obtained from the data. If the toise was 

 shortened by five lines exactly, it follows that Picard's toise 

 contained 869 lines of the corrected toise, or was to the cor- 

 rected toise in the ratio of l^frp to 1. Now ^j x 56,746 

 = 328 ; which being added to 56,746, gives 57,074, and not 

 57,070, as stated by Lalande in the passage above quoted, and 



