1887.] 337 [Taylor. 



putations of Mr. T. J. Cram (Silliman's Journal of Science for 1837, Vol. 

 xxxi, page 230), one degree of latitude at the pole is equal to 69.397.19375 

 miles, while one degree at the equator is only 68.70859375 miles — a differ- 

 ence of more than two- thirds of a mile ! In addition to all this there is 

 some reason for doubting whether different meridians are uniform in 

 length and curvature. An arc of the meridian south of the equator, 

 measured in 1752, by Lacaille (at the Cape of Good Hope) gave very un- 

 satisfactory results. 



But through the reductions of various eminent mathematicians we have 

 now the equatorial circumference of the earth as well and accurately 

 determined as any other measure of it. The two best and most recent 

 determinations of the earth's equatorial diameter, are those of Bessel and 

 Air}', who, by independent calculations, agree in the value 7925.6 miles, 

 and differ only by 234 feet ! Bessel making it 41,847,192 feet, and Airy, 

 41,847,426 feet. The mean of these results will give us 131,467,196 feet, 

 as probably a very close measure of the earth's equator. We have every 

 reason, therefore, for deducing our standard of measure from this line — 

 the only true circle by which the earth is circumscribed ; we have none 

 for going back to the irregular meridian. 



In no particular has the decimal principle of the French system proved 

 so signal and utter a failure as in its application to the division of the cir- 

 cle. We have already noticed that the sixth part of the circle is one of its 

 fundamental divisions — one which cannot be neglected for any theoretical 

 advantage of adherence to system. We have seen, moreover, how admi- 

 rably our present division of the quadrant into ninety parts or degrees 

 answers all the various purposes required. lu adding ten more degrees to 

 the whole, so as to make an even hundred, the French philosophers sacri- 

 ficed completely its primarj'^ and beautiful relations. The sextant no lon- 

 ger had a possible expression in the centesimal scale. A verj^ brief exper- 

 iment demonstrated what should have been cleaily anticipated without it, 

 that the new degrees were wholly impracticable. This part of the system 

 was therefore speedily and universally abandoned,* and yet this was really 

 a surrender of the very foundation of the metrical division. 



The metre had been made the 10 millionth part of the quadrant, that the 

 new degree might represent just 10 myriametres ; but the abolition of this 

 ideal degree left the myriametre (and with it of course the metre) a most 

 inconsequential and unmeaning unit. So that now the kilometre no lon- 

 ger represents a minute, and the decametre a second, as w'as its original 

 plan and purpose. 



The selection of the meridian necessarily involved a reference to its nat- 

 ural fraction, the quadrant — the distance from pole to equator ; but had 



• " The new metrology of France, after trying it [the principle of decimal division] in 

 its most universal theoretical application, has been compelled to renounce it for all the 

 measurcsof astronomy, geography, navigation, time, the|circlc and the sphere ; to modify 

 it even for superficial and cubical linear measure, and to compound witli vulgar fractions 

 in the most ordinary and daily uses of all its weights and all its measures" {Adams's 

 Report). 



PROC. AMER. PHILOS. SOC. XXIV. 126. 2q. PRINTED DP:C. 3, 1887. 



