444 THE YARD, PENDULUM, AND METRE. 



in which Q represents the length of the quadrant re- 

 quired, A that of the polar axis, cr the circumference of 

 a circle whose diameter is i, and /;/, one foiwth part 

 of the fraction expressing the eUipticity, or in this 

 case TTsT* 



Executing the calculation the result is. ..32, 813,000 feet. 

 Substract 10,000,000 metres = 32,808,992 



Remain, excess 4.008 



for the excess of the true quadrant over that assumed 

 as the basis of the metrical system, that is to say, one 

 8194 aliquot part of the whole, or one 2oSth of an inch 

 on the whole metre, which is therefore the quantity by 

 which the French standard is actually too short. 



(28.) It must not be denied that this is a very wonder- 

 ful approximation, and in the highest degree creditable 

 to the science, skill, and devotion of the French astrono- 

 mers and geometricians who carried on their operations 

 under every difficulty, and at the hazard of their hves in 

 the midst of the greatest political convulsion of modern 

 times. And adopted as it is over a large portion of 

 Europe ; were the question an open one what standard a 

 new nation, unprovided with one, unfettered by usages 

 of any sort, and in the absence of any knowledge 

 of the existence of the British yard, should select ; there 

 could be no hesitation as to its adoption (with that very 

 slight correction above pointed out which would in no 



the circumscribed circle internally. The circumference of this small 

 circle is the difference between those of the ellipse and of the larger 

 or circumscribing circle. 



