116 • MEASUREMENT OF ANARG 



/cos.MS S4 44 . {l.G032896)-.f Sii.* (13 34 44 \^ 



^0491.4! -^— — — ^~^-»^~. — «».-». — ~- — _ 1^50458.54 for the de-. 



^ (1.0032896)5 / "^ 



gree on the meridian whofe middle point is on the eqasitor.—Boucruers 

 degree meafured under the Gqa^tor in SoutA Amniccb was 6^482 fa- 

 thoms, which exceeds this by upwards of 23 fathams. Jt.is Boufruer's. 

 meafurement which the French Mathematicians have ufed with that of 



])£ Lamhres and they have made the compreflion to be » 



334 



For the length of the quadrantal arc of the elliptic meridian, fince a 

 is the longer diameter, a x 3, 14159 &c. will be the length of the 

 circumfcribing circle, or the circle whofe diameter is 6^)73905 fathoms. 



and circumference equal 6973905 x 3.14 &c. = 21908630 fathoms. 



Put i ~ I— — = ,00656 nearly. 



Then as i ': i— — — &c* : : a , 3 141 &c. ; a . 3. 14150 8lc» 



22 21 41 ■ - 



d ZiV' ■ - ' 



^x (1 »--^ &c.) — 21908630 X ^99^35^ equal %\%j%6^6 fa« 



thorns, the whole circumference of the elliptic meridiaOg 

 whofe tranfyerfe axis is the length a of the equatorial 

 diameter, or 6973905 fathoms, and whofe conjugate axis is b^ 

 equal 6950839 fathoms, the length of the polar axis,. Hence 



2(872655 



r-,— — ««^ :::z: 5468 1 64 fathoms, tlig length of . the quadrantal arc; 



which reduced to inches and divided by 10,000,000 will give 39.3708 

 f^^/z/A inches for the length oF the ir^^c,^ metre at the temperature 

 of 62°. But the French ftandard is at the temperature of 32% at which 

 the metre by their meafurement was 39,38272 EngUJh inches, which 



_SLCcordmg to the rate -of expanfion in brafs, of which the flandards 



