On the Length of the French Metre. 43} 
tion, and deduce from them the comparative lengths of the equi- 
valent pendulum, ¢, 7't, n”’é, and n't: and hence the value of z, 
of v, and of ¢ may be obtained, without determining w, and of 
course without employing the quantity r. 
> Mie 
2" + UV gt+y TEER Mel 3) Myie +) 
Rist, == 4, ath, =" bore i, 
+0 Zz w w 
A+y ee ofl2 zit? + ay 
Il. st+w= ; 3% +uwu= iF 3% +-u= Ty mt t w= mn 
n n © 
/ 7 ? tt WW 
Hil, z—2/=d'; z—2”=d" 3 z—2'"=d". 
IV. a= PY gies Pe Koel ee poled ai See stebe 
nit? t nll t Wig 
ee 22450 ate atthe, feo e-bee i2!8-by 
D ALORAT ig AS aia = Ae ae alll ge 
VI. By comparing the first of these equations successively with 
the second and third, and bringing the terms containing v to the 
same side, we obtain 
2 ain iD) 
v=(7-a7- m) G m Ne eae a = 
( a! n'd co nla, wa p+ te 
** This equation contains hehe the squares of the idan of z 
with known coefficients ; and if we substitute s—d’, x —d’, and 
—d" for x’, %”, aud z’”, respectively, we shall obtain an equa- 
tion in the form ex*-+ fz=g, whence z= + / (g+4f*)—4 
BS Ray Niae’ 
LXV. On the Length of the French Metre estimated in Parts 
of the English Standard. By Captain Henry Karer, 
BR.S.* 
Ose of the objects of the Committee of the Royal Society ap- 
pointed for the purpose of determining the length of the seconds 
pendulum, being the comparison of the French metre with the 
British Standard Measure, two métres were procured from Paris 
for that purpose, the one made in the usual manner, and called 
the métre a bouts, and the other a bar of platina, on which the 
length of the métre is shown by two very fine lines; this is 
named the métre a tra'ts. 
The width of the mére & bouts is one inch, and its thickness 
0:3 of an inch. On one side the word ** METRE” is engraved, 
* From the Transactions of the Royal Society for 1818, Part I. 4 
an 
