394 PROCEEDINGS OP THE AMERICAN ACADEMY 



Cm. Spaces. Inch Spaces. 



2 2 2 2 2 2 



I = — O.V -0.1/x +1.7^1 +1.7m +2.0/i +2.0n I = — l.Sja —1.3m -4.5^t — 4.5/i -4.2^i -4.2^i 



n = +0.2^ +0. V — 2.9/x — 1.2/x — 2.3ja — 0.3^t II = +l.lia —0.2^ — 0.1/x — 4.6n — 0.2;a -4.4^ 



in = —0.1m +0.0m +0.9m —0.3m +0.4m +0.1m III = —0.5m —0.7m +3.6m —1.0m +4.0m —0.4m 



IV = +0.4m +0,4m -0.2m —0.5m +0.2m +0.3m IV =: +0.3m —0.4m —1.6m —2.6m —2.1m —2.5m 



V = -0.4m +0.0m +0.5m +0 Om -0.2m +0.1m V = +1.3m +0.9m +3-3m +0.7m +4.2m +1.7m 



VI — —0.9m +0.0m -0.7m +0.0m -1.7m +0.0m 



Five Cm. Spaces. 



1=:— 0.8m —3.7m —4.8m 



n = +0.8m +3.7m +4.8m 



Equation betvteen the Imperial Yard and the Metre des 



Archives. 



The writer presented to the Montreal meeting of the American 

 Association for the Advancement of Science, in 1882, a paper in 

 which the following relation was announced: — 



Imperial Yai'd -{- 3.37015 inches = Metre des Archives. 



I stated at that time, however, with reference to this relation, that 

 for very obvious reasons I should not like to be held to a very strict 

 account with teference to the last decimal figure given, or even to the 

 last two decimal figures. 



The problem consists of two parts : — 



First, the determination of the relation at 62° F. or 16°. 67 C. be- 

 tween the particular yard and meter defined by H^^ and the original 

 standards from which these units were derived. 



Second, the measurement of the space 3.370-)- inches. 



Let M= the true value of the meter ^^"^ expressed in terms of the 

 Metre des Archives. 



Y' = the true value of the yard R^"'^ expressed in terms of the 

 Imperial Yard. 



X= R^' (meter) — R.^- (yard). 



Then Xz=M—Ti. 



In the investigation of 1882, a space of four inches was laid off upon 

 a short bar designated i?, having the same composition as R^. This 

 space was subdivided to inches. The third inch was subdivided to 

 tenths of an inch, and the seventh tenth was subdivided to hundredths 

 of an inch. The following relations between the subdivisions of R.^'^ 

 and B were then determined. 



