388 
thus exceding double the length of the Toise of Peru, by 
about 45 lines. Lenoir constructed a supplementary 
measure of this excess of length, and its exact relation 
to the toise was ascertained by numerous comparisons, 
for which other intermediate measures were employed, 
and their exact length determined. The actual com- 
parisons of the four brass metres were made not with the 
Toise of Peru itself, but with two standard toises con- 
structed by Lenoir, the length of each of which in relation | 
to the Toise of Peru had been carefully determined. In 
these comparisons the additional length of the measure 
of 45 lines was also employed. The comparing instru- 
ment was a comparateur made by Lenoir, which enabled 
very minute differences in measuring bars under com- 
parison to be read off on a subdivided scale by means of 
a contact lever. One division of this scale was equal to 
o'00001 toise, and one-tenth part of one of these divisions 
(= o'001949 mm.) could be read off with the aid of a 
vernier, It appears from the Report of MM. Borda and 
Brisson, dated July 17, 1795, that the result of a number 
of comparisons, including those of the four metres with 
each other, showed metre No. 2 to be nearest to the 
required length, being 443°4519 lines of the Toise of Peru 
at the mean temperature during the observations of 12°96 
Réaumur, thus very closely approaching its standard 
temperature of 13° Réaumur, and exceeding the required 
length at this temperature by only ovor1g line. It was 
accordingly selected as the provisional Standard Metre. 
But they considered that its standard temperature would 
more conveniently be fixed at 10° C., and as, according to 
Borda’s determination, the coefficient of dilatation of 
brass between o° and 32° C, was o'00001783 for 1° C, 
they determined its length at 10° C. to be 443'401 lines of 
the Toise of Peru. : 
For obtaining the definitive standard, which was to be 
the length of 443'296 lines of the Toise of Peru at 16°25 C., 
which was thus so nearly indicated by the provisional metre, 
two standard metres of platinum, and twelve metres of 
iron, were constructed by Lenoir, his comparing apparatus 
having been improved so as to show differences of o'ooI 
line. The Commission were not satisfied with making 
numerous comparisons of these metres and the provisional 
metre of brass among themselves, but they also compared 
them repeatedly with the four Rég/es de Borda and a new 
supplementary measure of above 45 lines, so as to deter- 
mine not only their relative and absolute length, but also 
the rates of expansion of the three metals of which they 
were composed. ‘he rates of expansion definitively 
adopted by the Commission, from observations made by 
Borda between o° and 32° C., were as follows :— 
In a metre. 
Coefficient of linear expansion of platinum for x° C.= 000000856, or 00031 mm. 
Af brass 3» = 000001783, OF 0°0092 4, 
> iron yy == O'00001I56, OF 0.0063 4, 
The comparisons and corrections of the several metres 
were continued until no difference amounting to o’ooo00I 
toise, or o’oo1 millimetre, could be found at the tempera- 
ture of melting ice, either in their desired absolute length 
of 443°296 lines of the Toise of Peru or in relation to 
each other. They were consequently all determined to 
be perfectly exact. One of the platinum metres, subse- 
quently known as the JZetre des Archives, from its place 
of deposit, was reserved as the new prototype measure of 
length ; the other was kept at the Observatoire at Paris, 
as its accessible representative. The twelve iron stan- 
dard metres were distributed amongst the several countries 
represented at the Commission. 
The primary Metre des Archives is a-rectangular plati- 
num bar, bearing no mark or description. Its breadth is 
25mm. (0'984 in.), its height 3°5 mm. (0.138in.). Its ends 
are planes perpendicular to its axis of length, and 
the straight line between them in this axis denotes the 
true length of the metre at o° C., or the temperature of 
melting ice. It thus constitutes what is termed a JZé¢re- 
a-bouts, or end-standard metre. ; 
° 
NATURE 
*! “sr ae Pre 
| S@pz. 11, 1873 
The unit of metric weight was defined to be the weight 
in a vacuum of a cubic decimetre of distilled water at its 
maximum density, or the temperature of 4° C. Distilled 
water was selected as the best material in nature for thus 
determining the unit of weight, from its being obtainable 
everywhere and at all hours in the greatest purity, its 
being perfectly homogeneous, and its density being invari- 
able at any given temperature. It was required first ac- 
curately to ascertain the weight of this volume of water, 
and then to construct a metallic standard of equivalent 
weight. The necessary operations for effecting both these 
objects were entrusted to M. Lefevre-Gineau in 1795. He 
had to decide between two modes of proceeding for accu- 
rately determining the volume of water to be weighed ; one, 
by measuring the internal capacity of a vessel to contain 
this volume of water ; the other, by measuring externally a 
solid or hollow body, in order to ascertain the weight of 
the volume of water displaced by it. He chose this last 
method, considering that the accurate external measure- 
ment of a metallic body was much less difficult than that 
of the internal capacity of a metallic vessel; and it was 
determined that the best form of this body was a cylinder 
of a height fequal to the diameter of the base, this form 
1G. 10.—Cylinder for determining cubic centimetre. 
being capable of being made and measured with the 
greatest precision. 
It was not thought requisite that the cylinder should be ; 
of the specified volume of a cubic decimetre, but only of 
the most convenient size for arriving at the desired result 
by computation. The cylinder actually used was made of 
brass, and hollow, being only so much heavier than the 
same bulk of water as to enable it to sink by its own 
weight when plunged in water. It was intended to be 
2'435 decimetres (about 94 inches) in diameter and 
height. 
To facilitate the accurate measurement of the cylinder, 
12 radial lines or 6 diameters were drawn on its base 
plane, dividing it into twelve equal parts; and corre- 
sponding lines were drawn on its upper plane. The ends 
of these two series of lines at the circumference were 
joined by vertical lines on the cylinder, thus dividing it 
vertically into twelve equal parts. Circular lines were 
also traced on the two plane surfaces at about 11 mm. 
from the circumference, and at half and two-thirds of the — 
radius from the centre ; and eight horizontal lines were 
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