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V. On the length of the French Mètre estimated in parts of the

English standard. By Captain Henry Kater, F. R. S.

Read February 5, 1818.

One of the objects of the committee of the Royal Society appointed for the purpose of determining the length of the seconds pendulum, being the comparison of the French mètre with the British standard measure, two mètres were procured from Paris for that purpose, the one made in the usual manner and called the mètre à bouts, and the other a bar of platina on which the length of the mètre is shown by two very fine lines; this is named the mètre à traits.

The width of the mère à bouts is one inch, and its thickness 0,3 of an inch. On one side the word “ METRE” is engraved, and on the other “ Fortin à Paris.” The terminating

" planes are supposed to be perfectly parallel, and the distance between them is the length of the mètre.

The mètre à traits is the same width as the mètre à bouts, but only a quarter of an inch thick. The lines expressing the length of the mètre are so fine that one of them is scarcely perceptible even with the assistance of a microscope, unless the light be very favourable. The situation of the lines may however be discovered by two strong black dots made with a graver at the extremities of each, and a fine line crosses them at right angles to indicate the parts from which the measurements are to be taken.

This mètre previous to being brought from Paris, was

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compared with a standard mètre by M. Arago, with all that care and ability which he is so well known to possess, and which so delicate an operation requires. The result was, that the distance between the lines was found to be less than a mètre by 1752 of a millimètre or ,00069 of an inch.

The same micrometer microscopes were used in the comparisons which I am about to detail, as have been already described in my account of experiments on the length of the pendulum, in the Philosophical Transactions of the present year, and as the length of the mètre is nearly 39,4 inches, I was enabled to refer it to the same divisions of Sir GEORGE SHUCKBURGH's scale as I had employed in the measurement of the pendulum.

I commenced with the mètre à traits. It was placed in contact with the standard scale, their surfaces being in the same plane. An excellent thermometer was laid upon the scale, and a piece of thick leather was placed upon its bulb in order to prevent its being affected by heat from the person of the observer.

The whole was suffered to remain in this state for two or three days, after which the following observations were made at various times, the microscopes being brought alternately over the mètre and the scale. The value of each division of the micrometer is z3563 of an inch.*

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* For the manner in which this value was obtained, see page 51 of the preceding paper.

Comparison of the mètre à traits.

Temperature.

Reading

Divisions to

Distance in in- Correction Distance in inches of the mi- Reading of

ches between for tempera

between the lines
be deducted
crom. at the microm. from 39,4 in- nating the me mals of

the lines desig- ture in deci-designating the
39,4 of at the mètre

mètre, the mètre
ches.
the scale.

inch.

being at 32°, and
the scale at 620.

an

tre.

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The comparison of the mètre à bouts, presented considerable difficulties, which I conceive it would be of little use to detail, as the necessity of comparisons of this kind are of very rare occurrence ; I shall therefore proceed to describe the method which was at last found successful.

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Four rectangular pieces of brass were prepared precisely similar to those described in the account of experiments on the pendulum in the Philosophical Transactions before referred to. These were marked C, C, D and d. The perfectly plane rectangular edges of the pieces C and c, being placed in contact, and kept thus by means of a spring, the distance of the fine lines drawn on their surfaces, parallel and very near to the rectangular edges, was found to be 500,5 divisions of the micrometer, and the pieces D and d being placed in like manner in contact, the distance of the lines on their surfaces estimated in the same divisions was 456,7.

The mètre à bouts being placed by the side of the brass scale and in contact with it, the pieces D and d were applied to its extremities, the surfaces of the brass pieces being a little below the surface of the mètre in order to preclude any error which might have arisen from the edges of the mètre projecting beyond its terminating planes. Each of the brass pieces was supported in this position upon a piece of lead of a sufficient thickness, and kept in close contact with the end of the mètre by means of a slight spring bearing against a pin driven perpendicularly into the lead.

In order to ensure a perfect contact between each brass piece and the terminating plane of the mètre, a flat ruler of brass was laid upon the surface of the mètre so as to project beyond its extremity, and the end of the lead was elevated or depressed so that the line of light seen between the piece of brass and the ruler, the eye being level with the surface of the brass, appeared to be equal in every part, when it was inferred that the surfaces of the mètre and of the piece of

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brass were parallel, and consequently that their rectangular ends were perfectly in contact.

The distance between the lines on D and d, was now taken by the microscopes, and transferred to the scale in the manner before described ; and when a sufficient number of comparisons had thus been made, the pieces D and d, were exchanged for those marked C and c, and the observations repeated with every precaution to ensure an accurate result, especially with respect to temperature.

The under surface of the mètre was then placed uppermost, and the apparatus being arranged as before, the same process was pursued as that which has just been described. The results are contained in the following tables.

Comparison of the mètre à bouts.

The pieces D and d, applied. Distance from D to d, 456,7

divisions. The word MÈTRE above.

Reading of Reading of Divisions to

Corr. for

Length of the Tempe- the microm. the microm. Differ- be deducted Length of the temperature Mètre, the mètre rature. at 39,4 of at the brass ence.

from 39,4

Mètre. in decimals being at 32 and the scale. pieces.

linches,

of an inch. the scale at 62o.

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The pieces C and c, applied. Distance from C to c, 500:5 divs.

The word MÈTRE above.

517,3

55,6 55,7 55,9 56,2 56,3

30,7
30,0
30,2
24,5
23,0

47,5
47,3
47,5
45,0
44,7

16,8
17,3
17,3
20,5
21,7

517,8
517,8
521,0
522,2

39,37786 1,00696
39,37784,00694
39,37784 ,00690
39,37770 ,00684
39,37765 ,00681

39,37090
39,37090
39,37094
39,37086
39,37084

Mean

39,37089

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