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N. B. The standards hitherto mentioned, I brought with me to this country at my first arrival in 1805, and ceded them some time after to John Vaughan, Esq. of Philadelphia, who has been so good as to lend them to me for the intended comparison.

4th. The brass metre standarded by Lenoir, No. 16 of the collection of instruments for the survey of the coast, which was compared at the Observatory of Paris, as per certificate of Mr. Bouvard and Arrago, its breadth is =1."1 English, its thickness =0."18. The cer. tificate, dated at the Observatory, 16th March, 1813, says of it: “ En applicant a nos mesures une correction dependante de l'inega6 litè de dilatation des deux metaux, il nous a semblé qu' a zero du 6 thermometre (centigrade) le metre en cuivre de Mr. Hassler, se6 roit plus court que l'Etalon en fer de nos archives de home. de 6 millimetre.”

Mr. Lenoir, who has been employed by the comitée of weights and measures to construct the standards, had taken the precaution, at that time, to make one brass metre, which passed all the comparisons with the others, at the standard temperature of oo centigrade, at which, therefore, it is equal to the authentic iron metres, and forms the only direct mean of comparison between French and English measure. Of this metre the present is a copy, which I thought so much more interesting to have, as the original is unique in its kind, and the comparison of it with the English standard possible by direct means.

5th. One iron toise of Lenoir, No. 15 of the collection of instruments for the survey of the coast. It is near two inches broad, and about a fourth of an inch thick. Its comparison at the observatory at Paris, by the certificate quoted above, says it to be exactly equal to the toise of Peru, preserved at the said observatory.

6th. One iron metre, standarded by Lenoir, No. 18 of the catalogue of instruments for the survey of the coast. It is of the same breadth and thickness as the iron metres of the comitèe, but was not compared at the observatory of Paris, on account of being received too late.

7th. An iron bar, similar to the metre just mentioned, which I intended to bring to the proper metre length, for myself, being yet too long. It was used in the comparison; as well as an operation necessary for its standarding, as to vary the means of combination in the comparisons. It has not been worked since this, having been reserved for a future comparison.

8th. A brass standard scale, of English measure, of 82 inches, divided on silver to every tenth of inches, made by Mr. Troughton, No. 14 of the catalogue of instruments for the survey of the coast. It has the arms of the United States engraved upon it, and " Troughton, London, 1813.” It is three inches broad, and half an inch thick.

To it belongs an apparatus for comparing measures by two compound microscopes, sliding on a rule of equal breadth and thickness with the standard ; and adjustable parallel to it one microscope, having a micrometer reading directly the godog of an inch.

A description of this arrangement existing already in Nicholson's Journal, though on a much smaller scale, all details may here be omitted.

The scale was divided by Mr. Troughton with the utmost care and accuracy, so justly praised in this eminent artist. It contains the double length of the principal part of his own scale, of which an account has been given in the paper of Sir George Shuckburgh, above quoted. Mr. Troughton compared his scale first again in itself, and made a table of errors for the same, in like manner as he has described in his method of hand dividing (Philosophical Transactions, 1809) and then laid off the scale here used, correcting each point according to this table.

To give to a bar of a certain thickness an accurate length, by a cut perpendicular to its length, is an operation which cannot be performed by the free hand, which will always work it uneven, and most likely rounded. To do this with accuracy I had a tool constructed, &c. &c.

(The description of this tool, the iron bars, and the manner in which they have been worked, inay here be passed over, merely mentioning that the four bars were of equal breadth and thickness with the metres, and lettered A, B, C, D.)

For the actual comparison, the unequal thickness of the different standards obliged to support them, so as to bring them exactly to the elevation of the thickest, for which the foci of the microscopes are adjusted, and the value of the micrometer determined. In the comparison of the metres the brass scale was the thickest, and in that of the toises the toise of Canivet. The influence of this necessary supporting, when done only partially, is very great, therefore I had pine rules, made of sufficient breadth and length to support fully the standards and the butting pieces, which were used in reading off, as will be said immediately, and of the accurate thickness to bring each of the metres exactly to the focus, and free from all parallax. As it is completely inadmissible to take the edge of a bar, if ever so sharp, as object under the microscope for the purpose of comparison, because it never forms a good image, pieces cut off from the end of the above mentioned bars,(which had originally been made purposely about nine inches too long) were placed at the two ends of the metres, under comparison, to make the reading from the separation lines, presented by their close contact, which were not thicker than the lines of the scale. These pieces were from two to four inches long, worked to the exact thickness of the metre, or toise, with which they had to serve, and by rubbing with emery and oil one against the other, turning them in all positions, they were brought to make exact contact on the whole surface, which afterwards joined to the metre did the same with it, and on account of their equal thickness presented a plane crossed by the partition line. Upon this the micrometer wires which cross each other under an angle of about 30°, were brought, by optical contact, so that the partition line bisected the angle exactly in the crossing point of the wires.

The microscopes were furnished with paper reflectors, by a piece of white paper placed in a forward inclined direction between the microscopes and their supports, by which the light was reflected upon the scale or standard in the direction of the division lines, as required to avoid all shades of the lines, or partitions, which prevent accurate reading.

To prevent the influence of the heat of the observer's body upon the scale and apparatus, a largo sheet of paper was nailed to the work bench, near the microscopes, where the observer approaches, and I worked with gloves on for the same reason.

From seven to twelve thermometers were constantly laying orer the scale and the standards, and read off at proper intervals of time.

The workbench itself was near double as long as the scale, to obtain a sufficient length fully accurate plane, it was in this respect accurately adjusted before the work, and so placed in respect to the windows, that each microscope corresponded to the best equal light from a separate window; the bench was made of two three inch planks at right angle, and upon six legs.

There was no fire made in the room during the comparison; and, for a number of days before, the windows were besides left open day and night, to bring the room to a steady temperature, being equal to that of the atmosphere.

For the intended comparison of a day all was prepared the day before, and left lying just fit to begin the observations the next day, in order that all parts might be fully at rest, and after verification in the morning the actual comparison begun.

All these precautions are necessary to obtain satisfactory results, as I think may be observed by what will follow.

The possible inaccuracy of the readings may be considered in the direct ratio of their number, having four metres, and the scale holding the sum of two, I had the mean to halve this error by comparing always two together alternately, reading their sum at once on the scale, and forming an equation between the results, to obtain the value of each individual metre. This method had yet the advantage of leaving the observer fully unprejudiced upon what he shall read, as the combination of the different measures and the different influence of temperature occasions a variation which precludes previous estimates.

To this effect, the microscopes were placed to the decimal on the scale nearest to the sum of two metres, viz: 78."7 or 78."8, which was taken from +1" to 79,"8, which approximated it nearest to the middle of the scale. When the scale had been removed, and the two metres with their support properly laid under, so as to bring the middle of their breadth under the centre of the microscopes, the middle contact was exactly made, and with a magnifying glass verified, then the butting pieces being laid on, the coincidence of one end with the crossing wires of the fixed microscope was obtained by longitudinal motion, and the micrometer wires being moved upon the other line of contact, between the metre end and the butting piece, the va

lue of the corresponding subdivisions was read on the micrometer, by its revolutions and subdivisions. The longitudinal motion cannot be made by hand; it is obtained by light strokes with a proper piece of wood, and requires dexterity and care, particularly not to separate the different pieces by the counter stroke.

The value of the micrometer parts was to be previously ascertaine ed by accurate and repeated measurements of a decimal on the scale in different places; by a mean of many, I found under the adjustment for the metres 0."1 on the scale = 1."004 of the micrometer.

At last the individual value of the distance used on the scale in relation to the mean value of the same distance resulting from the measurement of it, on as many parts of the scale as was admissible, was to be determined, in order to give the true mean value of the distance of the points of the scale compared. This was done by about 50 measurements principally after the comparison had been made, and before any alteration had been made in the microscopes. So I found the distance used, or 79."8 — 1."0 = 78."800172 of the mean value of the scale; to this, therefore, all the values obtained by the metre comparison were ultimately referred.

To shorten the manner of registering the results and the combination of the metres and their position, the following mode of notation was adopted: Mc denotes the iron metre of the committee of weights and measures.

- Lenoir.

brass metre of Lenoir. Mj

iron bar which I intended to bring to a metre length. Mc+

metre of the committee and that of Lenoir together,

all marks up. M3+2 - the same metres, all marks down.

And, in like manner, in the other combinations, the adding of the special marks at the top, denoting always the sum of the metres so indicated, and the inversion of the letters the inversion of these me.. tres.

The 15th March, early in the morning, the eleven thermometers which had been lying over night on the scales, prepared the evening before, were read; after having verified that all was in order, then it was further observed, as by the following table:

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(The four bars intended for the base measurement were now also compared, but the result is omitted as unimportant
here.)

The micrometer microscopes having, in the foregoing comparison, read by addition, or from 78."7 onwards, it
was, the 17th March, turned for one half revolution horizontally, so as to read by subtraction, or from 78.8 back-
wards, in order more effectually to compensate the influences possible from them by the following comparisons. The
micrometer values were verified, and found as before. Then all was prepared for the comparison of next day. All
other things being otherwise equally disposed.

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