Final State of the Report on Weights and Measures, [4 July 1790]
Final State of the Report on Weights and Measures
The Secretary of state to whom was referred, by the house of representatives, to prepare and report a proper plan or plans for establishing uniformity in the currency, weights and measures of the U.S. in obedience thereto, makes the following report.
To obtain uniformity in measures, weights and coins, it is necessary to find some measure of invariable length, with which, as a standard, they may be compared.
There exists not in nature, as far as has been hitherto observed, a single subject, or species of subject accessible to man, which presents one constant and uniform dimension.^{1}
The globe of the earth itself indeed might be considered as invariable in all it’s dimensions, and that it’s circumference would furnish an invariable measure. But no one of it’s circles great or small, is accessible to admeasurement through all it’s parts: and the various trials to measure definite portions of them have been of such various result, as to shew there is no dependance on that operation for certainty.
Matter then, by it’s mere extension, furnishing nothing invariable, it’s Motion is the only remaining resource.
The motion of the earth round it’s axis, tho’ not absolutely uniform and invariable, may be considered as such for every human purpose.^{2} It is measured obviously but unequally, by the departure of a given meridian from the sun, and it’s return to it, constituting a solar day. Throwing together the inequalities of Solar days, a mean interval, or day, has been found, and divided by very general consent into 86,400 equal parts.
A pendulum, vibrating freely in small and equal arcs, may be so adjusted in it’s length as by it’s vibrations, to make this division of the earth’s motion into 86,400 equal parts called seconds of mean time.
Such a pendulum then becomes itself a measure of determinate length, to which all others may be referred, as to a standard.
But even the pendulum is not without it’s uncertainties.
1. The difficulty of ascertaining in practice it’s center of oscillation, as depending on the form of the Bob and it’s distance from the point of suspension; the effect of the weight of the suspending wire towards displacing the center of oscillation; that center being seated within the body of the bob, and therefore inaccessible to the measure; are sources of considerable incertainty.
2. Both theory and experience prove that, to preserve it’s isochronism, it must be shorter towards the equator, and longer towards the poles.
3. The height of the situation above the common level, as being an increment to the radius of the earth, diminishes the length of the pendulum.^{3}
4. The pendulum being made of metal, as is best, it varies it’s length with the variations in the temperature of the atmosphere.
5. To continue small and equal vibrations through a sufficient length of time, and to count these vibrations, machinery and a power are necessary, which may^{4} exert a small but constant effort to renew the waste of motion: and the difficulty is so to apply these as that they shall neither retard nor accelerate the vibrations.
1. In order to avoid the uncertainties which respect the center of oscillation, it has been proposed by Mr. Leslie, an ingenious artist of Philadelphia, to substitute for the pendulum, an uniform cylindrical rod, without a Bob.
Could the diameter of such a rod be infinitely small, the center of oscillation would be exactly at two thirds of the whole length, measured from the point of suspension. Giving it a diameter which shall render it sufficiently inflexible, the center will be displaced indeed; but, in a Second rod, not the* 600,000th part of it’s length, and not the hundredth part as much as in a Second pendulum, with a Spherical Bob of proper diameter. This displacement is so infinitely minute then, that we may consider the center of oscillation for all practical purposes as residing at two thirds of the length from the center of suspension. The distance between these two centers might be easily and accurately ascertained in practice. But the whole rod is better for a standard than any portion of it, because sensibly defined at both it’s extremities.^{8}
2. The uncertainty arising from the difference of length requisite for the Second pendulum, or the Second rod, in different latitudes, may be avoided by fixing on some one latitude to which our standard shall refer. That of 38.° as being the middle latitude of the United states, might seem the most convenient, were we to consider ourselves alone. But connected with other nations by commerce and science, it is better to fix on that parallel which bids fairest to be adopted by them also. The 45th. as being the middle term between the Equator and Pole has been heretofore proposed in Europe; and the proposition has been lately renewed there under circumstances which may very possibly give it some effect. This parallel is distinguished with us also, as forming our principal Northern boundary. Let the completion of the 45th. degree then give the Standard for our Union, with the hope that it may become a line of union with the rest of the world.
The difference between the Second rod for 45.° of latitude, and that for 31.° our other extreme, is to be examined.
The Second pendulum for 45.° of latitude, according to Sr. Isaac Newton’s computation, must be of § 39.14912 inches English measure, and a rod, to vibrate in the same time, must be of the same length between the centers of suspension and oscillation; and consequently it’s whole length 58.7 (or more exactly 58.72368) inches. This is longer than the rod which shall vibrate seconds in 31.° of Latitude by about 1/679 part of it’s whole length; a difference so minute that it might be neglected, as insensible, for the common purposes of life. But in cases requiring perfect exactness, the Second rod, found by trial of it’s vibrations in any part of the U.S. may be corrected by computation for the† latitude of the place, and so brought exactly to the standard of 45.°^{10}
3. By making the experiment in the level of the ocean, the difference will be avoided which a higher position might occasion.^{11}
4. The expansion, and contraction of the rod with the change of temperature is the fourth source of uncertainty beforementioned, according to the high authority so often quoted. An iron rod, of given length, may vary, between summer and winter, in temperate latitudes, and in the common exposure of houseclocks from 1/1728 to 1/2592 of it’s whole length: which in a rod of 58.7 inches will be from about two to three hundredths of an inch. This may be avoided by adjusting and preserving the standard in a cellar, or other place, the temperature of which never varies.^{12} Iron is named for this purpose, because the least expansible of the metals.
5. The practical difficulty resulting from the effect of the machinery and moving power, is very inconsiderable in the present state of the arts; and in their progress towards perfection, will become less and less. To estimate and obviate this, will be the artist’s province. It is as nothing when compared with the sources of inaccuracy hitherto attending measures.^{13}
Before quitting the subject of the inconveniencies, some of which attend the pendulum alone, others both the pendulum and rod, it must be added that the rod would have an accidental, but very precious advantage over the pendulum in this country, in the event of our fixing the foot at the nearest aliquot part of either: for the difference between the common foot and those so to be deduced would be three times greater in the case of the pendulum than in that of the rod.^{14}
Let the Standard of measure then be an uniform cylindrical rod of iron, of such length as in lat. 45.° in the level of the ocean, and in a cellar or other place, the temperature of which does not vary thro’ the year, shall perform it’s vibrations, in small and equal arcs, in one second of mean time.
A standard of invariable length being thus obtained, we may proceed to identify by that the measures, weights, and coins of the U.S. but here a doubt presents itself as to the extent of the reformation meditated by the house of representatives. The experiment made by Congress in the year 1786. by declaring that there should be one money of account and paiment through the U.S. and that it’s parts and multiples should be in a decimal ratio, has obtained such general approbation, both at home and abroad, that nothing seems wanting, but the actual coinage, to banish the discordant pounds, shillings, pence and farthings of the different states, and to establish in their stead the new denominations. Is it in contemplation with the house of representatives to extend a like improvement to our measures and weights, and to arrange them also in a decimal ratio? The facility which this would introduce into the vulgar arithmetic would unquestionably be soon and sensibly felt by the whole mass of the people, who would thereby be enabled to compute for themselves whatever they should have occasion to buy, to sell, or to measure, which the present complicated and difficult ratios place beyond their computation for the most part.—Or, is it the opinion of the representatives that the difficulty of changing the established habits of a whole nation opposes an insuperable bar to this improvement? Under this uncertainty the Secretary of state thinks it his duty to submit alternative plans, that the house may at their will adopt either the one or the other exclusively, or the one for the present, and the other for a future time, when the public mind may be supposed to have become familiarised to it.
I.
And first on the supposition that the present measures and weights are to be retained, but to be rendered uniform and invariable, by bringing them to the same invariable standard.
The first settlers of these states having come chiefly from England brought with them the measures and weights of that country. These alone are generally established among us, either by law or usage, and these therefore are alone to be retained and fixed. We must resort to that country for information of what they are or ought to be.
This rests principally on the evidence of certain standard measures and weights, which have been preserved of long time in different deposits. But differences among these having been known to exist, the house of commons in the years 1757. and 1758. appointed committees to enquire into the original standards of their weights and measures. These committees, assisted by able mathematicians and artists, examined and compared with each other the several standard measures and weights, and made reports on them in the years 1758. and 1759. The circumstances under which these reports were made entitle them to be considered as far as they go, as the best written testimony existing of the standard measures and weights of England: and as such they will be relied on in the progress of this report.
Measures of length.
The measures of length in use among us are
The league of 3. miles; 
The ell of a yard and quarter; 
The mile of 8. furlongs; 
The yard of 3. feet; 
The furlong of 40. poles or perches; 
The foot of 12. inches; and 
The pole or perch of 5½ yards; 
The inch of 10. lines. 
The fathom of 2. yards; 

On this branch of their subject the committee of 1757. 1758. says that the Standard measures of length at the Receipt of the Exchequer are a yard, supposed to be of the time of H.7. and a yard and ell supposed to have been made about the year 1601. that they are brass rods, very coarsely made, their divisions not exact, and the rods bent: and that in the year 1742, some members of the Royal society had been at great pains in taking an exact measure of these standards by very curious instruments, prepared by the ingenious Mr. Graham; that the Royal society had had a brass rod made pursuant to their experiments, which was made so accurately, and by persons so skilful and exact, that it was thought not easy to obtain a more exact one; and the Committee in fact found it to agree with the standards at the Exchequer as near as it was possible. They furnish no means, to persons at a distance, of knowing what this standard is. This however is suppli[ed by the evidence of the Second pendulum, which according to the authority before quoted is, at London, 39.1682 English inches, and consequently the Second rod there is of 58.7523 of the same inches. When we shall have found then, by actual trial, the Second rod for 45.° by adding the difference of their computed length, to wit 287/10000 of an inch, or rather 3/10 of a line (which in practice will endanger less error than an attempt at so minute a fraction as the ten thousandth parts of an inch) we shall have the Second rod of London, or a true measure of 58¾ English inches. Or to shorten the operation, without varying the result,]^{17}
Let the Standard rod of 45.° be divided into 587⅕^{18} equal parts; and let each of these parts be declared a line;
10 lines an inch;
12 inches a foot;
3. feet a yard;
3. feet 9. Inches an ell;
6. feet a fathom;
5½ yards a perch or pole;
40. poles or perches a furlong;
8. furlongs a mile;
3. miles a league.
Superficial measures
Our measures of surface are the Acre of 4. rood; and the Rood of 40. square poles; so established by a statute of 33.E.1. Let them remain the same.
Measures of capacity.
The measures of capacity in use among us are of the following names and proportions.
the gill, 4. of which make a pint;
2. pints make a quart;
2. quarts a pottle;
2. pottles a gallon;
2 gallons a peck, dry measure;
8. gallons make a measure, called a firkin in liquid substances, and a bushel dry;
2. firkins or bushels, makes a measure called a rundlet, or kilderkin liquid, and a strike, dry;
2. kilderkins or strikes make a measure called a barrel liquid, and a coom^{19} dry; this last term being antient and little used;
2. barrels or cooms make a measure called a hogshead liquid, or a quarter dry; each being the quarter of a ton;
6. hogshead and a third make a tierce, or third of a ton;
2. hogsheads make a pipe, butt, or puncheon;
and 2 pipes make a ton.
But no one of these measures is of a determinate capacity. The report of the committee of 1757.8. shews that the gallon is of various content: and that being the Unit, all the others must vary with it.
The gallon and bushel contain
224. and 1792. cubic inches, according to the standard wine gallon preserved at Guildhall;
231. and 1848. according to the statute of the 5th. Anne;
264.8 and 2118.4 according to the antient Rumford quart of 1228. examined by the committee;
265.5 and 2124. according to three standard bushels preserved in the Exchequer, to wit, one of H.7. without a rim; one dated 1091, supposed for 1591. or 1601. and one dated 1601.
266.25 and 2130. according to the antient Rumford gallon of 1228. examined by the committee;
268.75 and 2150. according to the Winchester bushel, as declared by stat. 13.14.W.3. which has been the model for some of the grain states;
271. less 2. spoonfuls, and 2168. less 16. spoonfuls, according to a standard gallon of H.7. and another dated 1601. marked E.E. both in the Exchequer;
271. and 2168. according to a standard gallon in the Exchequer, dated 1601, marked E. and called the corn gallon;
272. and 2176. according to three standard corngallons last mentioned, as measured in 1688. by an artist for the Commissioners of the Excise, generally used in the seaport towns, and by mercantile people, and thence introduced into some of the grain states;
277.18 and 2217.44 as established for the measure of coal by the statute 12. Anne;
278. and 2224. according to a standard bushel of H.7. with a copper rim, in the Exchequer;
278.4 and 2227.2 according to two standard pints of 1601. and 1602. in the Exchequer;
280. and 2240. according to the standard quart of 1601 in the exchequer;
282 and 2256. according to the standard gallon for beer and ale in the Treasury;
There are moreover varieties on these varieties from the barrel to the ton inclusive: for if the Barrel be of Herrings, it must contain 28. gallons by the stat. 13. El.c.11.
If of Wine, it must contain 31½ gallons by the stat. 2.H.6.c.11 and 1.R.3.c.15.
If of Beer or ale, it must contain 34. gallons by the stat.l.W.&M.c.24. and the higher measures in proportion.
In those of the U.S. which have not adopted the statutes of W. and M. and of Anne before cited, nor their substance, the wine gallon of 231. cubic inches rests on the authority of very long usage before the 5th. of Anne, the origin and foundation of which are unknown; the bushel is the Winchester bushel by the 11.H.7. undefined; and the barrel of ale 32. gallons, and of beer 36. gallons by the stat 23.H.8.c.4.
The Secretary of state is not informed whether there have been any and what alterations of these measures by the laws of the particular states.
It is proposed to retain this series of measures, but to fix the gallon to one determinate capacity as the unit of measure, both wet and dry; for convenience is in favor of abolishing the distinction even between wet and dry measures.
The wine gallon, whether of 224. or 231. cubic inches, may be altogether disregarded, as concerning principally the mercantile, and the wealthy, the least numerous part of the society, and the most capable of reducing one measure to another by calculation. The gallon is little used among the mass of farmers, whose chief habits and interests are in the size of the corn bushel.
Of the standard measures before stated two are principally distinguished in authority and practice. The statute bushel of 2150. cubic inches, which gives a gallon of 268.75 cubic inches, and the standard gallon of 1601. called the Corn gallon, of 271. or 272. cubic inches which has introduced the mercantile bushel of 2176. inches. The former of these is most used in some of the grain states, the latter in others. The middle term of 270. cubic inches may be taken as a mutual compromise of convenience, and as offering this general advantage, that the bushel being of 2160. cubic inches is exactly a cubic foot and a quarter, and so facilitates the conversion of wet and dry measures into solid contents and tonnage, and simplifies the connection of measures and weights, as will be shewn hereafter. It may be added in favor of this as a medium measure that eight of the standard or statute measures before enumerated are below this term, and nine above it.
The measures to be made for use being foursided, with rectangular sides and bottom,
The Pint will be 3. inches square and 3¾ I. deep;
The Quart 3. I. square and 7½ I. deep;
The Pottle 3. I. square and 15. I. deep, or 4½, 5, and 6. I.
The Gallon 6. I. square and 7½ I. deep, or 5, 6, and 9. I.
The Peck 6, 9, and 10. I.
The Halfbushel 12. I. square, and 7½ I. deep;
and the Bushel 12. I. square, and 15. I. deep, or 9, 15, and 16. I.
Cylindrical measures have the advantage of superior strength: but square ones have the greater advantage of enabling every one, who has a rule in his pocket to verify their contents, by measuring them. Moreover till the circle can be squared, the cylinder cannot be cubed, nor it’s contents exactly expressed in figures.
Let the measures of capacity then for the U.S. be
A gallon of 270. cubic inches;
The gallon to contain two pottles;
The pottle 2. quarts;
The quart 2. pints;
The pint 4. gills;
2. gallons to make a peck;
8. gallons a bushel or firkin;
2. bushels or firkins a strike or kilderkin;
2. strikes or kilderkins a coom^{19} or barrel;
2. cooms or barrels a quarter or hogshead;
A hogshead and a third one tierce;
2. hogsheads a pipe, butt, or puncheon;
and 2. pipes a ton.
And let all measures of capacity of dry subjects be stricken with a strait strike.
Weights.
There are two series of weights in use among us; the one called Avoirdupois, the other Troy.
In the Avoirdupois series
The Pound is divided into 16. ounces;
The ounce into 16. drams;
The dram into 4. quarters.
In the Troy series,
The Pound is divided into 12 ounces;
The Ounce (according to the subdivision of the Apothecaries) into 8. drams;
The Dram into 3. scruples;
The Scruple into 20. grains.
According to the subdivision for gold and silver
The Ounce is divided into 20 pennyweight;
and the pennyweight into 24. grains.
so that the pound Troy contains 5760. grains, of which 7000. are requisite to make the pound avoirdupois. Of course the weight of the pound Troy is to that of the pound Avoirdupois as 5760. to 7000. or as 144. to 175.
It is remarkeable that this is exactly the proportion of the antient liquid gallon of Guildhall of 224. cubic inches to the corn gallon of 272. for 224. are to* 272. as 144. to 175.
It is further remarkeable still that this is also the exact proportion between the specific weight of any measure of wheat, and of the same measure of water. For the statute bushel is of 64. pounds of wheat. Now as 144. to 175. so are 64. ℔. to 77.7. ℔. But 77.7 ℔. is known to be the weight of§ 2150.4 cubic inches of pure water; which is exactly the content of the Winchester bushel as declared by the stat. 13. 14. W. 3. That statute determined the bushel to be a cylinder of 18½ inches diameter, and 8. inches depth. Such a cylinder, as nearly as it can be cubed, and expressed in figures, contains 2150.425 cubic inches: a result which reflects authority on the declaration of parliament and induces a favorable opinion of the care with which they investigated the contents of the antient bushel, and also a belief that there might exist evidence of it as that day unknown to the committees of 1758. and 1759.
We find then in a continued proportion 64. to 77.7 as 224. to 272. and as 144. to 175. that is to say: the Specific weight of a measure of wheat, to that of the same measure of water, as the cubic contents of the wet gallon, to those of the dry; and as the weight of a pound Troy to that of a pound Avoirdupois.
This seems to have been so combined as to render it indifferent whether a thing were dealt out by weight or measure. For the dry gallon of wheat, and the liquid one of wine, were of the same weight; and the Avoirdupois pound of wheat, and Troy pound of wine were of the same measure. Water and the vinous liquors which enter most into commerce, are so nearly of a weight, that the difference, in moderate quantities, would be neglected by both buyer and seller; some of the wines being a little heavier, and some a little lighter than water.
Another remarkeable correspondence is that between weights and solid measures. For 1000. ounces avoirdupois of pure water, fill a cubic foot with mathematical exactness.
What circumstances of the times, or purposes of barter or commerce, called for this combination of weights and measures with the subjects to be exchanged or purchased, are not now to be ascertained. But a triple set of exact proportionals representing weights, measures, and the things to be weighed and measured, and a relation so integral between weights and solid measures, must have been the result of design, and scientific calculation, and not a mere coincidence of hazard. It proves that the dry and wet measures the heavy and light weights must have been original parts of the system they compose: contrary to the opinion of the committee of 1757. 1758. who thought that the avoirdupois weight was not an antient weight of the kingdom, nor ever even a legal weight, but during a single year of the reign of H. 8. and therefore concluded, otherwise than will be here proposed, to suppress it altogether. Their opinion was founded chiefly on the silence of the laws as to this weight. But the harmony here developed in the system of weights and measures, of which the avoirdupois makes an essential member, corroborated by a general use, from very high antiquity, of that, or of a nearly similar weight under another† name, seem stronger proofs that this is a legal weight, than the mere silence of the written laws is of the contrary.
Be this as it may, it is in such general use with us, that, on the principle of popular convenience, it’s higher denominations, at least, must be preserved. It is by the Avoirdupois pound and ounce that our citizens have been used to buy and sell. But the smaller subdivisions of drams and quarters, are not in use with them. On the other hand, they have been used to weigh their money and medecine with the pennyweights and grains, Troy weight, and are not in the habit of using the pounds and ounces of that series. It would be for their convenience then to suppress the pound and ounce Troy, and the dram and quarter avoirdupois; and to form into one series, the avoirdupois pound and ounce, and the Troy pennyweight and grain. The Avoirdupois ounce contains 18. pennyweight 5½ grains Troy weight. Divide it then into 18. pennyweight, and the pennyweight as heretofore into 24. grains, and the new pennyweight will contain between a third and a quarter of a grain more than the present Troy pennyweight; or more accurately, it will be to that as 875. to 864. a difference not to be noticed either in money or medicine below the denomination of an ounce.
But it will be necessary to refer these weights to a determinate mass of some substance, the specific gravity of which is invariable. Rain water is such a substance, and may be referred to every where and through all time. It has been found, by accurate experiments, that a cubic foot of rainwater weighs 1000. ounces avoirdupois, standard weights of the Exchequer. It is true that among these standard weights, the committee reports small variations. But this experiment must decide in favor of those particular weights, between which and an integral mass of water, so remarkeable a coincidence has been found. To render this standard more exact the water should be weighed always in the same temperature of air; as heat, by increasing it’s volume, lessens it’s specific gravity. The cellar of uniform temperature is best for this also.^{20}
Let it then be established that an ounce is of the weight of a cube of rainwater, of one tenth of a foot or rather that it is the thousandth part of the weight of a cubic foot of rain water weighed in the standard temperature; that the series of weights of the U.S. shall consist of pounds, ounces, pennyweights, and grains whereof
24. grains shall be one pennyweight;
18. pennyweight one ounce;
16. ounces one pound.
Coins.
Congress in 1786. established the Money unit at 375.64 Troy grains of pure silver. It is proposed to enlarge this by about the third of a grain in weight, or a mill in value; that is to say, to establish it at 376. (or more exactly 376.02985) instead of 375.64 grains,^{21} because it will be shewn that this, as the Unit of coin, will link in system with the Units of length, surface, capacity and weight, whenever it shall be thought proper to extend the decimal ratio through all these branches. It is to preserve the possibility of doing this that this very minute alteration is proposed.
We have this proportion then. 875. to 864. as 376.02985 grains Troy to 371.30261^{22} the expression of the Unit in the new grains.
Let it be declared therefore that the Money unit, or Dollar of the U.S. shall contain 371.3^{23 }American grains of pure silver.
If nothing more then is proposed than to render uniform and stable the system we already possess, this may be effected on the plan herein detailed; the sum of which is 1. that the present measures of length be retained and fixed by an invariable standard: 2. that the measures of surface remain as they are, and be invariable also as the measures of length to which they are to refer: 3. that the Unit of capacity, now so equivocal, be settled at a medium and convenient term, and defined by the same invariable measures of length: 4. that the more known terms in the two kinds of weights be retained, and reduced to one series, and that they be referred to a definite mass of some substance, the specific gravity of which never changes: and 5. that the quantity of pure silver in the money unit be expressed in parts of the weight so defined.
In the whole of this no change is proposed, except an insensible one in the Troy grain and pennyweight, and the very minute one in the Money unit.
II.
But if it be thought that, either now, or at any future time, the citizens of the U.S. may be induced to undertake a thorough reformation of their whole system of measures, weights and coins, reducing every branch to the same decimal ratio already established in their coins, and thus bringing the calculation of the principal affairs of life within the arithmetic of every man who can multiply and divide plain numbers, greater changes will be necessary.
The Unit of measure is still that which must give law through the whole system: and from whatever unit we set out, the coincidences between the old and new ratios will be rare. All that can be done will be to chuse such an Unit as will produce the most of these. In this respect the Second rod has been found on trial to be far preferable to the Second pendulum.
Measures of length.
Let the Second rod then, as before described, be the Standard of measure; and let it be divided into five equal parts, each of which shall be called a Foot: for perhaps it may be better, generally to retain the name of the nearest present measure, where there is one tolerably near. It will be about one quarter of an inch shorter than the present foot.
Let the foot be divided into 10. inches;
The Inch into 10. lines;
The line into 10. points;
Let 10. feet made a decad;
10. decads a rood;
10. roods a furlong;
10. furlongs a mile.
Superficial measures.
Superficial measures have been estimated, and so may continue to be, in squares of the measures of length, except in the case of lands, which have been estimated by squares called roods and acres. Let the Rood be equal to a square, every side of which is 100. feet. This will be 6.483^{24 }English feet less than the‖ English rood every way, and 1311.^{25} square feet less in it’s whole contents; that is to say, about one eighth, in which proportion also, 4 rood will be less than the present acre.
Measures of capacity
Let the Unit of capacity be the cubic foot, to be called a Bushel. It will contain 1620.23^{26} cubic inches English; be about ¼less than that before proposed to be adopted as a medium; 1/10 less than the bushel made from 8. of the Guildhall gallons, and 1/14 less than the bushel made from 8. Irish gallons of 217.6 cubic inches.
Let the bushel be divided into 10. pottles;
Each pottle into 10. demipints;
Each demipint into 10. metres, which will be of a cubic inch each.
Let 10. bushels be a quarter, and
10. quarters a last or doubleton.
The measures for use being foursided and the sides and bottoms rectangular,
The bushel will be a foot cube;
The pottle 5. inches square and 4. inches deep;
The demipint 2. inches square and 2½ inches deep;
The Metre an inch cube.
Weights.
Let the weight of a cubic inch of rainwater or the thousandth part of a cubic foot be called an ounce; and let the ounce be divided into 10 double scruples; the double scruple into 10. carats; the carat into 10. minims or demigrains, the minim into 10. mites.
Let 10. ounces make a pound; 10 pounds a stone; 10 stone a kental; 10 kental a hogshead.
Coins.
Let the Moneyunit, or Dollar contain eleven twelfths of an ounce of pure silver. This will be 376^{27} Troy grains (or more exactly 376.02985^{28} Troy grains,) which will be about a third of a grain (or more exactly .38985^{29} of a grain) more^{30} than the present Unit. This with the twelfth of alloy, already established, will make the Dollar or Unit of the weight of an ounce, or of a cubic inch of rain water exactly. The series of Mills, Cents, Dimes, Dollars and Eagles to remain as already established.
The Second rod, or the Second pendulum, expressed in the measures of other countries, will give the proportion between their measures and those of the U.S.
Measures, weights, and coins thus referred to standards, unchangeable in their nature, (as is the length of a rod vibrating seconds, and the weight of a definite mass of rain water) will themselves be unchangeable. These standards too are such as to be accessible to all persons, in all times and places. The measures and weights derived from them fall in so nearly with some of those now in use, as to facilitate their introduction; and being arranged in decimal ratio, they are within the calculation of every one who possesses the first elements of arithmetic, and of easy comparison, both for foreigners and citizens, with the measures, weights, and coins of other countries.
A gradual introduction would lessen the inconveniences which might attend too sudden a substitution, even of an easier, for a more difficult system. After a given term, for instance, it might begin in the Custom houses, where the merchants would become familiarised to it. After a further term, it might be introduced into all legal proceedings, and merchants, and traders in foreign commodities, might be required to use it in their dealings with one another. After a still further term, all other descriptions of people might recieve it into common use.—Too long a postponement on the other hand, would increase the difficulties of it’s reception, with the increase of our population.^{31}
The measures, weights and coins of the Decimal system estimated in those of England now used in the U.S.
1. Measures of length.
Feet  Equivalent in English measure  
The  Point  .001  .011 Inches  
Line  .01  .117  
Inch  .1  1.174  about 1/7 more than the English inch.  
Foot  1.  11.744736 .978728 Feet 
about 1/48 less than the English foot.  
Decad  10.  9.787  about 1/48 less than the 10. feet rod of the carpenters.  
Rood  100.  97.872  about 1/16 less than the side of an English square rood.  
Furlong  1000.  978.728  about ⅓ more than the English furlong.  
Mile  10000.  9787.28  about 1 6/7 English mile: nearly the Scotch and Irish mile, and ½ the German. 
2. Superficial measure.^{32}

Rood. 
square feet 

The Rood. 
1. 
9579.085 
about ⅛ less than the English Rood. 
3. Measures of capacity.
Bushels  cub. Inches  
The  Metre  .001  1.6202^{33}  
Demipint  .01  16.202^{34}  about 1/24 less than the English half pint.  
Pottle  .1  162.022^{35}  about ⅙ more than the English pottle.  
Bushel  1.  1620.229596620920160256^{36} .937632868414884352 cub. feet 
about ¼ less than the middle sized English bushel.  
Quarter  10.  9.376^{37}  about ⅙ less than the English quarter.  
Last  100.  93.763^{38}  about 1/7 more than the English Last. 
4. Weights.  
Pounds  Avoirdupois  Troy  
The Mite  .00001  .041 grains  about ⅕ less than the  
Minim or 
English mite.  
Demigrain 
.0001  .4102^{39}  
about ⅕ less than the Halfgrain Troy. 

Carat. 
.001  4.102^{40}  
about 1/40 more than the Carat Troy. 

Double Scruple 
.01  41.021^{41}  
about 1/40 more than two scruples Troy. 

Ounce 
.1  .937632868414884352^{42} oz  {410.214379931511904  about 1/16 less  
{ 85461 oz.^{43}} than the Ounce  avoirdupois  
Pound 
1.  {9.376  }  .712175℔^{44} about ¼ less th  
{ .586020540093 ℔}  Pound Troy  
Stone 
10.  {93.763 oz. }  71.217^{45}  about ¼ less than the  
{ 5.8602 ℔ }  Eng. Stone of 8. ℔  
Kental 
100.  {937.632 oz. }  71.217^{46}  about 4/10 less than the  
{ 58.602 ℔ }  avoirdupois.  Eng. Kental of 100.  
Hogshead  1000.  {9376.328 oz. }  712.175^{47}  ℔. avoirdupois.  
{ 586.0205 ℔ } 
5. Coins.
Dollars  
The  Mill  .001  
Cent  .01  
Dime  .1  Troy grains  
Dollar  1. 


Eagle  10. 
* In the Second pendulum with a Spherical Bob, call the distance between the centers of suspension and of the Bob, 2 x 19.575, or 2d. and the radius of the Bob = r. Then 2d : r :: r : r²/2d and ⅖ of this last proportional expresses the displacement of the center of oscillation, to wit 2rr/5 x 2d = rr/5d. 2 inches have been proposed as a proper diameter for such a Bob.^{5} In that case r. will be = 1. I and rr/5d = 1/97.87 I.
In the Cylindrical Second rod, call the length of the rod 3 x 19.575, or 3d. and it’s radius = r. and rr/2 x 3d = rr/6d will express the displacement of the center of oscillation. It is thought the rod will be sufficiently inflexible if it be ⅕ of an inch in diameter. Then r. will be = .1 I. and = rr/6d = 1/11745I. which is but the 120th. Part of the displacement in the case of the pendulum, with a Spherical Bob;^{6} and but the 689710th. part of the whole length of the rod. If the rod be even of half an inch diameter, the displacement will be but 1/1879 of an inch, or 1/110356 of the length of the rod.^{7}
^{§} Sr. Isaac Newton computes the pendulum for 45.° to be 36. pouces 8.428 lignes. Picard made the English foot 11. pouces 2.6 lignes, and Dr. Maskelyne 11. pouces 3.11 lignes. D’Alembert states it at 11. pouces 3. lignes, which has been used in these calculations as a middle term, and gives us 36 po.—8.428 li. = 39.1491 inches. This length for the pendulum of 45.° had been adopted in this report before the Bishop of Autun’s proposition was known here. He relies on Mairan’s ratio for the length of the pendulum in the latitude of Paris, to wit, 504 : 257 :: 72. pouces to a 4th. proportional, which will be 36.71428 pouces = 39.1619 inches, the length of the pendulum for Lat. 48°—50.’ The difference between this and the pendulum for 45.° is .0113 of an inch: so that the pendulum for 45.° would be estimated according to Mairan at 39.1619—.0113 = 39.1506 inches, almost precisely the same with Newton’s computation herein adopted.^{9}
† Sr. Isaac Newton’s computations for the different degrees of latitude from 30.° to 45.° are as follows.^{15}

pieds 
lignes 

pieds 
lignes 
30° 
3 “ 
7.948 
42° 
3 “ 
8.327 
35. 
3 “ 
8.099 
43. 
3 “ 
8.361 
40. 
3 “ 
8.261 
44 
3 “ 
8.394 
41. 
3 “ 
8.294 
45 
3 “ 
8.428 
‖ ‘Virga penduli in horologio tres pedes longa, paulo quidem longior erit tempore aestivo quam hiberno; sed excessu quartam partem lineae unius vix superante.—Virga ferrea pedes tres longa, tempore hyberno, in Anglia, brevior est, quam tempore aestivo, sexta parte lineae unius, quantum sentio.’^{16} Newt. Princip. L. 3. prop. 20. prob. 4.
* Or more exactly 144 : 175 :: 224 : 272.2
§ Or more exactly 62.5 : 1728 :: 77.7 : 2150.39
† The Merchants weight.
‖ The English rood contains 10890 square feet = 104.355 f. square
MS (DLC: TJ Papers, 65: 11247–57); entirely in TJ’s hand; containing numerous deletions, corrections, and one note pasted over another (see note 10, below); TJ’s symbols keying footnotes to text were changed to numbers at the time FC was executed; contains 21 numbered pages and may be dated with precision as belonging to the period 12–30 June 1790. MS is a composite. It was originally a fair copy made by TJ from MS of Document v. In that state TJ sent a (missing) PrC of it to Rittenhouse on 12 June 1790, inappropriately calling it a rough draft: it was not even a tentative draft in the sense that its prototype was, for its lines extended not halfway across the page but full measure, and there were almost no corrections on it as it then stood. Three days later, after receiving Talleyrand’s proposition, TJ cancelled the last page of MS (that page is now in DLC: TJ Papers, 59: 10175, being page 21, and agrees precisely with the final form of corresponding page in its prototype, even to the diagonal cancellation mark (Document v, note 54). He then prepared the draft of a substitute page (see MS 1, below) and attached it to MS (f. 11257), sending a (missing) PrC of it to Rittenhouse on 15 June 1790. Immediately afterward he procured a copy of Newton’s Principia and revised MS to include “alterations … rendered necessary by the bishop of Autun’s plan. Those in the first four pages being numerous,” as TJ explained to Rittenhouse on 17 June 1790, “I wrote those pages anew, so that you will be so good as to substitute the new for the old. I have only noted the other smaller alterations by the page and line” (PrC in DLC). These revisions TJ made in the first instance on MS of Document v, thereby causing it to become in part a rough draft for the above MS. He then cancelled (and perhaps destroyed) p. 1–4 of MS as originally transcribed and substituted therefor the revision of which he had sent Rittenhouse a (missing) PrC. A day later he received the text of Sir John Riggs Miller’s speech of 13 Apr. 1790 and this involved further revisions: these TJ described in his letter to Rittenhouse of 20 June 1790 and incorporated them in MS. Four days afterward he received Rittenhouse’s initial criticisms and incorporated these and other alterations on the “first sheet” (that is, p.1–4 of MS). He thereupon recopied those pages, including the troublesome note on p. 3 that he had quoted in his letter of 20 June 1790, and sent Rittenhouse a (missing) PrC of the “third edition of that sheet,” making another substitution in MS of the pages now designated as f. 11247–8v—the pages that were supplanted being no doubt destroyed in this instance also (TJ to Rittenhouse, 26 June 1790). Unhappily, his letter crossed in the post that from Rittenhouse of 25 June calling attention to the error in the note. On 30 June 1790 TJ acknowledged the error, deleted the second revision, and pasted the slip onto p. 3 containing the third and final revision of the note, of which he sent Rittenhouse a copy. Thus, except for the cancelled page at f. 10175, what remains of MS as originally transcribed from MS of Document v is that part covering f. 11249–56, pages 1–4 and 21 being substitutes for cancellations. This evolution of MS is proved by a variety of facts and particularly by N (DLC: TJ Papers, 59: 10176–7), a 2page document in TJ’s hand listing the alterations to be made on pages 2, 3, 4, 7, 13, 16, 17, 19, 20, and 21 of MS as it was originally, and including a draft of the text of the most extensive of these (i.e., those on p. 3 and 4 of the cancelled pages); undated, but compiled 18–20 June 1790. In employing N to make these revisions on p.1–4 of MS, TJ began copying on the substitute “first sheet” with the paragraph at the bottom of p. 4 in order to make its text conjugate with that beginning at the top of p. 5. Afterward, he began transcribing the revision at p. 1 and, overestimating the space required, so crowded his lines as to leave a blank space in the middle of p. 4. This misled Rittenhouse and incidentally, through his comment on the blank space, proved that it was a PrC of the “first sheet” as finally revised that TJ sent him on 26 June (see note 15 below, and Rittenhouse to TJ, 2 July 1790). MS contains the text of report as submitted to the house of representatives on 4 July 1790, except for such additions and corrections as are indicated in the notes below. For later revisions, see Documents viii and ix. Dft (DLC: TJ Papers, 59: 10163–74; 233: 41948–51, 41592–4; and 59: 10149–62); the folios here cited are the MS, Dft, and Tr, respectively and in the order given, for the second state of the report as described in Document v, note. Most of the revisions from 12–30 June for MS as printed above were placed by TJ on MS of Document v, though some are to be found also on Dft and Tr, making all in some degree the draft prototype for MS above. FC (DNA: RG 59, Record of Reports of Thomas Jefferson, p. 18–63); agrees with MS as printed above except as indicated in notes 21, 22, 23, 26, 28–9, 31, 32–47, and 49, which incorporate the alterations made necessary by the discovery of the error pointed out in Document viii. On the printed texts of the report, see Editorial Note. The following documents were also employed in the preparation of the final state of MS:
MS 1: DLC: TJ Papers, 59: 10177, a 2page MS in TJ’s hand; undated but written on 15 June 1790; containing on verso the draft of the substitute text for p. 21 of MS and, on recto, TJ’s “Notes from the Bishop of Autun’s propositions sur les poids et mesures.” These notes were all taken from p. 136 of text, the essential part of which reads: “The second pendulum of 45.° has been proposed as a middle term between the Equator and pole. This pendulum should be the aune. 2. aunes should be a toise and the toise should be 6 feet. 3 inches cube (or 27 cubic inches) of water distilled once in the temperature of 14.° 4 Reaumur’s thermometer should be a pound. This would be a little heavier than the present pound. The length of the Second pendulum for 45.° has been calculated at 36 pouces 8.52 lignes. There may be an error in this of 1/10 of a line. As the experiment should be made near the level of the sea, some place near Bordeaux would be proper.” Below this TJ drew a line and added: “Sr. I. Newton makes the pendulum of Paris (48.°50.’) to be…39.16049 inches.”
MS 2: DLC: TJ Papers, 233: 41977, consisting of a single leaf on the recto of which is the following unfinished letter written ca. 20 May12 June 1790 (possibly intended for Madison), reading: “Sir, Reflecting today on a part of the report I had communicated to Dr. [William Samuel] Johnson, an inaccuracy occurred to me which had before escaped me. I called on him therefore for it” on this same leaf TJ later recorded the first drafts of the revisions for MS indicated below in notes 1, 5, 6, 10, and 16. These revisions were made between 20 and 30 June 1790. On verso of this leaf TJ made the calculations prompted by Rittenhouse’s letter of 25 June 1790 and stated the equation as follows: “As his 45.° 39.11546 : to my 45.° 39.14912 :: so is his 48.5 39.12683 : to what should be my 48–50. And again as his 45.° 39.11546 : to my 45.° 39.14912 :: so is his 5131 39.13468 : to what should be my 5131.” On solving these equations on that leaf, TJ quickly found that the calculations confirmed his earlier estimates. On an adjoining leaf (f. 41976) he stated the reasons for the discrepancy between his and Rittenhouse’s results:
“Ritt. Makes  Eng. I.  
pendulum  
of Lat.  51. °31’  = 39.13468 
Do.  48–50  = 39.12683 
45.  = 39.11546. 
But in this he cupposes the English foot = 11 po.3.11 1. = 135.11. If I’ve supposed it = 11 po.3 1. his numbers must be enlarged in the proportion of 135.11 : 135.” TJ acknowledged his error in division in calculating the latitude of Paris, but declined to accept Rittenhouse’s estimate for the English equivalent of the French foot: Rittenhouse depended in this on Maskelyne and TJ depended on Newton (see Rittenhouse to TJ, 25 June 1790; TJ to Rittenhouse, 30 June 1790).
MS 3: DLC: TJ Papers, 233: 41973, consisting of a single leaf in TJ’s hand containing notes taken from Newton’s Principia. It contains the equivalent in French measure of the second pendulum for degrees of latitude in multiples of five from 0° to 90,° except for latitudes 40° to 50° where the equivalent for each degree is given; this table furnished the matter from which the data given in note 11, below, were drawn. Opposite this TJ wrote: “Sr. I. Newton supposes an iron rod 3. feet long is from ⅙ to ¼ of a line shorter in winter than summer in England, in the common situations of pendulums. Were it exposed to the immediate action of the sun, the difference would be greater. But in their common situation they never are in a degree of heat equal to that of the human body.—11 pouces3 lignes equal to the English foot‥‥ The weight of a given mass of matter in any two latitudes is reciprocally as the radii of the earth at the places respectively. The weight of a cubic foot of water at the pole is to the same at the equator as 230 : 229. The earth being a spheroid, Sr. I. Newton, calculating it’s radii in the different latitudes, deduces thence the above lengths of pendulums for each in French feet and lines. From this datum that at Paris in Lat. 48.°50’ the second pendulum is 3. pieds. 8 ⅝ lignes.”
MS 4: DLC: TJ Papers, 233: 41974, consisting of a single leaf in TJ’s hand, on verso of which is the draft for the paragraph in MS indicated by note 4, below; on recto TJ listed the data for the length of the second pendulum for London, Paris, and north latitude 45.° as derived by him from the calculations of the Bishop of Autun, Miller, and Newton. His conversion of the Bishop of Autun’s figure for the length at the latitude of Paris was derived from the following equation: “504 : 257 :: 72 : 36.71428 pouces” the erroneous result produced by faulty division is set down on MS 4 at 39.1923 and following this, in brackets, TJ inserted the corrected figure of 39.1619. At f. 41975 there is also a note in TJ’s hand reading as follows:
inches  
“Mr. Huygen’s length of the inches Pendulum, by Sr. John [qu. Jonas] Moore’s reduction, now known erroneous  39.2 
Mr. Emerson’s by which he computes his table of the length of the pendulum in different latitudes  39.1[…] 
Dr. Desagulier’s length of the London Pendulum, by which Mr. Ferguson computes his table  39.128 
Mr. Graham’s length, found by a nice experiment in 1723, made with a standard English foot  39.126 
Mr. Whitehurst’s deduced from the interval between two pendulums, according to himself is  39.1196 
Do. corrected by the Reviewers, who made a deduction for the small rod of his pendulum  39.1189” 
Both of these memoranda are undated but were drawn up ca. 18–20 June 1790, except of course for the correction which was entered ca. 29–30 June.
MS 5: DLC: TJ Papers, 233: 41591, being a MS entirely in TJ’s hand concerning the money unit and evidently drawn up at the time he was preparing the second state of the report (that is, before 20 May 1790), but with later additions. This MS reads:
“Congress, in Oct. 1786 declared that the mint price of pure gold should be 209.77 Dollars, and of 11 oz. pure silver should be 13.777 Dollars. This fixes the relative value of silver and gold to be as 13.777 : 209.77 :: 1 : 15.226 in the U.S. According to this proportion the silver dollar containing 375.39555 grains of pure silver, the golden dollar must contain 24.6549 grains of pure gold.
<To find the relative value of gold and silver in England, and the par of exchange between their money and ours, we have these data. 1.> In England at the mint 11 oz. 2 dwt. of fine silver are cut into 62. shillings. Then the shilling of silver must contain 11 oz.2/62 = 85.9354838 grains of fine silver: and 11 oz. fine gold are cut into 44½ guineas containing 934½ shillings. Then the shilling of gold must contain 5280 / 934.5 = 5.65 grs. of pure gold. Consequently the value of silver there is to that of gold as 5.65 : 85.9354838 :: 1 : 15.20982.
The silver dollar of the U.S. contains 375.39555/85.9354838 = 4.36834 shillings sterl. or 4s. 4d. 1.68 grs. and the pound sterl. contains 4.57839 dollars, which is consequently the par in silver. The golden dollar of the U.S. contains 24.6549/5.65 = 4.3637 golden shill. sterl. or 4s. 4d. 1.45 grs. The par of exchange then in gold is 246.549 guineas for 118.65 eagles or £21164 for 100 Dollars both counted in gold.
In a book of respectable authority (the Encyclopedie Methodique) wherein the different monies are rated in As of Holland, a weight whereof 10240 make a pound poid de Marc we are informed that the pound sterl. of account contains 151.11 As of Holld. pure gold and 2295.21 do. of pure silver. Consequently the shilling sterl. of account contains 7.555 As of Holld. of pure gold and 114.7605 do. of pure silver. The livre of account contains 6.51 do of pure gold and 94.97 of pure silver. Then as As in 1/ silver 114.7605 : As in 1 94.97 :: Troy grains silver in 1/ 85.9354838 : Troy grs. silver in 1 71.11587. And as As in 1/ gold 7.555 : As in 1 gold 6.51 :: Troy grs. gold in 1/ 5.65 : Troy grs. pure gold in 1 4.8681. The silver was to gold as 4.8681 : 71.11587 :: 1 : 14.608 before the edict of Nov. 1. 1785. That edict reduced the quantity of pure gold in the Louis of 24. in the proportion of 242 6/11 : 227 3/7 :: 242.54 : 227.428571. Then as 242.54 : 227.42857i :: 4.8681 : 4.56469 Troy grains of pure gold in a livre at this day. Then silver is now to gold as 4.56469 : 71.11587 :: 1 : 15.5795. The Silver dollar of the U.S. contains 375.39555/71.11587 = 5.2786livres or 5 5s 6.864 d. when at par: and the golden dollar contains 24.6549/4.56469 =5.4012 golden livres the par of exchange in gold.
To find the number of As of Holland of pure silver in the Doll. of the U.S. we have these two proofs As grs. silver in 1/ 85.9354838 : grs. silver in 1 D. 375.39555 :: As in 1/ 114.7605 : As in 1 D.501.31 and again as grs. silver in 1 1.11587 : 375.39555 :: As in 1 94.97 : 501.31.” Later TJ added the following note to this MS: “All the preceding calculations are made on the money unit reformed to the standard of 38.° lat. viz. 375.39555 grs. Troy of pure silver. They must be remodelled to that of 45.° viz. 376. 02985 English Troy grs. = 371.30261 American Troy grs. = of the American decimal ounce.—Observe that Sr. I. Newton found
dwt.  grs.  mit.  standard silver 

the Piaster of Spain or Seville peice of 8. to contain  17   10   2  
the Mexico peice of 8.  17   8   14  
the Pillar peice of 8.  17   9  
52   3   11  
Averaging  19   9   5 
So that 17 dwt. 9¼ grs. = 417.25 grs. standard metal may be considered as the fair worth of the Spanish dollar. 120 : 111 :: 417.25 : 385.95625 grs. pure silver in Sp. dol.”
A rough draft of the substantive part of this MS (except for the later additions, which were probably added ca. Jan. 1791, is to be found in the right column of Dft (f. 41591v). From that place TJ transferred a brief extract to p. 21 of MS before cancelling it, as indicated in note 48 below. Some of his calculations for MS 5 are to be found in DLC: TJ Papers, 55:9338–9, on verso of first of which is the following: “Th: Jefferson’s compliments to Mr. [John] Brown and begs the favor of him to call on him as he goes to Congress this morning. Monday May 31.” This tends to confirm the conjectural date of MS 5 as belonging to the report at the second state, with later additions.
 In MS 2 TJ made two drafts for this revision, one of which read: “There exists not in nature as far as has been hitherto observed a single thing or species of thing<s> accessable to man of one constant and uniform dimension.” Revised version is on Dft (f.10163). This alteration was made because of Rittenhouse’s criticism (Rittenhouse to TJ, 21 June 1790; TJ to Rittenhouse, 26 June 1790).
 This sentence also revised in Dft (f.10163) in consequence of Rittenhouse’s criticism (same).
 This paragraph inserted in Dft (f.10163v) by TJ after receiving the text of the Bishop of Autun’s proposition, because it had “been thought worth mention” (TJ to Rittenhouse, 15 June 1790). See note on MS 1, above.
 This paragraph (the rough draft of which is in MS 4) was inserted by TJ in Dft (f.10163v) and at this point, both in Dftand in MS, the passage originally read: “… a power which shall exert,” &c., and then was altered in both places to read as above. See TJ to Rittenhouse, 12 June 1790; see also note 15, below.
 The rough draft of this footnote is in MS 2; there TJ first wrote at this point and then deleted: “In the case of the Pendulum Mr. Wh[itehurst] supposes a bob of 2 I. diameter necessary.”
 In MS 2 TJ first wrote at this point and then deleted: “proposed by Mr. Wh[itehurst].”
 This sentence is not in MS 2, but was inserted in Dft after slip was pasted on left column of p. 3 and text runs on to right column.
 This paragraph inserted at bottom of p. 2 of Dft (f.10163v) and continues on to the slip pasted on the left column of p. 3; the footnote is also on this slip. The rough draft for this insertion is in MS 2, wherein TJ first wrote and then deleted: “Could this [672] diameter be infinitely small the center of oscillation would be exactly at <one> two thirds of the whole length <of the rod> measured from the <lower extremity>; and the smaller the rod the less will that center be removed from that point: giving it just so much diameter as may render it sufficiently inflexible (as suppose ¼ of an inch) the center will not be displaced <the 500,00th part> but 459,816th. part of the whole length. This being scarcely an object of calculation, much less of the senses, we may safely consider the center of oscillation as residing at one third of the length of the rod.” TJ made several alterations in this, then deleted all after the first sentence in MS 1 and began over. This paragraph was inserted in MS to meet Rittenhouse’s criticism (see Rittenhouse to TJ, 21 June 1790; TJ to Rittenhouse, 26 June 1790).
 This is the text of the footnote as sent to Rittenhouse on 30 June 1790 (its rough draft is in MS 2). It is pasted over the following at p. 3 of MS, which is the state of the text as set forth in TJ’s letter to Rittenhouse of 20 June 1790: “The length of the pendulum has been differently estimated by different persons. Knowing no reason to respect any of them, more than Sr. Isaac Newton, for skill, care, or candour, his estimate of 39.149 I. had been adopted in this report, before the propositions of the Bishop of Autun, or of Sir John Riggs Miller were known here. The former gentleman quotes Mairan’s ratio for the length of the pendulum in the latitude of Paris, to wit, as 504 : 257 :: 257:72 French inches to a 4th proportional, which will be 36.71428 French inches, equal to 39.1923 English, the length of the pendulum desired. The difference between the pendulum for 48°50’ (the latitude of Paris) and 45.° is .0112 I. so that the pendulum for 45.° would be estimated according to the Bishop of Autun at (39.1923—.0112 = ) 39.1811 inches. Sr. John Riggs Miller proposes 39.126 I. being Graham’s determination for the latitude of London. The difference between the pendulum for 51. 31’ (the lat. of London) and 45.° is .019 I. so that the pendulum for 45.° should be estimated according to Sr. John Riggs Miller at (39.126— .019) = 39.107 I. Now dividing our respect equally between these two results, by taking their mean to wit, 39.181 + 39.107/2 = 39.144 we find ourselves almost exactly with Sr. Isaac Newton, whose estimate 39.149 had been before adopted.” The rough draft of this text is on two slips pasted over left column of p. 4 of Dft (f.10164v); after Rittenhouse pointed out the error, TJ went back to this draft and corrected the figures.
 Preceding three paragraphs are written in the right column of p. 3 after the slip was pasted over the left column.
 Draft of this paragraph is on one of the two slips pasted in left column of p. 4 of Dft (f. 10164v), and of course was not entered there until TJ prepared the “third edition” of p. 1–4 of MS ca. 24–26 June 1790 (see note 2 above; also TJ to Rittenhouse, 26 June 1790).
 Rittenhouse pointed out TJ’s error in calculating the extremes caused by expansion (Rittenhouse to TJ, 21 June 1790; TJ to Rittenhouse, 26 June 1790). The correction was made by overwriting on two states of Dft (f. 10164v and f. 10151).
 Draft of this paragraph is inserted at top of page 5 of Dft (f. 10165). At this point in MS as it stood when TJ made the “third edition” of p.1–4, there occurs the blank space of about two inches between this and the succeeding paragraph, as described above. See Rittenhouse to TJ, 2 July 1790.
 Draft of this paragraph is in MS 2 and its text is inserted at top of page 5 of Dft (f. 10165).
 See description of MS 3, above.
 Draft of this footnote is inserted on p. 4 of Dft (f. 10164v).
 At top of p. 9 of Dft (f. 10167), TJ first wrote draft of substitute text for the passage in brackets (supplied). That draft read: “ed the evidence of the Second pendulum before mentioned, from which it appears that the English inch is a measure whereof 39.1682 are equal to the pendulum vibrating seconds in the lat. of London and consequently the Second rod for that latitude is 58.7523 I. (which is 1/1958.3 of it’s whole length longer than the standard rod for 45.°) that of 45.° being as before stated only 58.72368 I. Let it be found by actual trial and add to it 3/10 of a line. This will give us a measure of 58¾English inches, or to shorten the operation.” TJ copied this form of the substitute text in his letter to Rittenhouse of 20 June 1790, then deleted it there (and also in Dft) and wrote the text in Dft as it appears above, which is [673]substantially the same as that which TJ then interlined in the letter to Rittenhouse.
 The original figures in this sentence are so overwritten in Dft (f. 10167) and in MS as to be indecipherable. Yet it is clear that, as the text stood when TJ sent it to Rittenhouse on 12 June 1790, the passage read: “… 38° then be divided into 587 equal parts.” On 15 June, on recalculating the length of the pendulum for 45° TJ arrived at 587⅕, which must have been the figure transferred to MS at that time, as it certainly was when TJ wrote Rittenhouse on 20 June 1790. On 28 June 1790 TJ received Professor Kemp’s letter of that date suggesting that this was an error and that the figure should be 587½ But the fraction remained as above.
 The spelling of this word in early stages of text (e.g., Dft) is coomb; this is also the spelling in FC, so that TJ evidently returned to it as being preferable.
 The draft for these two sentences is written in right column of p. 17 of Dft (f. 10171) and is also interlined in MS.
 In MS TJ originally wrote: “It is proposed to make this less by about the quarter of a grain; or fifteenth of a cent; that is to say, to establish it at 375.4 instead of 375.64 grains”—that is, the form at which it stood in Dft (f. 10158v). He then changed this in MS to read as above, entering the alteration also in Dft (f. 10171v). FC reads: “(or more exactly 375.989343).
 The proportion originally read in MS, as in final state of Dft (f. 10159): “875. to 864. as 375.4 grains Troy to 370.68” and was then altered by overwriting to read as above. FC reads: “875 to 864 as 375.989343 grains Troy to 371.2626277.”
 Altered in MS and in Dft (f. 10171v) by overwriting from “370.68.” FC reads: “371.262.”
 This figure altered in MS and in Dft (f. 10172v) by overwriting from “4.355.”
 This figure altered in MS and in Dft (f. 10172v) from “1321.”
 This figure altered in MS and in Dft (f. 10173) from “1617½” FC reads: “1620.05506862.”
 This figure altered in MS and in Dft (f. 10173v) from “375.4.”
 This figure altered in MS and in Dft (f. 10173v) from “375.39555.” FC reads: “375.989343.”
 This figure changed in MS and in Dft (f.10173v) from “.24445.” FC reads: “.349343.”
 In MS TJ originally wrote “a quarter of a grain … more,” and then altered the passage in MS and in Dft (f.10173v) to read as above.
 At this point FC reads: “Thomas Jefferson Secretary of State.” This is followed by: “Appendix. Containing Illustrations and Developments of some passages of the preceding Report.” This appendix contains the footnotes as given by TJ, but numbered from 1 to 8 instead of being keyed to the text by symbols as above. The 8th footnote is the comparative view of the proposed decimal system and of the English system, as taken from final page of Dft and MS, but varying from that as indicated in the following notes.
 FC reads instead:
“Superficial Measures The Hundredth .01 95.79 Square feet English Tenth .1 957.9 Rood 1. 9579.085 Double Acre 10. 2.199, or say 2.2 Acres English Square Furlong 100. 22.”  FC reads: “1.62.”
 FC reads: “16.2.”
 FC reads: “162.005.”
 FC reads:
“ 1620. 05506862 ” .937531868414884352 Cub.ft.  FC reads: “9.375.”
 FC reads: “93.753.”
 FC reads: “.4101.”
 FC reads: “4.101.”
 FC reads: “41.017.”
 FC reads: “.937531868414884352.”
 FC reads:
“ 410.170192431 ” .85452 oz.  FC reads:
“ 9.375 .712101 .,” &c. .585957417759 .  FC reads:
“ 93.753 oz. 7.121,” &c. 5.8595 .  FC reads:
“ 937.531 oz. 71.21,” &c. 58.5957 .  FC reads:
“ 9375.318 oz. 712.101.” 585.9574 .  On Dft (f.41594) TJ wrote the following opposite the unit of money: “The English standard of silver being 11 oz. 2 dwt. cut into 62/ the English shilling contains 93.6774193 &c grains of pure silver 375.39555/93.6774193 = 4.0073 so that our Unit or Dollar will be almost exactly equal to 4/ sterling and our Eagle to 40/ sterling, the half eagle to the Pound sterling.” He copied this on the cancelled page of Dft (f.10174v) and of course it appeared on its PrC (f.41595). Both were then deleted, and the note is not on the revised substitute page 21 of MS as it was when TJ sent it to Rittenhouse on 15 June 1790 (f.10175). Both versions of the note were drawn from MS 5. See note above.
 FC reads: “375.98934306 pure silver 34.18084937/410.17019243” alloy