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# V. Second State of the Report on Weights and Measures

[April-20 May 1790]

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, these subjects may be compared.

There exists not in nature, as far as has been hitherto observed, any one body accessible to man, which presents a single invariable dimension.

The globe of the earth itself indeed may 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.1

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 is uniform and invariable. It is measured obviously, but unequally, by the departure and return of a given meridian to the sun, 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.

[It is liable however to the following incertainties.

1. Both theory and experience prove that to preserve it’s isochronism, it must be shorter towards the equator and longer towards the poles.

2. Being best made of metal, it is liable to vary it’s length with the variations in the temperature of the air.

3. If the Bob be a ball (which form can be produced in practice more exactly than any other) the length of the pendulum is not the distance from the center of suspension to either the center or bottom of the ball, but to a point between the two, called the center of oscillation; and this point being within the body of the ball and consequently inaccessible to the measure, becomes one source of incertainty.

4. If the suspending thread be of nearly insensible weight, it will be so flexible as to be liable to bend in it’s vibrations, and consequently to shorten the length of the pendulum. If it be sufficiently inflexible, it will then be of weight sufficient to displace the center of oscillation, and so also shorten the true length.

These incertainties indeed are minute: yet if a substitute can be found which is clear of some of them at least, it ought to be preferred.

The vibrating rod, of uniform diameter, tried heretofore by others for other purposes, has been suggested for this by Mr. Leslie, an ingenious artist of Philadelphia.]2

Any3 diameter, sufficient to render it inflexible in it’s vibrations, may be taken; because be the diameter great or small, the center of oscillation remains the same.

This center being known to reside at one third of the whole length of the rod, measured from the bottom4 might be easily and accurately ascertained in practice. But the whole rod is better for a standard than any portion of it because it is sensibly defined at both it’s extremities.

[The rod then, instead of the pendulum, avoids the incertainties arising from the inaccessibility of the center of oscillation, and from the weight of the suspending thread.

But, like the pendulum, it’s length will vary with the latitude, and with the temperature of the atmosphere.

To lessen the first variation, the middle latitude of the U.S. may be declared to be that which is to give the standard, and the completion of the 38th. degree may be taken as the middle latitude, neglecting as to this purpose the parts beyond the 31st. and 45th. degrees.

The extent of the variations from this standard Northwardly and Southwardly can then be examined.]5

The Second pendulum for 38.° of latitude, according to Sr. Isaac Newton’s computation, must be of 39.1285 inches English measure; and a rod, to be isochronous with respect to a pendulum, must be of the same length between the centers of suspension and oscillation, and consequently it’s whole length 58.69275 inches. This is buty6 1/18 of an inch too long for the Southern limit of 31.° and 1/33 of an inch too short for the Northern one of 45.° These differences are so minute that they may be neglected as insensible for all the common purposes of life. But in cases meriting perfect exactness, the second rod, found by trial of it’s vibrations in any part of the U.S. may be corrected by the computations of the same author for the latitude of the place, and brought exactly to the standard of 38.°7

The expansion and contraction of the rod with the change of temperature will occasion a greater variation in it’s length. According to the high authority8 before quoted, an iron rod of given length may vary, between summer and winter, in temperate latitudes and in the common exposure of house clocks, from 1/144 to 1/215 of it’s whole length, which, in a rod of 58.69277 I. will be from about a quarter to 4/10 of an inch. This is too sensible a variation to be neglected. It may be avoided by adjusting and preserving the standard in a cellar or other place, the temperature of which never varies. Iron is named for this purpose because it is the least expansible of the metals. It should be gilt to protect it from the rust which might in time shorten it.9

Let the Standard of measure then be an iron rod, of uniform diameter, and of such length as, in latitude 38.° 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 United States. 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 the money of account and paiment should be the same 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 familiarized 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 length10

The measures of length in use among us are

• the league of 3. miles the mile
• of 8. furlongs the furlong of 40. poles, or perches
• the pole or perch of five yards and a half
• the fathom of 2 yards
• the ell of a yard and a quarter
• the yard of 3. feet
• the foot of 12. inches
• and the inch of 10. lines.

On this branch of their subject the committee of 1757. 1758. sais 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 supplied by the concurrent testimony of the learned of that nation, who agree very generally that the second pendulum, as computed by Sr. Isaac Newton for the latitude of London, is 39.2 inches of their measure. Consequently the second rod for that latitude would be 58.8, which is a line, or 1/10 of an inch longer than the standard rod of 38.° that is to say 1/588 of the whole rod.

Let the standard rod of 38.° then be divided into 587 equal parts and let each of these 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;
• 5 yards and a half a perch or pole;
• 40. poles or perches a furlong;
• 8. furlongs a mile;
• 3 miles a league.

Superficial measures.

Our superficial measures 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 a quart;
• 2 quarts a pottle;
• 2 pottles a gallon;
• 8 gallons make a measure called a firkin in liquid substances and a bushel dry;
• 2 firkins or bushels make a measure called a barrel liquid and a coomb dry, this last term being antient and little used;
• 2. barrels, or coombs, make a measure called a hogshead liquid, or a quarter dry; each being the quarter of a ton;
• a 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.

There is moreover the Rundlet or Kilderkin containing 2. firkins, peculiar in measure as well as name to the liquids, and the peck of 2 gallons, peculiar in measure and name to the dry substances.11

But no one of these measures is of a determinate capacity. The report of the committee of 1757. 1758 shews that the gallon is of very various content; and that being the Unit, all the others must vary with that. 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 5. 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.12
• 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.13
• 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 the 3. standard corn gallons last mentioned, as measured in 1688. by an artist for the Commissioners of the Excise, generally used in the sea-port towns and by mercantile people, and thus introduced into some of the grain states.14
• 277.18 and 2217.44 as established for the measure of coal by the stat. 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. 1. W. & M. c.24.

and the higher measures in proportion.

In those of the U.S. which have not adopted the statutes of W. & M. and of Anne before cited, nor their substance, the wine gallon of 231. cubic inches stands 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 be15 altogether disregarded as concerning principally the wealthy and the mercantile, the least numerous part of the society, and the most capable of16 reducing one measure to another by calculation. This 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 cubic 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. deep17 the Gallon 6 I. square and 7½. I. deep18 the Peck 6.19 the Half bushel 12 I. square and 7½. I. deep and the Bushel 12 I. square and 15. I. deep.20

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.21

Let the measures of capacity then for the U.S. be a gallon of 270. cubic inches:

• The gallon to contain 2. 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;22
• 2. strikes or kilderkins a coomb or barrel;23
• 2. coombs or barrels a quarter or hogshead;
• 2. 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 straiht round strike of <equal> uniform diameter from one end to the other.24

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 one subdivision)25 into 8. drams
• The Drams into 3. scruples.
• The Scruple into 20. grains:

According to another subdivision26 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 5760:7000::144:175. It is remarkable that this is exactly the proportion of the antient liquid gallon of Guildhall, of 224. cubic inches, to the corn gallon of 272. for 224:272::144:175.27

It is further remarkeable still that this is also the exact proportion between the specific weight of wheat and that of water. For the statute bushel is of 64. pints, and each pint a pound of wheat. Now as 144:175::64:77. But 77.77 is known to be the exact [weight of 2150. cubic inches of rain water, from which, taken as a bushel, would result a gallon of 266½ cubic inches, which is but one cubic inch more than the gallon formed from three of the four standard gallons in the Exchequer and but half an inch more than the antient gallon of Rumford of 1228. and a fourth of an inch less than the gallon averaged from all the standards.]28

[We29 find then in a continued proportion 64:77.77::224:272::144:175. 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.30

Another remarkeable correspondence is that between weights and solid measures. For 1000 ounces avoirdupois of rain31 water fill a cubic foot with mathematical exactness.

What circumstances of the times,32 or purposes of barter or commerce called for this combination of weights and measures with the subjects 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:33 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 concluded34 to suppress it altogether. Their opinion was founded chiefly on the silence of the laws as to this weight. But the harmony before 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,35 seem stronger proofs that this is a legal weight than the mere silence of the written laws is of the contrary. Perhaps the weight is of higher antiquity than the written law.36]

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 citizens37 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 medicine 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 this pennyweight, as now,38 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 875:864. a difference not to be noticed either in money or39 medecine, 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 thro’ all time. It has been found by accurate experiments that a cubic foot of rain water weights 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.

Let it then be established that an ounce is of the weight of a cube of rain water of one tenth of a foot; 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 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 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.40

We have this proportion then. 875 : 864 :: 375.4 Troy grains: 370.68 American grains, 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 370:68 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,41 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 thro’ 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 5. equal parts, each of which shall be called a Foot.42 It will be about ¼ 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 make a decad;
• 10 roods a furlong;
• 10 furlongs a mile.

They may be thus noted and compared with the English measures.43

 Method ofNotation Equivalent inEnglish Measure The Point .001 .011 Inch Line .01 .117 Inch .1 1.173 about 1/7 more than the English Inch. Foot 1. 11.738 I. about 1/48 less than the English foot .978 f. Decad 10. 9.782 about 1/48 less than the 10. foot rod of the Carpenters. Rood 100. 97.821 about 1/16 less than the side of an English square rood. Furlong 1000. 978.212 about ⅛ more than the English furlong. Mile 10000. 9782.125 about 1 6/7 of an English mile: nearly the Scotch and Irish mile, and ⅙ the German.

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 4.355 English feet less than the English rood every way, and 1321 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 Metre; or, if it be thought better to retain the name of the nearest present measure, it may be called]44 a bushel. It will contain 1617½ cubic inches English, be about [1/10 less than the smallest English bushel, and ¼ less than that before proposed to be adopted as a medium.]45 Let this be divided into 10 pottles;

each pottle into 10. demipints;

each demipint into 10.[Roquilles, each of which will be 1/14 less

than the measure of that name in France, and so will serve as

a link between their measures and ours.]46

Let 10. metres or47 bushels be a quarter, and

10. quarters a Last or double ton.

They may be thus noted and compared with English measures.43

 Method of Notation Equivalent inEnglish Measures Roquille48 .001 1.61749 Inches Demipint .01 16.1749 about 1/24 less than the English half pint. Pottle .1 161.749 about ⅙ more than the English pottle. Metre or47 Bushel 1. 1617.496547987 I..936051243048 cu.f. about ¼ less than the middle-sized English bushel. Quarter 10. 9.3605 about ⅕ less than the English quarter. Last 100. 93.605 about 1/7 more than the English Last.

The Measures for use being four-sided, and the sides and bottom rectangular the Metre or47 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 Roquille48 an Inch cube.

Weights

Let the weight of a cubic inch of rain water be called an ounce; and Let the ounce be divided into 10. double-scruples;

the double-scruple into 10. carats;

the carat into 10. demi-grains or minims.49

Let 10. ounces make a pound;

10. pounds a stone;

10. stone a kental;

They may be thus noted and compared with English weights.43

 Methods of Notation Equivalent in English weights Avoirdupois Troy Demigrain or Minim. .0001 .409522418 grains about ⅕ less than the half grain Troy. Carat .001 4.09522418 almost exactly the Carat Troy Double-scruple .01 40.9522418 about 1/40 more than two scruples Troy. Ounce .1 .9360512 oz. 409.522418 grs..8531717 oz. about 1/14 less than the ounce avoirdupois. Pound [qu.Marc?] 1. 9.360512 oz. .585032 lb. .7109764 lb. about ¼ less than the Pound Troy. Stone 10. 93.60512 oz. 5.85032 lb 7.109764 about ¼ less than the English stone of 8 lb Kental 100. 936.0512 oz. 58.5032 lb. 71.09764 aboty 4/10 less than the Kental English. Hogshead 1000. 9360.512 oz. 585.032 lb. 710.9764.

Coins

Let the Money-Unit, or Dollar, contain eleven twelfths of an ounce of pure silver. This will be 375.4 Troy grains (or more exactly 375.39555 Troy grains) which will be a quarter of a grain (or more exactly 24445 of a grain) less 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 United States.

Measures, weights and coins thus referred to standards unchangeable in their nature, (as in 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 one50 who possesses the first elements of arithmetic, and easy of comparison51 both for foreigners and citizens with the measures, weights, and coins of other countries.

A gradual introduction might perhaps lessen52 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 Customhouses, 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 receive it into common use.53 Too long a postponement, on the other hand, would increase the difficulties of it’s reception, with the increase of our population.54

1In margin of TJ added: “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.” incorporates this reading.

2In TJ deleted the passage enclosed in brackets (supplied) and substituted the following in the adjacent column: “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 uncertainty.—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. Being made of metal, as is best, it varies it’s length with the variations in the temperature of the atmosphere.

1. In order to avoid the <first of these sources of uncertainty> uncertainties which respect the center of oscillation, it has been proposed by <a> Mr. Leslie, an ingenious artist of Philadelphia, to substitute for the Pendulum, a rod of uniform diameter, without a Bob.” This revision is incorporated in , but with its second paragraph placed before that beginning: “Any diameter. …”

3At this point in there is an asterisk and a footnote keyed to it reading: “A convenient one might perhaps be that which would make the whole rod of the weight of the bob of the common house clock.” incorporates this addition.

4This word deleted and “lower extremity” interlined in in substitution. Madison suggested the alteration and incorporates it (see Document vi).

5In TJ deleted the passage enclosed in brackets (supplied) and substituted the following in the adjacent column: “<But the rod, like the Pendulum, will vary it’s length with the latitude of the place, and the temperature of the atmosphere>—2. The uncertainty arising from the difference of length requisite for the second pendulum, or the second rod, in different latitudes, <mentioned as another source of uncertainty> may be avoided by fixing on some one latitude to which our standard shall refer. The middle latitude of the United States <may be declared to be that which is> would seem the most convenient to give the standard to the others and the completion of the 38th. degree may be taken as the middle latitude neglecting as to this purpose, the parts beyond the completion of the 31st. and 45th degrees.—The difference between a rod so adjusted to 38° Latitude, and those for the extremes of 31. ° and 45. ° are to be examined.” This revision is incorporated in and was, of course, made after TJ had consulted Madison and before he received the comments of Rittenhouse. It is also to be considered in the light of the revision set forth in note 2, its numbered paragraph being in sequence with that.

6Keyed to this point by a dagger, TJ wrote in the blank column of the following footnote:

 Sr.I.N’spo. computationlignes pouces inches “31° 36 — 7.978 = 36.6483 = 39.0915 < 35°-8’-30° 36 — 8.1036 = 36.6753 = 39.1203 —.0288 = 39.0915 > + .0288 39.1491 38.° 36 — 8.1962 = 36.68301 = 39.1285 —.037 = 39.0915 + .0206 = 39.1491 45° 36 — 8.428 =36.7023 = 39.14912 51°-31’ 36. — 8.6426 = 36.7202 = 39.1682*

*<The conversion of French into English measures 11 pouces 3 lignes are taken as accurately equivalent to the English foot.> … The pendulum vibrating seconds in the latitude of London is the result of this proportion 11 po.-3 li.: 12 Inches : : 36 pouces-8.6426 lignes : 39.1682 inches. Yet most English authors state the length of the second pendulum for London, as computed by Sr. Isaac Newton, to be 39.2 inches; which supposes this ratio 11 pouces- 2.89 lignes : 12 Inches : : 36. pou.- 8.6426 lignes : 39.2 inches. They must either have taken 39.2 as the nearest simplification of the fraction 39.1682 or they must have supposed the equation of French and English measures to be 11 pouces 2.89 lignes = 12 Inches instead of 11 po.-3 li. = 12 I. or they have assumed some latitude for the city of London other than that of 51.°-31’ here <assumed> supposed.” This addition must have been in at the time that Madison saw it (see Document vi), and afterward TJ deleted the passage just quoted and substituted for that part following the asterisk (in ), the phrasing which found its way into and the final version:

“Sr. Isaac Newton computed the second pendulum for 51°-31’ (the latitude of London) to be 36. pouces-8.6426 lignes French measure, which is 39.1682 inches English at 11 po.-3 li. to the English foot, at less than which this foot cannot be estimated according to the best authorities. Yet most English authors state Sr. I. Newton’s computation at 39.2 English inches, which would suppose the English foot to be only 11 pouces-2.89 lignes or perhaps they adopt 39.2 inches as the nearest simplification of the fraction. Some late experiments and calculations by Messrs. Whitehurst and Hutton make the length of the second pendulum 39.1196

 Dr. Halley’s calculations made it 39.125 Sr. Isaac Newton’s according to the equation of the English foot 11-3 French 39.1682 The same according to the common statement of it 39.2.”
This version (with the tabular figures at the head of that which preceded it) was incorporated as a footnote in , and was the form in which TJ sent the text to Hamilton, Rittenhouse, and perhaps others around 12 June 1790. The justification for the assumption that Madison saw the first of these revisions and was responsible for the second rests not only on his query, as noted above, but also on the fact that it was he who brought the copy of Whitehurst’s book to TJ from Philadelphia. Hence the revisions took place between 20 May and 12 June 1790 (TJ to speaker, 4 July 1790; TJ to Rittenhouse, 12 June 1790).

7TJ altered this passage in so as to make it read, as it does in , “by computations for the latitude of the place.” Keyed to the word computations, the following footnote is in margin of :

“<These are> Sr. Isaac Newton’s computations for the different degrees of latitude from 30.° to 45.° are as follows.

 Lat. pieds lignes 30.° 3—7.948 35 3—8.099 40 3—8.261 41 3—8.294 42 3—8.327 43 3—8.361 44 3—8.394 45 3—8.428
(In converting and reconverting English and French feet, D’Alembert’s statement of the Eng. foot = 11 p.-3 has been adopted. Picard had made it 11.-2.8 and Maskelyne makes it 11.-3.11.” Footnote is incorporated in .

8 has footnote keyed to this point: “Princip. L. 3. prop.20. prob.4.”

9This sentence deleted in and not in .

10 begins at this point.

11This sentence is not in , being deleted in and having the text altered to read: “2. gallons a peck dry measure …2 firkins or bushels make a measure called a kilderkin liquid and a Strike dry. 4 kilderkins or strikes make a measure called a barrel liquid,” &c. follows the table as thus altered.

12At this point the following is deleted in and is not in or : “268.2 and 2145.6 according to a brass standard bushel of H. 7. measured in 1696 [Everard’s stereometry].”

13Preceding eleven words not in .

14Preceding nineteen words not in .

15In TJ wrote “abolished” and then deleted it.

16In TJ wrote “most capable of conforming themselves,” and then altered the text to read as above.

17In margin of , TJ wrote: “or 4½, 5, and 6 I.” This alternative was the result of Madison’s criticism. incorporates this change.

18In TJ wrote “5, 6, and 9 I.” and then deleted and later restored the figures; they are incorporated in and in as alternative measures. Madison may have influenced this change also.

19Thus in , but has “6, 9, and 10.I.” these figures are in margin of and are in .

20 reads “or 9, 15, and 16 I.” these figures are in margin of and are in .

21TJ interlined the following in : “Moreover, till the circle can be squared, the cylinder cannot be cubed, nor it’s contents expressed in figures.” This sentence is in margin of and is in ; it may have been added in reaction to Madison’s suggestion.

22 reads: “2. firkins a rundlet or kilderkin” was altered to read as above, and agrees with .

23 reads: “4. bushels or firkins a coomb or barrel.”

24Thus in also; reads: “And let all measures of Capacity of dry subjects be stricken with a strait strike.” This was an alteration that was probably in response to Madison’s suggestion (see Document vi).

27, , and have a symbol keyed to a footnote reading: “more exactly, 144 : 175 :: 224 : 272.2.”

28At this point in , keyed to text with an asterisk, TJ listed the figures giving the numbers of cubic inches of the gallon as variously defined—seventeen in all, according to the text above, running from 224 to 282 cubic inches—from which he derived the average as 266.7. His table omitted the gallon “as measured in 1688. by an artist for the Commissioners of the Excise,” but this was an error of transcription, for its capacity (272 cubic inches) is included in TJ’s total; however, he erred in the calculation, for the average was 266.87 instead of 266.7 as he figured it. This may have been the error that he referred to in the unfinished letter quoted in Document vii, note on 2, and it probably was discussed by him and Madison. For, before was executed, TJ deleted the table in (but not in ) and caused the passage in brackets (supplied) to read: “weight of 2150.4 cubic inches of pure water [keyed by asterisk to this point in this footnote: “more exactly, 62.5 ℔. : 1728 :: 77.7 : 2150.39”] 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 of a cylinder of 18½ I. diameter and 8.I. 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 <probability> belief that there might exist evidence of it at that day unknown to the committees of 1758. and 1759.” TJ recorded this alteration in and this interesting variation in the phrasing occurs there: “and induces a favorable opinion … and also <a suspicion that they must> probability that there might exist,” &c. The progression from conjecture to probability to conviction is thus to be found in the variant versions of and . incorporates the revisions.

29Except as indicated in notes 30, 31, 32, 33, and 34, the matter in brackets (supplied) follows text in as revised and placed in right column of f.41951 in substitution for the following, deleted in left column: “So that here in a continued proportion 64 : 77.77 :: 224 : 272 :: 144 : 175. that is the Specific weight of wheat is to that 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. A series of 3 sets of exact proportionals could not have been the effect [of] chance. It shews a well concerted harmony between our antient weights and measures, and the things to be weighed and measured <it would induce one to conjecture that the weights and measures> that they have been so proportioned as to render it indifferent whether a thing was sold by weight or measure, according to the taste of the buyer or perhaps the different usages of different countries. 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.—Let it be further observed that weights and solid measures are as remarkeably related. For 1000 oz. Avoird. of rain water fill a cubic foot with mathematical exactness. A relation so integral <has not been the work of chance> is not to be ascribed to chance: but is evidently part of a system <scientifically calculated> of scientific combinations and judicioussly adapted to the circumstances of the times for which it was formed.—This harmony of the different parts of the system of weights and measures is developed and insisted on here because it is evidence that each is <a> part of <the> a whole. The Committee had supposed from proofs less satisfactory that the Avoirdupois was not <a part> an antient.” It is clear that TJ had developed his remarkable inference even before Madison saw it and had reached a conclusion in advance of his early conjectures as set forth in the revisions of ; and he continued to insist upon its validity even after Madison expressed a doubt about it.

30This passage as interlined in (see note 29) reads: “Wine and water are nearly of the same weight, some of the kinds of wine being a little heavier and some a little lighter than water.” In this was also interlined and revised to read: “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.” incorporates this latter version of the change.

31In both and TJ first wrote “rain” and then altered both to read “pure,” which is the reading in .

32As revised in (see note 29), TJ began this paragraph with the following and then deleted it: “Whether different laws or habits in different parts of the country required different alternatives in the mode of buying and selling, or what other circumstances of the times, is not now to be ascertained, but it is evident that there has been a scientific.”

33As revised in (see note 29), TJ wrote: “…were original and constituent parts of one whole,” and then altered the passage to read as above. agrees with .

34At this point in TJ interlined the following: “<contrary to what> otherwise than will be here proposed,” and incorporates the addition.

35In margin of , keyed to this point, TJ wrote: “The merchants weight.” incorporates the addition.

36This sentence is in and as revised (see note 29), but is deleted in and is not in . The deletion in was probably made after Madison saw it and may have been urged by him.

37In and in these two words are in substitution for “the people,” deleted.

38In this word is deleted and “heretofore” substituted. follows the revision.

39In the preceding eight words are interlined in substitution for “absolutely insensible in the most useful kind of,” deleted.

40As originally phrased in this paragraph read: “Congress having established the Unit and subdivisions of their coins, and that that unit shall contain 375.64 Troy grains of pure silver, we have this proportion, 875 : 864 :: 375.64 : 370.917. Disregarding the tenth of a grain, let it be declared that the Money unit or dollar of the U.S. shall contain 371. American grains of pure silver.” TJ transcribed this in and then deleted it at bottom of f.10171, beginning again at top of f.10171v to transcribe from the passage as there revised by interlineation, overwriting, and a marginal insertion of two sentences: “Congress in 1786 established the money Unit at 375.64 Troy grains of pure silver. It is proposed to make this a quarter of a grain less, say of 375.4 grains because it will be shewn that this Unit of coin will link the Units of length, surface, capacity, and weight into one system whenever it shall be thought proper to extend the decimal ratio to them also <… and tho this should not be done in the present day it seems worthwhile>: to preserve the possibility of doing <it at a future time by this> this is the object in proposing this very minute alteration. We have this proportion then 875 : 864 :: 375.44 : 370.68, the expression of the unit in the new weights. Let it be declared then that the Money unit or dollar of the U.S., shall contain 370.68 American grains of pure silver.” But in the course of transcribing this revision from , TJ altered its text to read as above. incorporates the revised form as recorded at f. 10171v of .

41This word interlined in in substitution for “confused,” deleted.

42At this point in TJ interlined the following: “for perhaps it may be better generally to retain the name of the nearest present measure, where there is one tolerably near.” incorporates this reading.

43This explanatory line and the tables of comparison of the units of length, surface, capacity, and weight are placed under their respective headings in (where the tables occur in the blank column) and in . Afterward, and before was executed, they were crossed out in and and then consolidated in one set of tables at the end of and . See note 54 below.

44The words in brackets (supplied) are deleted in and and are omitted in .

45The words in brackets (supplied) are deleted in and in margin TJ substituted the following: “¼ less than that before proposed to be adopted as a medium; 1/10less than the bushel made from 8. of the Guildhall gallons, and 1/14 less than the bushel made from 8 Irish gallons of 317.6 cubic inches.” agrees with this revision.

46The words in brackets (supplied) are deleted in and the following interlined in substitution: “cubic inches which are to be called <Roquilles) (Metres> Metres” this revision is similarly recorded in . TJ then altered the phraseology in to read: “each demi-pint into 10. metres which will be of a cubic inch each.” incorporates the latter revision.

47Preceding two words deleted in and in and are not in .

48In and in this word is deleted and “Metre” interlined. agrees.

49This line altered in and to read: “…into 10 minims or demi-grains; the minim into 10 mites.” agrees with this revision.

50This passage in originally read: “This system then, being of weights and measures and coins thus built on two things <circumstances> unchangeable in nature, the length of a rod vibrating seconds, and the weight of a definite mass of rain-water: will themselves be <invariable> unchangeable. These standards too will be accessible to all persons in all times and places. Arranged in a decimal ratio, they are within the calculation of every man,” &c.

51This phrase is altered in to read “of easy comparison.” Thus in . For a comment on this, see note, Document vi.

52 reads: “…<might> would perhaps lessen.” follows this revision, but there “perhaps” is deleted. reads “would lesson”

53 ends at this point. The sentence that follows is in both and .