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The evolution of weighing.

The history of weighing from biblical times to the implementation of the metric system is recounted with special emphasis on the origin of atomic weights

The art of weighing is of extreme antiquity. There are numerous depictions on Egyptian papyri of weighing scenes when the heart of man is weighed against a feather on an equal arm balance. Should the heart be heavy with sin it is tossed to the Devourer who is standing by. We likewise have from Genesis 23:16: "And Abraham weighed to Ephron the silver he had named in the audience of the sons of Heth, four hundred shekels of silver, current money with the merchants." and Josephus' Antiquities of the Jews (c.AD.93) says: "He (Cain) also introduced a change in that way of simplicity wherein men lived before and was the author of weights and measures. And whereas they lived innocently before while they knew nothing of such arts he changed the world into cunning craftiness." This implies that cheating in commerce was not unknown to the Hebrews and the Torah (Deuteronomy 25:13-15) says: "Thou shalt not have in thy bag diverse weights, a great and a small. Thou shalt not have in thine house divers measures, a great and a small. But thou shalt have a perfect and just weight, a perfect and just measure shalt thou have." [And seven other injunctions in similar vein.]

Then a long time later we have instructions in the Talmud (Baba Bathra, 88b.; the text of rabbinical directions on trade, finalized before A.D. 500.) "...and a shopkeeper must allow the provision scale to sink a handsbreadth lower than the scale of weights...". Here the weighing is not by level beam but by inclined beam, and if he gives exact weight (by level beam), he must allow him 1/20, (5%) when weighing provisions. The idea of inclined beam weighing continued into the middle ages and beyond.

Thus, Liber de Antiquis Legibus (A.D. 1257) "The King's beam in the City of London."

"The usual provision is when goods are weighed on a balance that the beam incline towards the goods except gold and silver which are always weighed on a level beam, neither drawing towards the weights nor towards the gold and silver...but from the Sabbath following the Feast of St. Nicholas in the XLI year of the reign of King Henry [Henry III], son of King John, all goods are to be weighed as gold and silver without drawing towards the goods, in lieu of which the seller must give the buyer four pounds in every hundred." Further, the English Tractatus de Ponderibus et Mensuris (1250-1300) says: "A sack of wool ought to weigh 28 stone, that is 350 lb. and in some parts 30 stone, that is 375 lb. and they are according to the greater or lesser pound," so we must prepare ourselves for finding at least two different pounds for measuring wool in England. When level beam weighing was made mandatory in 1340, the weight of the sack on the level beam was given later as 364 lb. (of the same pounds), which is just 4 lb. per hundred more than 350: (3.5 x 4 = 14; 350 + 14 = 364), but it is still the same sack. This is close to the Judaic 5% and indicates that wool was being weighed on an inclined beam before the fourteenth century and wool was the principal export at the time.

In Figure 1, the mass of S remains constant; it is the mode of weighing that has changed. The weights using the inclined beam were called the weight of the goods and taxed accordingly even though it was known that the true weight was the weight needed to make the beam come level. The only thing extra was the additional weights in the other pan. The tax to be paid was per sack and it mattered not which weighing method was used. The system used was invariably that of the overseas market to which the goods were destined.

Pegolotti's La Pratica della Mercatura (1340) confirms that the weight for bullion and money in London was Tower weight, the weight in use at the English mint in the Tower of London. The Tower lb. was of 12 oz. of 450 gr. so 5400 gr. Here we use Troy grains (gr.) to describe weights, not that the various cities all used Troy weight (and indeed we believe Troy did not come into general use until about 1380), but because its use leads at once on to the English system which was in widespread use throughout the world until the last few decades. Tower weight (in particular the English silver penny of 22.5 gr., with 20 pennies to the oz. of 450 gr.) was one of the fixed points in medieval weighing.

Pegolotti gave numerous equivalents of the weights of one town with those of another and in particular that the Paris mark of 8 Paris oz. was 8 oz. 8d Tower. There were 20 pence in an oz., so the Paris mark was 8.4 oz. Tower = 8.4 x 450 = 3780 gr. The Paris oz. was therefore 472.5 gr., 16 of which made the Paris pound of 7560 gr., and it appears that all of Northern Europe took Paris weight as standard.

We find the following equivalents given.

96.15 lb. Paris = 100 lb. London (7269 gr., for spices) = 100 lb. Antwerp.

92.45 lb. London = 100 lb. Bruges (6720 gr., heavy goods).

78 lb. Bruges = 100 lb. Florence (5242 or 5240 gr., sottile).

138.7 lb. Florence = 100 lb. London.

Put another way, we have the following relationships:

100 lb. Paris = 104 lb. London (for spices)

= 104 lb. Antwerp (for spices)

= 112 1/2 lb. Bruges

= 144 1/4 lb. Florence.

All this fits well (to better than 1%). Florence was the great wool centre of the period and there they used only the steelyard, a horizontal beam device and the sack was 500 of their sottile (fine goods) pounds. English and Scottish wool was initially shipped to Bruges and thereafter it was dispersed to the Flemish weaving centres and to the Italian market, principally to Florence using initially inclined beam weighing (Bruges) and then level beam weighing for Florence.

The true mass of the sack in Florence was 500 'sottile' (i.e. high value weight) pounds each of 5240 gr. so the sack was 2620000 gr. The English had a special pound for wool, one of 7200 gr. and 500 Florentine pounds of 5240 gr. are the same as 364 of these English pounds.

Using the inclined beam (and not getting the true mass) the English woolsack was 350 lb. and 350 x 7200 = 2520000 gr. To those cities using the inclined beam, such as Bruges, this was the (apparent) weight of the sack. Pegolotti states that the Bruges sack was 360 lb. We also know that the Scottish sack was 360 lb. so the Scots had borrowed the entire pound of Bruges. For wool, the Bruges pound was 2520000/360 = 7000 gr. The Tractatus said there were also pounds of 375 to the sack. Taking 2520000/375 we get 6720, which is the pound of Bruges for heavy goods, England, therefore, had its own wool pound of 7200 gr. at 350 to the sack (inclined) or 364 lb. (level). The Tractatus in giving the sack as 350 and as 375 was helpfully giving the weight of the sack (inclined beam) in English wool pounds and in Bruges heavy goods pounds of 6720 gr. to assist exporters. In Bruges, wool could either be weighed by the wool pound of 7000 gr. or by the heavy goods pound of 6720. For level beam weighing, 375 becomes 390 lb., again of 6720 gr. for a total of 2620800 gr. as above.

Besides the sottile pound, Florence has a 'grosse' pound of 6989 gr. for heavy goods. Now the 6720 gr. lb. of Bruges increased by 4% is exactly 6989 so a parcel of goods weighing X lb. on the inclined beam at Bruges would weigh X pounds of 6989 gr. on the level beam at Florence. This was very convenient, linking London-Bruges-Florence. We are suggesting that the origin of Avoirdupois weight (7000 gr. pound) had its origin in the fourteenth century pound of Bruges and Florentine grosse pound of 6989 gr. They are very close to each other.

The Hundredweight

Only recently has it been discovered that the hundredweight was a universal mass like the sack. In England, prior to 1309, there was one cwt of 108 lb. which was thereafter divided according to the merchandise involved into one of 104 and one of 112 lb., the former for spices, the latter for heavy goods,

The Paris hundredweight was one of 100 Paris pounds, so was equal to 756400 gr. and this was the standard. Consider how the various pounds fit using the above figures:

= 99 x 7636.4 gr. Antwerp wool pound

756000 = 100 x 7560 gr. Paris pound (16 oz. x 472.5 gr.)

= 104 x 7269 London/Antwerp spice lb.

= 105 x 7200 London wool lb. (16 oz. x 450 gr.; 15 oz. x 480 gr.)

= 108 x 7000 Bruges wool wt; later the avoirdupois lb.

= 112 x 6750 English heavy goods lb. (15 oz. x 450 gr.)

= 112.5 x 6720 Bruges heavy goods lb. (14 oz. x 480 gr.)

= 120 x 6300 Antwerp pound wt. (Half clove of 12600)

= 140 x 5400 English silver weight (12 oz. x 450 gr.)

= 144 1/4 x 5240 Florentine sottile lb. (12 oz. x 436.7 gr.)

These are only a selection of the various pounds which all fit together.

The British System

Contrary to beliefs held as recently as a decade ago, it is now clear that Tower weight in England and Scotland preceded Troy weight, Tower weight was based on the weight of the silver penny at 22.5 gr., 20 of these to the ounce of 450 gr. and 12 oz. to the lb. of 5400 gr. Troy weight appeared after 1340, perhaps in 1380 and was destined to cause problems for while the penny weighed 22.5 gr., the Troy penny-weight weighed 24 gr., the oz. was 480 gr. and the 12 oz. pound 5760 gr. Of these only the Troy oz. for bullion remains but is now (W & M Act 1985) not defined in grains but as 12/175 of the Avoirdupois pound. The Avoirdupois system is also of the fourteenth century although its pound of 7000 oz. was in use earlier as the Bruges wool pound and very near to the grosse lb. of Florence (6989 gr.). There was much confusion in the fifteenth and sixteenth centuries as to what exactly was Avoirdupois weight for the weight of a penny (22.5 gr.) was confused with the pennyweight of 24 gr. and it was not clear whether there was 15 or 16 oz. to the pound. It took three Elizabethan 'Royal Commissions' to finally determine it in 1588 when that monarch's third series of weights appeared. Avoirdupois weight was with us until the onset of metrication.

The Metric System

One of the most remarkable achievements of the last two centuries was the setting up in the late 1790s of a new system of weights and measures in France based on scientific principles which replaced the totally chaotic system then in use. To do this in normal times would have been remarkable; to do it in the midst of a revolution was well nigh impossible yet the impossible was achieved. The survey of the Earth's quadrant from which the metre, litre and kilogram were to be created took 9 years. The fact (discovered later) that the metre was not exactly one ten millionth part of the Earth's quadrant did not pose a deterrent for it was agreed to use the physical standards which had been produced from the survey as the fundamental units of the system "in the form in which they are found", without any reference to a natural origin. The change from the toise, the boisseau, and the livre was not accomplished overnight any more than in late twentieth century Canada, for the system was not in universal application in France until 1840. Three conferences, in 1870, 1872, and in 1875, led to twenty nations subscribing to the Metric Convention. Britain did not subscribe to the Convention until 1884 and not until 1897 was the system made legal for trade. Canada, then a British colony, did what Britain did. There were now faithful equivalents linking pounds to kilograms, gallons to litres, and yards to metres but they were not used to any extent. It was the Weights and Measures Acts of 1963 and 1985 which set Britain firmly on the Dad to metrication. But even today, beer and milk are being sold in pints with pint milk bottles having embossed on the side '568 ml'. One can see at once why these industries would resist a change. People would settle for a half litre instead of a pint, creating a loss in sales of 13.6%. Canada, in 1907, (no longer a colony) acquired the right to obtain standards directly from Paris rather than via London, a right the country exercised in 1950 with the acquisition of Kilogram K50. In the 1970s, industry by industry, Canada switched over and while we are not totally metric we are further ahead than Britain.

A standard kilogram should have an uncertainty, in its mass of no more that 12[[micro]gram]. For the last 7 years K50 has been displaying fluctuations of about 35 [[micro]gram]. due to tiny cracks in the surface which adsorbed and released water from the air. In January 1993 NRC acquired its second kilogram, number K74 which is now the primary standard of our nation.

Atomic Weights

Dalton, New System of Chemical Philosophy (1808), showed that elements combined with one another in definite proportions. William Prout suggested in 1815 that the weights of the atoms of all elements were multiples of the weight of the hydrogen atom. Eight grams of oxygen combined with one gram of hydrogen, but when reacting volumes were considered it became plain that it was 16 grams of oxygen which combined to form 18 grams of water. Berzelius published his table of atomic weights in 1826 with quite a few that were not an integral multiple of that of hydrogen. This sent Prout's hypothesis into an eclipse. Dalton had naturally used hydrogen as his standard of atomic weights, being the lightest element, but Berzelius used oxygen. In 1842, Dumas, with limited accuracy, found O/H to be 15.96 but in 1865, Stas, with much better accuracy showed that the ratio could not be greater than 15.96. He suggested going over to O=16 as the standard, but this was not accepted even though oxygen combined with more elements than hydrogen did and the practice became of finding the weight relative to oxygen and then converting to hydrogen. Soon the weight relative to oxygen was better known than the O/H ratio so in converting accuracy was lost. In 1898, it was recommended that a move to oxygen be implemented. The American Committee on Atomic Weights in 1896 published its table on both H and O and found that on the latter, the atomic weights came much more nearly to whole numbers reviving interest in Prout's hypothesis. In 1906, the International Committee moved to O=16.

Although isotopes were unknown at the time, William Crookes, in 1886, suggested that atomic weights might only be averages of a variety of different kinds of the same atom and this was confirmed when J.J. Thomson, beginning in 1906 and employing positive rays, showed that neon, atomic weight 20.2 consisted of neon 20 and neon 22. This was verified in 1919 by Aston with a mass spectroscope and he greatly expanded this work examining many elements and determining the relative abundances of many isotopes, a word invented by Soddy in the first decade of this century. With an accuracy of 1/10 000 Aston was able to obtain the mass of 12C relative to 16O as 12.0036.

A difficulty arose when oxygen was shown in 1929 to consist of three isotopes, 16O (99.76%); 17O (0.04%) and 18O (0.20%).

Physicists used 16O = 16 while chemists used the natural mixture, 16.0044 on this scale. The discovery, in 1935, that the percentages of the oxygen isotopes were not everywhere constant was a definite disadvantage to using oxygen as a base for atomic weights. The ratio from water vapour in the atmosphere varied from that found in surface waters, enough to cause embarrassment. Mass spectroscopic measure merits were soon to outpace chemical determinations of atomic weights. In the late 1950s there was much discussion on the possibility of unifying the two scales.

Four possibilities were envisaged; 16O = 16; 19F = 19; 12C = 12 or 18O = 18. After much discussion and analysis of the consequences, it was decided to recommend 12C = 12 and this was adopted by the General Assembly of IUPAC in 1960, thus unifying the chemical and physical scales. The new unit of mass was termed 'u' so 12C = 12u. This we have today.

Author's Note: The sections on commercial weighing represent a small portion of a major study on the weights of Northern Europe in the thirteenth and fourteenth centuries by A.D.C. Simpson and R.D. Connor (Forthcoming). For the section on atomic weights, I have drawn considerably from the paper 'Evolution of the Unified Scale of Atomic Mass, 12C = 12u.' by H.E. Duckworth and A.O. Nier in International Journal of Mass Spectroscopy and Ion Processes, 1988, 86, 1-19.

R. D. Connor is a retired Professor of Physics and Dean Emerritus at the University of Manitoba in Winnipeg MB.
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Title Annotation:Focus on Education
Author:Connor, R.D.
Publication:Canadian Chemical News
Article Type:Cover Story
Date:Mar 1, 1995
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