Of Ells and Kilderkins

After more than a century and a half a Carmarthen schoolboy's work-book has come to light. The book belonged to Henry Williams, who lived at Pen-y-bryn, which lies about half a mile from the trunk road A40 (the Turnpike in those days) north of Alltygog between White Mill and Nantgaredig. It shows a great deal of work done during the period it was used and throws light on the standard and methods of arithmetic as taught in the early ninteenth century, when Grammar School pupils in Carmarthen were required to pay between 6s. 0d. and 7s. 6d. a term extra for tuition in the subject. The results of the tuition which Henry received are interesting for the in-sight they give into the modes of instruction and the light they throw on the social history of the period. The book also provides evidence that boys could be prepared for a career in the business and commercial world as well as the more familiar preparation for the professions.

Measuring 8" by 13½", the book was bound by David Morris of Carmarthen and contains paper marked J. Snelgrove 1818. Henry, who 'was born the 9th December 1805, about 8 o'clock in the night', used the book in 1820 and 1821. The first date he entered was 10th August 1820, but it is possible that he used the book before then. One can measure the amount of work done. In 1821, for instance, he did ten exercises in February, fifteen in March, eight in April, six in May, there being an upsurge in the following two months, when he did twelve and fifteen exercises. He seems also to have carried on throughout the winter with sustained application, for Christmas seems not to have been the festive vacation that later generations came to enjoy, if we are to judge from the fact that he was working on December 25, 26, 28 and 29 in the year 1820. Even so, unlike the lads of Dotheboys Hall, he enjoyed the privilege of school holidays. Henry used the book for about a year and it is noticeable how his writing and presentation improved and matured during that time.

In the teaching of arithmetic, presentation was evidently important, the pattern being to begin with the Heading, after which came the appropriate definition, then the Rule, followed by worked examples. During his schooling Henry was taught twenty-eight topics and had to learn many tables. The book began with the 'Multiplication of Whole Numbers' in respect of which it 'Teacheth how to increase the greater of two numbers given as often as there are in the lefs; and compendiously performs the office of many additions: to this Rule belong these principal numbers, viz. 1 The Muhiplicand, or number to be multiplied. 2 The Multiplier, or number by which you multiply. 3 The product, or number produced by multiplying. Rule: Begin with that figure that stands in the units place of the Multiplier and with it multiply the first figure of the units place of the Multiplicand. Set down the units and carry the tens in mind'.

Barleycorns and Ankers
Multiplication was followed by Division and then by Addition of Money, Weights and Measures. The tables of Weights and Measures were comprehensive and doubtlessly had to be learnt by rote. Although readers may still remember them, it is worth repeating some of the tables, which no longer find a place in school curricula. In Troy weight '24 grains maketh 1 pennyweight, 20 pennyweights 1 ounce, 12 ounces 1 pound'. Apothecaries' weight brings to mind some candle-lit shop, with strange bottles on the shelves, where '20 grains maketh 1 scruple, 3 scruples 1 dram, 8 drams 1 ounce, 12 ounces 1 pound'. Less familiar is the Cloth Measure. Who now knows '4 Nails 1 Quarter of a Yard, 3 Quarters 1 Flemish ell, 4 Quarters 1 Yard, 5 Quarters 1 English ell, 6 Quarters 1 French ell'? Though many will remember that in Long Measure '3 miles make a league', there must be few nowadays who can boast the knowledge that '3 barleycorns make 1 inch'.

The schoolboy of 1820 was expected to be proficient in Liquid and Dry Measures and to appreciate that wines came in different quantities from those of ale and beer. Thus in Wine Measure '10 gallons make 1 Anker of brandy, 18 gallons 1 Runlet, 31½ gallons half a Hogshead, 42 gallons 1 Tierce, 2 Hogsheads 1 Pipe or Butt, 2 Pipes 1 Tun'. Ale and beer, however, received different treatment, 4 guarts making 1 gallon, as they still do, but 1 firkin of beer was 9 gallons, whereas 1 firkin of sale was 8 gallons; thereafter 2 firkins equalled 1 kilderkin, 2 kilderkins 1 barrel, 2 barrels 1 puncheon. In Dry Measure 2 pints made 1 quart, 2 quarts 1 pottle, 2 pottles 1 gallon, 2 gallons 1 peck, 4 pecks 1 bushel. Thus far, older people will not be surprised, but it went on and on: 2 bushels 1 strike, 4 bushels 1 comb, 2 combs 1 quarter, 4 quarters 1 chaldron, 5 quarters 1 wey, 2 weys 1 last. Square Measures now all but forgotten included: 30 acres 1 yard of land, 100 acres 1 hide of land. In Solid Measure (cube) 1,728 inches made 1 solid foot, 27 feet 1 yard or load of earth, while 40 feet of round timber or 50 feet of hewn timber made 1 ton or load [a ton in this context being a measure and not a weight].

Some of the problems set are eternal ones like: If 8 men do a piece of work in 12 days, how many days can 10 men perform the same in? But many are more relevant to the times. Some reflect the experience of the Napoleonic period, as with: A privateer of 250 men took a prize which amounted to £125. 15s. 6d. to each man. What was the value of the prize? Or: In an army consisting of 187 squadrons of horse, each of 157 men, 207 battalions, each of 560 men, how many effective soldiers, supposing that in seven hospitals there are 473 sick? Or: An army of 20,000 men took and plundered a city of £12,000. What was each man's share, the whole being equally divided among them?

Other problems illustrate social customs. Of a family of seven persons, one problem says that 'there are drank out two kilderkins of beer in 12 days', and asks, 'How many kilderkins will there be drank out by another family of 14 persons in 8 days?' Although the question fails to provide an essential assumption, it does indicate a staple beverage of the times. Tea had not yet taken its place in the diet of the masses; at twenty-three shillings a pound it could hardly have been otherwise. The importance of the dowry as part of the marriage contract is confirmed by the frequent references to it. For example: 'A Tradesman gave his daughter as a marriage portion a Scrutorie [Henry's spelling is at fault; he meant a scrutoire, i.e. an escritoire or writing desk] in which were twelve drawers, in each drawer were six divisions and in each division there were £50, four Crown pieces and eight half crown pieces, how much had she to her fortune?' High living is illustrated by the following: 'A Nobleman before he went out of town was desirous of paying all his tradesmen's bills and upon inquiry he found that he owed 82 guineas for rent, to his wine merchant £72-5-0, to his confectioner £12-13-4, to his Draper £47-13-2, to his Taylor £110-15-6, to his Coachmaker £157-15-0, to his Tallow Chandler £8-17-9, to his Cornchandler £107-6-8, to his Brewer £52-17-0, to his Butcher £122-11-5, to his Baker £37-9-5, to his servants for wages £53-18-0. I desire to know what money he had to raise in the whole, when we add to the above sums £100 which he wished to take with him'. Perhaps this smacks more of the 18th century, especially the bill of the Tallow Chandler, as gas had come even to Carmarthen by 1822. Of special interest is the following problem, which suggests that liability for restitution following highway robbery fell upon the parishes: 'A robbery being committed on the highway, an assessment was made on a neighbouring hundred for the sum of £386-15-6, of which four parishes paid each £37-14-2, four hamlets £31-1-2, each and the four townships £18-12-6; how much was the deficiency?'

Sometimes mnemonics were used. The Georgian schoolboy remembered the Rule for Reduction, for instance, by reciting:

When your Reduction must descend
Observe the strictures of a friend
The given number multiply
With each denomination by
Add to each product as you go
The next inferior one below
And when ascending you divide
Just by the same you multiplied
The numbers then reversed appear
And proof each other very clear.

Tare, Tret and Clod
One hopes that this and other doggerel was effective, as there were many items concerning business and commerce to master. Practice for trade and business had eight rules, and technical terms were clearly defined, e.g. Tare was the allowance made to the buyer of any commodity for the weight of the box, cask, etc containing the same; Tret, an allowance of 4lb in every 104lb or 1lb in 20lb on account of waste, dust etc.; Cloff, an allowance of 2lb in every 3 cwt or 1lb in 168lb to make the weight hold out when retailed; Suttle weight, when part of the allowance is deducted from the Gross; Neat weight, pure weight when all allowances are deducted. More advanced methods included simple and compound interest, Selling and

Buying of Stocks, Brokage (allowance to brokers for helping merchants or factors to buy or sell their goods), Discount, Equation of Payments (mean time for paying whole debts), Barter (exchanging one commodity for another, the Traders so proportioning their goods that neither may sustain loss), Alligation Medial (finding the mean price of a mixture of several supplies of different prices and quantity). There were also Alligation Partial and Alligation Alternate. Exchange involved a knowledge of foreign currency; for France, 12 deniers=1 sol [long since more familiar as the sou], 20 sols=l livre, 3 livres=1 crown (4s. 6d. at par); for Spain, 34 marvedies=1 rial, 8 rials=1 piastre or piece of eight (4s. 6d.), 10 rials=1 dollar; in Venice 6 solidis= 1 gross, 20 gross=1 ducat (a ducatoon was worth 4s. 6d. at par).

Problems included: 'At what rate per cent will £540 amount to £734-8-0 in 9 years lent' or 'What is the discount of £85-10 due Sept 8, this being July 4th, rebate at 5 per cent per annum'. Bills made out to various traders included references to commodities of interest to the social historian, although it is possible that the given prices were out-dated. Cambridge butter was 6d a 1b, Cheshire cheese 4d a lb, lump sugar 6½d a lb, rice 3d a lb, malaga raisins 5d a lb, fine serge 3/9 a yard, drugget 9/-, superfine scarlet £1-2-0, shallon 1/9 a yard; cambric 12/6, muslin 8/3, painted linen 5/4 a yard; flowered silk 17/4, rich brocade 19/8, sarsanet 3/2, genoa velvet 27/6 a yard; kid gloves 2/2 a pair, fans 3/- each; stockings came in various textiles, the cheapest thread at 3/2 a pair, worsted 4/6, cotton 7/6, and black silk 14/- a pair.

Decimals were known to Henry as well as Arithmetical and Geometrical Progression. He learnt to appreciate geometrical progression by working out the following : 'A country gentleman going to a fair to buy some oxen, met with a person who had 23; he demanded the price of them, was answered £18 a piece: the gentleman bids him £15 a piece, & he would buy all; the other tells him it could not be taken, but if he would give what the last ox would come to, at a farthing for the first & doubling it to the last, he should have all. What was the price of the oxen?' Henry's answer was £4369 1s. 4d.

The work book concludes with Vulgar Fractions, Square Roots and the application of the theorem that the square on the 'hypothenuse' is equal to the sum of the square on the other two sides, or the base and the perpendicular, as Henry referred to them.

Henry bade farewell to his schooldays with the brief statement that he 'Left school the 12th Day of August 1821'.