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MATHEMATICS IN THE AGE OF JANE AUSTEN: ESSENTIAL SKILLS OF 1800

Source: Mathematics Teacher, Nov2000, Vol. 93 Issue 8, p670, 10p, 1 diagram, 8bw

Author(s): Gray, S. I. B.

THE ACADEMY AWARD-WINNING MOVIE Sense and Sensibility presented a wonderful vision of life in early nineteenth-century England. In the absence of television, radio, movies, and videos, families sought entertainment in a manner far different from today's. The Dashwood girls--Elinor, Marianne, and Margaret--filled their days with visiting, reading, practicing the pianoforte, needleworking, and letter writing, not to mention gossiping and matchmaking. Long days were highlighted by a wonderfully relaxed midday family meal, during which conversation was paramount. Above all, Jane Austen portrays a concern for the thoughts and feelings of one's immediate acquaintances and pride in one's village.

An upper-middle-class family of the landed gentry-the Dashwoods--would have been interested in a proper education for their children. The textbooks of that era are a clue as to what was considered essential mathematics. Gender and class differences abound. Books were scarce. Paper was not mechanically produced until 1801, and power driven printing machines did not appear until 1812. Only a few books were available for instructors and students.

The mathematics books for both "young ladies" and "young men" open with a discussion of the four fundamental operations--addition, subtraction, multiplication, and division. All books' carefully discuss these concepts and the related vocabulary. Students were asked to learn the terms addend, minuend, subtrahend, difference, multiplicand, multiplier, product, divisor, dividend, and quotient. Each section included basic algorithms for calculating. In general, both the algorithms and vocabulary have endured and are similar to those found in contemporary American textbooks. Although explanations were brief, the basic material is the same.

After the opening sections on the basics, the differences are great. Commonly, the four operations are followed with a chapter on the "rule of three direct," or "golden rule," which is now called ratio and proportion and is solved by cross multiplying. After learning four operations and one method for finding an unknown quantity, students were thought to be prepared for adult mathematics. Books ended with tables--especially for weights, measures, and money--all of which were notoriously awkward in the English system.

We next examine the unique features of three books that were widely circulated between 1800 and 1810, or during the height of the Napoleonic era. An effort has been made to preserve the original grammar, spelling, capitalization, and punctuation.

MATHEMATICS TEXTBOOKS FOR THE YOUNG LADIES

Like the accomplished and distinguished writer Jane Austen, William Butler (1806) furnishes the reader with a sample of domestic detail in his book intended for "young ladies." See figure 1. Butler asserts that he is an experienced teacher of young ladies. His book presents mathematics in an unusual format. We find 619 problems, which are organized in alphabetical and numerical order. The topics range from astronomy, anchovies, and cork to parchment, the plague, and the steam engine. The literary content of the problems is worthy of an Austen. The problems display an integrated approach to teaching mathematics and cut across literature, history, science, and geography. They include quotations from Virgil, Milton, Pope, Shakespeare, and the Bible. Moreover, beginning with addition, the author apparently tried to increase the degree of difficulty of the mathematics as he progressed through the arrangement. Reading a problem or two helps one appreciate the scope and sequence of the curriculum.

Addition

No. 36 Pay a baker's bill of two pounds, a grocer's of three pounds, a milliner's of five pounds, a linen-draper's of sixteen poufids, and a cheesemonger's of seven pounds, and find the amount of the whole.

No. 38 Virgil, the celebrated Latin poet, was born near Mantua, in Italy, seventy years before the nativity of our Saviour; how many years have elapsed since that event to the present year 18057

Subtraction

No. 92 Magna Charta. Runnymede... is reverenced by every son of liberty, as the spot where the liberties of England received a solemn confirmation... [and is] considered the bulwark of English LIBERTY. The celebrated charter in question was wrenched from John in 1215; How long has that happy event preceded 18057

Ans. 590 years.

Multiplication

No. 133 Coaches. Coaches, as well as almost all other kinds of carriages which have since been made in imitation of them, were invented by the French, and the use of them is of modem date. Under Francis I who was a contemporary with our Henry VIII there were only two coaches; that of the queen, and that of Diana, natural daughter of Henry II. The kings of France, before they used these machines, traveled on horseback; the princesses were carried on litters, and ladies rode behind their squires. Till about the middle of the 17th century there were but few coaches in Paris; but prior to the late revolution in that capital, they were estimated at 15,000, exclusive of hackney-coaches (horse drawn taxis), and those let out for hire.

The introduction of coaches into England is ascribed by Mr. Anderson, in his History of Commerce, to Fitz Allen, earl of Rundl, in the year 1580; and about the year 1605, they were in general use among the nobility and gentry of London.

In the beginning of the year 1619, the earl of Northumberland, who had been imprisoned since the Gunpowder-Plot, obtained his liberation. Hearing that Buckingham was drawn about with six horses in his coach (being the first that was so) the earl put on eight to his, and in that manner passed from the Tower through the city.

Hackney-coaches, which, according to Maitland, obtained this appellation from the village of Hackney, first began to ply the streets of London, or rather wait at inns, in 1625, and were only twenty in number. So rapid, however, has been their increase since that period, that London and Westminster now contains 1100.

Suppose each coach to earn 16 shillings a day on an average, which is deemed a very moderate computation, the sum of £880 sterling is expected daily in the metropolis, in coach-hire, exclusive of what is spent in glass coaches, or unnumbered ones. What is the weekly, monthly, and yearly expenditure in the use of these vehicles?

Ans. £6,160 per week; £24,640 per month, and £321,200 per year; reckoning 13 months 1 day to the year.

A common form for correcting the calendar was to add a thirteenth month from time to time. This method was used in 1806. Butler's answer may be calculated using 365 + 1 days.

Multiplication of money, or compound multiplication

No. 219 Potatoes. Potatoes are the most common esculent (succulent) root now in use among us, though little more than a century ago they were confined to the gardens of the curious, and presented as a rarity. They form the principal food of the common people in some parts of Ireland:

Leeks to the Welsh, to Dutchmen butter's dear; Of Irish swains, potatoes are the cheer.

--Gay

Potatoes were originally brought to us from Santa Fe, New Mexico, North America, and as has been asserted, by Sir Francis Drake, in the year 1586. Others mention the introduction of them into our country about 1623; whilst others affirm that they were first cultivated in Ireland, about Younghall, in the county of Cork, by Sir Walter Raleigh, in 1610, and that they were not introduced into England till the year 1650. Peru, in South America, is the natural soil of potatoes, particularly the fertile province of Quito, whence they were transplanted to other parts of America. It is the root only of the potato plant that is eatable.

There are two varieties in general use; one with a white, and the other with a red root. And besides these, there is a new kind, first brought from America, which that "patriot of every dime," the late Mr. Howard, cultivated in 1765 at Cardington, near Bedford. They were also propagated in from the adjacent counties. Many of these potatoes weigh four or five pounds each; and hogs and cattle are found to prefer them to the common sort. They are moreover deemed more nutritive than others; being more solid and sweet, and containing more farina or flour. As an esculent plant, they appear also worthy of cultivation; being it is said, when well boiled, equal, when roasted, preferable to the common sort.

Immense quantities of potatoes are raised in Lancashire for exportation. Mr. Pennant says, that 30 or 40,000 bushels are annually exported to the Mediterranean Sea from the environs of Warrington, at the medium of 1 shilling 2 pence per bushel. A single acre of land sometimes produces 450 bushels. What are 179 bushels of potatoes worth at one shilling, 2 pence per bushel?

Ans. £10 8 shillings 10 pence.

Division

No. 243. Velocity of light.

Lot there be light, said God, and forthwith light Ethereal, first of things, quintessence pure, Sprung from the deep ....
--Milton

Mathematicians have demonstrated, that light moves with such amazing rapidity, as to pass from the sun to our planet in about the space of eight minutes. Now, admitting the distance, as usually computed to be 95,000,000 of English miles, at what rate per minute does it travel?

Ans. 11,875,000 miles.

At 438 pages, this book is longer than most textbooks of the Austen era. Butler includes elaborate notes, footnotes, and references for further study. See figure 2. He closes with twenty-seven pages of arithmetic tables, including the essential monetary conversions, abbreviated here for the contemporary reader. The one obvious omission in this highly successful book is illustrations. Not one drawing is included.

4 farthings = 1 pence [4 qrs. = 1 d.]

12 pence = 1 shilling [12 d. = 1 s.]

20 shillings = 1 pound sterling [20 s. = 1£]

21 shillings make 1 guinea

MATHEMATICS TEXTBOOKS FOR YOUNG MEN

A young man's mathematics instruction was designed to give "secret satisfaction to the possessor, and contribute to render him an agreeable and useful Member of Society." Unlike the problems in Butler, those in Wallis's The Self-Instructor, or, Young Man's Best Companion (1811) are stated without elaboration:

What is the value of 21 gallons of brandy at 7 shillings 9 pence per gallon?

What is the value of 108 lbs. of indigo lahore at 7 shilling 8 pence per pound?

Reduce 246 Venetian ducats de Banco into sterling money.

Admit an army of 32,400 men were formed into a square battalion. Find the rank and file.

For the golden rule or rule of three, that is, ratio and proportion, the student is advised that the "chief difficulty is the placing of the numbers."

If 12 gallons of brandy cost £4, 10 shillings, what will 134 gallons cost?

The author suggests that £4, 10 shillings be changed to "the lowest mentioned."

The Self Instructor, or, Young Man's Best Companion contains chapters for "Joiners, Painters, Glaziers, Sawyers, and Bricklayers," as well as a chapter on "Planometry." See figures 3 and 4. The book discusses such unusual regular figures as the undecagon, which has eleven sides, and the quindecagon, with fifteen sides. It includes globes, cones, and pyramids, including the frusta, as well as algorithms for taking square and cube roots. It teaches a method for finding the length and mast of a ship. The young man is given information on the financial arrangements for bookkeeping, wills, and legal matters. The sections on longitude and latitude, which were important measures for a seafaring country, include the following: "New Mexico, including California, is bounded by 'unknown lands' on the north, Louisiana on the East, Old Mexico, and Pacific on West. The chief town is Santa Fe 36 degrees north latitude and 104 degree west longitude." The book closes with the statement that algebra was first known in Europe in 1494 and that printing-of all types--had been carried on in Westminster Abbey from that time until now.

Decimals are included, and the book describes unusual methods of handling "vulgar [common] fractions" (Wallis 1811, p. 96).

To reduce fractions

To reduce a fraction, a prime common divisor, not necessarily the greatest common divisor, was written in the position of an exponent.

56[sup 2]|28[sup 2]|14[sup 7]|2/84|42|21|3

To add fractions

A product of the denominators, not the LCD, was used.

3/4 + 2/7 + 5/6 = 126/168 + 48/168 + 140/168 = 314/168