Guru of mental arithmetic’s golden rule helped barleycorn expert with his sums

The Reverend Isaiah Steen
The Reverend Isaiah Steen

My apologies if last Friday’s page caused News Letter readers undue strain trying to count 241,920 barleycorns laid end-to-end between Belfast and Ballymena or attempting to tot up 89,600 turns of a carriage wheel between Belfast and Dublin!

Those were some of the Reverend Isaiah Steen’s methods of measuring distances, in his book called Steen’s Mental Arithmetic.

Work Out The Number of Shopping Days Till Christmas (2019!)

Work Out The Number of Shopping Days Till Christmas (2019!)

Born and brought up near Coleraine, Isaiah was minister of Ballycopeland Presbyterian congregation in Co Down before becoming head of maths in the Royal Belfast Academical Institution in 1832.

Until he retired in 1869, Rev Steen was hailed as “a gifted and painstaking teacher”, regularly referring to his 196-page book in the classroom.

And it apparently enjoyed extensive sales!

A fourth edition was published two years after the first print-run in 1844, but anyone who found it too baffling when it re-emerged on Friday’s page – stop reading now because a return to Steen’s Mental Arithmetic was promised, and it gets even more complicated!

Professor James Thomson. Guru of The Golden Rule

Professor James Thomson. Guru of The Golden Rule

The Rev Steen greatly relied on another local mathematician to help him with his calculations – from Annaghmore, near Ballynahinch in Co Down.

On page 131 of the book, in a chapter entitled Proportion – Isaiah refers to a mathematical rule “often called The Rule of Three, or The Golden Rule,” he explained “which consists of finding a fourth proportional to three given numbers”.

I warned you that things would get more complicated!

“The method of effecting this,” Rev Steen continued “is more clearly stated by Professor Thomson, in his Arithmetic, than by any other writer, so far as I have observed.”

Thomson’s Arithmetic, published in 1819, boasted a jaw-dropping 72 editions until it went out of print in 1880.

And judging by the paragraphs that Rev Steen quoted from it, Professor Thomson’s mathematical ruminations were as complex as his own!

Incidentally, the professor also taught mathematics at the Belfast Academical Institution and was father of William Thomson (Lord Kelvin), Belfast’s historically acclaimed physicist and engineer, hailed with a statue in the Botanic Gardens.

Professor James Thomson, brought up on a farm, went to school at Ballykine, near Ballynahinch.

Hoping to become a Presbyterian minister he went to Glasgow University in 1810, graduated in 1812, and two years later was appointed headmaster of the School of Arithmetic, Bookkeeping, and Geography in the newly established Academical Institution, Belfast.

Several years later, he became a professor.

In 1832 he was appointed Professor of Mathematics in the University of Glasgow, a post he held until his death in 1849.

But back now to his Rule of Three, or the Golden Rule.

“The following is the substance of it,” Rev Steen announces in Steen’s Mental Arithmetic before embarking on a mathematical formula that must have driven many little Inst-boys to absolute despair during Maths lessons!

“Arrange the three given terms (numbers) in the same line, in succession, placing the one which is of the same kind with the required term the third in order; and, if it appears, by the, nature of the question, that the required term is to be greater than the third term, put the greater of the other two terms in the second place…” and so it continues!

What was it all about and what was Professor Thomson driving at?

“Many questions in this rule contain too much work to be effected easily by mental arithmetic,” writes Rev Steen comfortingly, adding “the following exercises will be useful and will illustrate the subject”.

What follows is a series of mathematical exercises about everything under the sun – yards of cloth, depth of ditches, gallons of wine, tons of coal – all based on Professor Thomson’s Golden Rule or Rule of Three.

It starts with the basics!

“Find a fourth proportional to 4, 6, and 12,” the first exercise poses, and the answer is apparently 18.

“Find a fourth proportional to 5, 7, and 10,” the second exercise asks, and the answer seems to be 14.

And then, out of the blue, we’re back to Rev Steen’s favourite theme – barleycorns!

Exercise 23 asks – “a field of corn was to be reaped by 40 men in 10 days, but 10 of the men did not make their appearance: in what time would the remaining number reap the field?”

The answer, if anyone is still interested, is 13 and one third days, and whether or not the remaining reapers had time to lay their handywork end-to-end between Belfast and Ballymena is not recounted!

However, there’s one thing that Isaiah and James worked out between them that might still be useful, particularly at this time of the year.

They introduce their curiously entitled ‘Table of Interest’ thus – “The following table may be useful in finding the number of days from any day of one month to any day of any other month.”

It’s already December so it’s too late to work out the number of shopping days left till this Christmas but cut out the table and keep it for next year!

Meanwhile it could have other very practical purposes – like how many days till the 12th?!

And there’s some additional information from James and Isaiah which might help…or hinder – “the table gives the days between any day of any month and the same day of any other month, which must be increased or diminished by the days in excess or defect.”

Roamer reckons the time would pass quicker counting barleycorns!