If we’re exploring the countryside most of us consult maps, satnavs or kindly local folk for directions and distances.

But barleycorns were used to calculate the length of journeys in a locally-penned mathematics book published in 1842.

The ubiquitous cereal featured in the second of three questions in the book’s opening chapter:

(1) How many times would a carriage wheel, which is two yards in circumference, go round between Belfast and Dublin?

(2) Three barleycorns laid end to end make one inch, how many barleycorns would reach from Belfast to Ballymena?

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(3) If a man in walking takes a yard at every step, how many steps will he take between Londonderry and Coleraine?

Answers come at the end of my perusal of the book, after

by introductions to two esteemed mathematicians from Northern Ireland.

The Rev Isaiah Steen, minister of the Presbyterian congregation in Ballycopeland, County Down, was born near Coleraine in 1798.

He resigned from his congregation in 1832 and became head of Mathematics in the Royal Belfast Academical Institution where he was much acclaimed as “a gifted and painstaking teacher.”

He also wrote ‘Steen’s Mental Arithmetic’, which enjoyed such extensive sales that a fourth edition was published two years after the first print-run in 1844.

It was published by the Dublin, London and Glasgow-based educational printing company Simpkin and Marshall whose ‘Select List of School Books’ encompassed tempting tomes like ‘Virgil’s Bucolics With Literal Translations into English Prose’ and ‘Bosworth's Compendious Grammar of the Primitive English or Anglo-Saxon Language’!

Other popular and equally-alluring class-room titles proffered by Simkin and Marshall included ‘Cowie's Questions on Ditto’, ‘Hodgkin's Sketch of the Greek Accidence’ and ‘Crombie's Etymology and Syntax.’

I’m very glad I didn’t go to school in those days!

Whilst in charge of RBAI’s wonderfully-named ‘Mathematical and Mercantile School’ Steen wrote his 196-page schoolbook about mental arithmetic starting with a basic introduction which vividly characterised the era:

“Mental Arithmetic is the method of calculating in

the mind, without the use of paper or slate, or anything

else on which to perform the operation.”

Rev Steen greatly relied on another local mathematician to help him with his calculations, James Thomson - from Annaghmore, near Ballynahinch in County Down.

In a chapter of Steen’s Mental Arithmetic entitled ‘Proportion’ Isaiah referred to a mathematical rule “often called The Rule of Three or The Golden Rule,” he explained “which is more clearly stated by Professor Thomson, in his Arithmetic, than by any other writer, so far as I have observed.”

Professor James Thomson was author of another popular maths book, ‘Thomson’s Arithmetic’, published in 1819.

It boasted a jaw-dropping 72 editions until it went out of print in 1880.

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

In 1812 James was appointed headmaster, and later Professor, in the School of Arithmetic, Bookkeeping, and Geography in Belfast’s newly established Academical Institution.

I can’t for the life of me understand his Rule of Three, or Golden Rule, but Isaiah deployed it to devise a chart called ‘the Table of Interest’ which “may be useful in finding the number of days from any day of one month to any day of any other month,” he explained.

The chart still works brilliantly - for the same date in one month to the same date in any other month!

On page 130 Steen’s book outlined four examples of the mental arithmetic required to calculate the number of days

between different dates in different months and different years, offering sub-calculations for leap years!

Even though I don’t understand any of this I find it strangely comforting to know that away back in the 1840s the little chart did everything that a modern computer can do today.

And there was another warming thought amidst Steen’s and Thomson’s complicated calculations - a ditty from my schooldays which I still use today, regularly, and which no pocket calculator can match:

“Thirty days are in September,

April, June, and in November;

February has twenty-eight alone;

And all the rest have thirty-one.”

And finally, as promised, a barleycorn was an Anglo-Saxon unit of length that’s still used in the shoe industry.

It’s the length of a grain of barley, or about 1/3 inch, and you’d need 241,920 of them, end-to-end, to reach from Belfast to Ballymena!

Isaiah’s carriage wheel would have turned round 89,600 times

between Belfast and Dublin and a man ‘in walking’ would need to take 52,800 steps to get from Londonderry to Coleraine.

Professor Thomson passed away on 12 January 1849 aged 63 and the Rev Steen died on 3 August 1871 aged 73 but their clever calculations live on.