How many ounces are in a quart? Is a liter larger than a quart? If a liter costs ten Euros, how much is that in Swiss francs? If you don't spend those ten Euros, what will they be worth in ten years if you deposit them in a bank at 3% simple interest? If you exchange your ten Euros for gold, what weight should you expect in return if the gold is 18k? If the gold is 24kt?
The modern world routinely turns to electronic and online calculators of various types when faced with such questions. But in the days before calculators, such questions were routinely handled by a wide and diverse array of printed books known as ready reckoners:
As Bruce Williams and Roger Johnson observe in a recent article, ready reckoners were
...printed books of tables of pre-calculated results of all kinds of multiplication useful for commerce, principally price per unit times units or price per pound weight times pound weight but also for calculating wages and interest.
All aids for commerce had to combine high precision, speed, and accuracy with the ability to handle non-decimal measures and currencies, and be cheap enough to be bought for every day use by clerks and shop assistants.
...Ready Reckoners were far more important in terms of volume sales than all the mechanical devices put together, and ... this was because Ready Reckoners out-performed [early mechanical] devices on all the key factors in the buying decision: ... price, number of significant figures, accuracy, ability to handle non-decimal multiplications, time to learn how [to] use ...and time per calculation....
As these authors note, the earliest ready reckoners were simply tables of frequently used arithematical calculations consulted by merchants during the course of their sales -- e.g., how many pence equal a pound, or how much X yards of cloth cost at a price of Y per yard:
But over time, ready reckoners were developed that contained tables of calculations that were much more specific. This was because ,as Williams & Johnson point out,
...before having a list of sums of money to add on an invoice ... or in creating columns of Debits and Credits, a price had to be multiplied by a quantity to get the amount of a transaction. Consider what is involved in a typical single transaction [like selling manufactured steel parts such as] a square of steel plate, a length of steel joist and a circle of steel plate. First the area of the pieces of plate had to be worked out, and from this the weight could be derived. The weight of the joist was looked up in a table per linear foot. All these weights then had to be multiplied by the price per ton to give the line value. Consequently ...one invoice involved eight multiplications, all non decimal times non decimal, averaging two to three per invoice line. The total weight was later reconciled with the weigh ticket for the total ... load. Note that Item 2 involves not one multiplication but the squaring of a number, its multiplication by π, with the result being divided by 4. In addition, although the length is shown in ft and inches, this would have to be converted into inches....
Such complex calculations were routine for sales of items like lumber:
Ready reckoners are often collected in stand-alone fashion, although they are just as often collected as part of private libraries devoted to mathematics and/or computing. Having been printed for over three centuries, the range of what's available in the marketpalce, often quite inexpensively, is enormous....
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