physics

Promptuary

Promptuary is a physics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Promptuary rather than just read about it. In short: A promptuary, also known as a card abacus, is a calculating machine invented by the 16th-century Scottish mathematician John Napier and described in his book Rabdologiae in which he also described Napier's bones. It is an extension of Napier's Bones, using two sets of rods to achieve multi-digit multiplication without the need to write down intermediate results, although some mental addition is still needed to calcu…

Key takeaways

Promptuary belongs to physics; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Promptuary to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Promptuary from memory before moving on to harder problems.

Reference excerpt

A promptuary, also known as a card abacus, is a calculating machine invented by the 16th-century Scottish mathematician John Napier and described in his book Rabdologiae in which he also described Napier's bones. It is an extension of Napier's Bones, using two sets of rods to achieve multi-digit multiplication without the need to write down intermediate results, although some mental addition is still needed to calculate the result. The rods for the multiplicand are similar to Napier's Bones, with repetitions of the values. The set of rods for the multiplier are shutters or masks for each digit placed over the multiplicand rods. The results are then tallied from the digits showing as with other lattice multiplication methods. The final form described by Napier took advantage of symmetries to compact the rods, and used the materials of the day to hold system of metal plates, placed inside a wooden frame.

Design of the promptuary The promptuary consists of four parts:

a set of number strips, engraved with a large digit at one end and with many small digits along the strip a set of mask strips, which Napier called excised or perforated strips. Each has a single digit engraved at one end and various triangular holes cut in it a board on which to place the strips when performing a calculation a box to store the strips. In Napier's design, the top of the box was the board on which the calculations were performed. The dimensions of the strips depends on the maximum number of digits in the numbers to be multiplied. For a device capable of multiplying two N-digit numbers together, the strips should be (N+1) times as long as they are wide, and there should be 10N number strips and 10N mask strips. So for example, for a promptuary capable of multiplying two five-digit numbers together, the strips should 6 times as long as they are wide, with 50 number strips and 50 mask strips. Napier's example specified strips 1 finger (19mm) wide and 11 fingers (209mm) long, enabling the device to multiply two 10-digits numbers to produce a 20-digit result. Napier specified that the number strips should be a different thickness from the mask strips - one quarter of a finger (5mm) versus one eight of a finger (2.5mm). This is not necessary for the operation of the device. The promptuary contains a lot more pieces than a set of Napier's Bones. A set of Napier's Bones with 20 rods is capable of multiplying numbers of up to 8 digits. An equivalent promptuary needs 160 strips. In the examples and illustrations below, N is set to 5 - that is, the illustrated promptuary can multiply numbers of up to 5 digits.

Number strips The number strips are divided into five squares, with about half a square free at each end. A large digit, known as the simple, is marked in the space at the top of the strip. A multiplication table is placed in each of the five squares. Each of these multiplication tables is identical—it lists the multiples of the simple and is laid out in a particular way: The square is divided into nine smaller squares in a three-by-three arrangement. Each of these is divided into two triangles by a diagonal line running from lower left to upper right. The multiples of the digit at the top of the strip, the simple, are marked in the table as in the diagram.

The simple itself is marked in the triangle labelled × 1. The number that is two times the simple is marked in the two triangles marked × 2. If the number is two digits, the first digit is placed to the left of the main diagonal (marked in red) and the second digit to the right of the diagonal. If the number is a single digit, it is marked to the right of the diagonal The number that is 3 times the simple is written in the triangles marked × 3 in the same way as the multiple of 2 The other multiplies of the simple are marked in the other triangles in the same way. Zeroes may be written in or left blank. This does not affect the operation of the device. The triangle in the bottom left of the table is always blank. The following diagram shows the multiplication table for the simple 7:

Complete number strips for the simple 7 and the simple 2 are shown in the following diagram. The lines delineating the triangles have been omitted.

The mask strips Mask strips are placed horizontally across the calculating board, that is, from left to right rather than from top to bottom. They have a large digit written in the space at one end and the rest of the strip contains five squares. Each square has triangular holes cut in it according to the patterns given in the following diagram.

So for example the mask strips for the simples 3, 6 and 9 will look as follows:

The guide lines in the patterns are for positioning the holes. They do not need to appear on the strips. The main diagonal line of each mask pattern, however, shown here in red, is marked on the mask strip. It is an important part of the device. The pattern given here for the simple 0 is from later editions of Napier's book. The version of the 0 strip in the first edition had no holes in it.

Performing a multiplication Number strips for the first of the numbers to be multiplied, the multiplicand, are placed on the calculating board side by side, running from top to bottom of the board. In the example shown here, the multiplicand is 772. Mask strips for the second number, the multiplier, are placed horizontally on top of the number strips. In the example, the multiplier it 396.

The result of the multiplication is read from the device by examining the digits visible through the triangular holes in the mask strips. Those parts of the number strips that are not covered by the mask strips are ignored. The diagonal lines on the mask strips divide the device into diagonal bands containing digits visible through the holes.

… excerpt ends here. Continue reading the full article.

Illustrations

Worked examples

Example 1 — a first encounter with Promptuary

Start with the simplest possible case. Write down what Promptuary claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In physics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Promptuary before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Promptuary ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Promptuary

In research: Promptuary appears in physics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Promptuary in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Promptuary is common in secondary-school and first-year university syllabi. It links to neighbouring topics Mechanical calculators, Multiplication, Scottish inventions, so understanding it makes those chapters shorter.
In everyday life: Look for Promptuary outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Promptuary in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Promptuary means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Promptuary out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Promptuary in simple terms?

Why does Promptuary matter?

Because it connects several physics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Promptuary?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Promptuary.