Dots and Slashes in Early Modern English Account Books: A Window into the Material Practices of Reckoning

Let’s look at the examples from last week’s Folger Mystery again, this time with the answer underneath each one and a link to the full page on which they appear.

How? What? Huh? Just when you think you’ve found a pattern, the clusters change shapes, or a new cluster appears!

That was the initial reaction of Ray Schrire, Peter Stallybrass, and I as we set out to understand what was going on with these fleeting dots that sometimes appear at the bottom of account book pages. The Folger Mystery examples are taken from the account books of the Office of the Tents and Revels from 1547 to 1555 (part of the Papers of the More family of Loseley Park, Surrey, with the last example coming from the same collection, but among the accounts of Sir William More in the 1560s).

These dots and slashes are an almost invisible trace of a material practice, mindset, and skillset that was in common use in early modern England. While England was slowly adopting the new cutting-edge calculation method of manipulating handwritten numerals with a pen on paper, an object-based symbolic system of reckoning that did not require literacy, or even the ability to write Roman numerals or Arabic numerals, was still prevalent. One of the earliest English reckoning manuals, An introduction for to lerne to recken with the pen, or with the counters (London, 1539) (sig. l1v), explains:

For as much as there been many persons that be unlearned, and can not write, yet nevertheless the craft or science of algorithm and reckoning is needful for them to know, wherefore I shall hereafter declare & write of this science in the best and shortest wise that may be possible, how that ye shall order your self in reckoning and to cast a counter. [modernized]

In addition to being a good option for “unlearned” people, it was also used at the highest levels of bureaucracy, including the Exchequer, Star Chamber, and the Revels. Sums were calculated on a gridded counting board using metal tokens known as counters, and then the final arrangement of counters on the board was recorded as clusters of pen and ink dots, with each dot representing a counter. The location of a dot on the grid determined its value.

Calculating with Counters

People in England often used counters from Nuremberg, such as this one, below, which depicts how the counter is to be used (counters were also used for gaming, like poker chips).

Merchants, stewards, government officials, and shopkeepers would use the counters at a table that might look like the one below, in order to add up multiple amounts of money. The horizontal lines on the table are labeled in Roman numerals in order of magnitude (I=1, X=10, C=100, M=1000). Counters would be placed on or between the lines, starting at the bottom. The grid is also divided into columns for libre (pounds), solidi (shillings), denari (pence), and obuli (half-pence).

The title page to the first edition of Robert Recorde’s The Ground of Arts (London, 1543) depicts a group of people around a counting board, manipulating counters and writing out Arabic numerals.

Casting was often a group sport: one person read aloud the itemized list of expenses, another person (the counter) would manipulate a stack of counters with his or her thumb–in early modern England, women were often in charge of the household and were considered more numerate than men–onto a flat surface with lines representing place values, another person might observe for errors, and a scribe might add the final tally to the bottom of a page and convert it into Roman or Arabic numerals. For an excellent demonstration of how to use a counting board to add and subtract numbers, please watch Jessica Otis’s YouTube video, “Adding and Subtracting with an Early Modern Counting Board.”

Here are two helpful diagrams, that, despite being unlined, represent the value of each line and space in a counter system.

From counters to dots

Robert Recorde describes the use of counters and the representation of pounds, shillings, and pence with dots and slashes as “common casting.” He demonstrates two forms of casting: merchants cast vertically, from bottom to top, and auditors cast horizontally, from right to left. (Pro tip: The dots are not infrequently represented incorrectly and inconsistently from edition to edition, which can lead to hours of confusion and frustration! The ones shown in this post are correct!).

Back to the Folger examples (which reflect the horizontal, right-to-left, auditor-style system), and the toolkit you’ll need to decipher them:

Each series of dots represents the “sum total” of the expenses on that page, and is helpfully accompanied by the “sum total” represented as Roman numerals. These Roman numerals gave us an indication of the amount that the dots should represent.

For example, the third example in the top row (Folger MS L.b.41, leaf 70v) includes the total amount in Roman numerals to the right of it, which reads “Summa paginæ — xvili iiis iiiid,” or 16 pounds, 3 shillings, 4 pence:

It is also crucial to keep these facts handy:

12 pence = 1 shilling

20 shillings = 1 pound

As we went through each example, trying to reconcile the dots with the Roman numerals, we consulted Robert Recorde’s The Grounde of Artes (at least 45 editions between 1543 and 1699), the preface to the second edition of Charles Trice Martin’s The Record Interpreter (1910), and Jessica Otis’s By The Numbers (Oxford University Press, 2024). In a sense, we were moving backwards from the recorded dots to how they were calculated with counters, rather than the other way around.

Here is Martin’s concise explanation of how to read an auditor’s dots and dashes (from his Preface, xii-xiii):

In case this isn’t as clear as hoped, some further explication. Imagine that a central horizontal line divides the dots that appear on the top row from the clusters beneath them. Dots below this line (the cluster) count as single units. The clusters are not consistent in terms of how the dots are arranged, so don’t worry if they are 2-across or 3-across or 4-across, or contain multiple rows. In general, rows of counters or dots tended not to contain more than three or four units, since that’s the maximum number of units most people can instantly recognize without having to count them individually (a concept now known as subitizing).

In the pence column, a dot above the line equals 6 (it doesn’t matter if it is left, right, or center). There can only ever be one dot above the line in this column because 2 dots would equal 12 pence. 12 pence equals 1 shilling. If you get to 12 in the pence column, you remove all the counters and add a single counter to the shillings cluster.

In the shillings and pound columns, a left dot above the line equals 10, and on the right equals 5. You would never have more than a left and a right dot above the line because another 5 would bump you to 20, which would bump you into the pounds column since 20 shillings equals one pound. Similarly for pounds, 20 pounds equals one “score,” which has its own column.

What Martin leaves out is that for really large numbers, you sometimes get extra columns, for scores of pounds, for hundreds of pounds, for thousands of pounds, and even scores of thousands, as Robert Recorde shows us in this example for 97,869 pounds, 12 shillings, 9 pence, one half penny, and one farthing (again, this is represented incorrectly in many editions, but it is correct below!).

We are certainly not the first researchers to notice these dots, but as we started working through dozens of examples from the Folger, Harvard Business School’s Baker Library, and University of Cambridge’s Archives, we learned that dots and slashes notation is not as straightforward as Charles Trice Martin would have you believe. Jessica Otis describes the flexibility of calculating with counters and recording with dots: “Unlike Arabic numerals, with their fixed 10 symbols, counters actually had the flexibility to function not just for base-10 arithmetic, but base-12, base-20, or any other base the user could imagine. All that was necessary was for the user to declare the meaning of the lines and spaces; the counters and the board remained the same” (p. 55).

This means that looking at these dots in isolation, as we shared them in the Folger Mystery, was completely unfair. You need to see the whole page in order to understand what each section of dots represents. You can’t really begin calculating until you know whether you are counting things (base-10) or sums of money (base-12 for pence and base-10 and base-20 for everything else). For sums of money, you also need to know whether the person is including dots for scores (20) of pounds, hundreds of pounds, scores of hundreds, thousands, etc. You also have to account for the possibility that the dots and dashes are incorrect, or represented inconsistently even within the same document.

All this learning about calculating with counters and recording with dots can get kind of tedious. Here’s how one student passed the time while pretending to study dot-addition and dot-division:

If you’ve encountered dots and slashes in your own research, we’d love to hear about it!