Making the Promptuary Slips
by Jim Hansen
Note: This section describes the detailed steps that I used to physically make the Promptuary slips. Their logical design and layout are described here.
Promptuary calculations are performed using what Napier called “slips,” the heart of the Promptuary. There are two types of slips. One carries a table of numbers, the other a mask that typically reveals only two of the 18 possible numbers. The slips are numbered according to the table or mask that they carry, and when a mask slip is positioned over a table slip, only the product of those two numbers is exposed.
Ever practical, Napier called the slips carrying the tables “vertical slips” since they are placed vertically during calculation. The slips with the masks are placed horizontally over the vertical slips for the solution readout, and these Napier called the “horizontal slips.” I decided to use the terms “table slips” and “mask slips” as being more descriptive of the slip type involved.
The Promptuary is designed to perform up to 10 by 10 multiplication, and so each slip has its table or mask repeated 10 times along its length.
The mask and table slips work together in an almost magical way. The product of the the slip numbers suddenly appears out of table slip numbers as the mask falls into place. For example, if a number 7 table slip is covered by a number 3 mask slip, only the result, 21, appears through the mask. The table and mask design and Promptuary use are given in Design and Using the Promptuary, elsewhere on this site.
The following information describes how to create the slips from start to finish. This part of the project can easily absorb two or three weekends. For those who are faint of heart, I’ve included all the files necessary to make the slips which will lighten your load considerably. They can be printed as needed.
Napier’s Original Slips
Napier specified that 200 wooden slips were to be made for Promptuary use. One hundred would serve as the vertical or table slips, be a quarter finger thick and be hand inscribed with the tables. The remaining one hundred were to be "filed" to half that thickness. These would have holes bored in them to produce the horizontal mask slips. The outer dimensions of all the slips was one finger wide by eleven long. (A “finger” was a common dimension in the 16th and 17th centuries. Today a finger is defined as 3/4 of an inch (or about 19mm) long.)
Thus Napier's recommended slip size was about 8.25in by .56in (21cm by 1.4cm). This seems much too small. Each table on the slip is organized as a 3 by 3 array divided by diagonals to create 18 number positions. The present-day definition of a finger would thus create the array about .56 inches on a side, only a little over a half inch. This array is then divided into a 3 by 3 array, each cell of which would be a third that, or .187 inches on a side, or less than a quarter inch. Then the diagonals are to be drawn to halve those cells. This is too small, and so I suspect that the “finger” Napier used must have been larger than today’s definition.
Whether or not this is so, unlike Napier who proposed writing the tables directly onto the slips, I wanted to use a computer to do the layout, and with my failing eyesight, I also wanted the numbers large enough so that I could easily read the results.
Note: This table slip is a copy of Napier's original slip example. Credit: John Napier, translator William Richardson, translator, from "Rabdology," reprinted by MIT Press ISBN 0-262-14046-20, © Copyright 1990. Used by Permission.
My Slip Layout
I designed my slips to be an inch wide and 11 inches long and printed on 8.5in by 11in paper. The final table slips are printed on 110lb card stock (I picked an off-white color) while the mask slips are printed on standard overhead transparency stock. Each sheet is large enough to hold five slips plus a generous inch to be shared by the slip number label and the top and bottom margin. (See below for a full view of a table and mask slip.)
The placement of the numbers on the table slip is challenging because accurate and consistent placement is required if all the masks are to work on all 10 table positions throughout the slip collection. The numbers must be uniformly placed so they are always aligned under the mask.
Note: The fine line detail printed at 600dpi resolution in this layout image is not visible when resized down to this extent. This image is included only to show the overall layout that I used. You can examine individual original source files provided in full resolution. In the Promptuary Downloads picture section, look for "TableSlipScan.jpg," a scanned image which unfortunately is itself degraded by the scanning process.
Software Tool Search
I had difficulty finding suitable software for setting up the slips. One would think that a word processor could be used to set up a table and fill it in. Accurate and repeatable placement of table characters and slip size tolerance is everything in this project. As can be seen in the two photos above, each table row consists of numbers on two different baselines. And once the table is created, the diagonals have to be added. These serve as a user aid when setting up and solving problems by defining the "diagonal columns." Once you manage to get a usable table, it must then be copied and stacked ten high. Both Word and WordPerfect failed in this role.
A pure graphic approach fails too, because they don't handle the character baselines very well. I didn’t have the skill or patience to make twenty different slips all precisely formatted exactly the same.
My slip design uses a one by ten-inch slip, plus a label on top and a bottom margin. The box is divided vertically in thirds, then horizontally so it is filled with an array of 90 absolutely square cells. Diagonal lines are drawn through each square, resulting in 180 triangular cells spread along the length of the slip. The label is placed on top of this array. The bottom paper margin provides the bottom clearance for the slip. At this point we have a blank slip that can be used as a template for consistency.
The table numbers are now entered according to Napier's original table design. This was expected to be an entirely repetitious adventure that required double and triple checking, and I wasn't disappointed in this respect. I will not go into the details of how I arrived at the proper layout, but rest assured it took a great many hours to arrive at the final template version.
Probably the last thing you will be thinking about, but one that is important to consider, is your choice of font. Once you've set up the template, you'll not be able to switch fonts around without, in many cases, destroying the layout. The font I picked is called New Hampshire. I wanted something that looked a little like Napier's hand-drafted slip (see above), and I liked this one, found at some forgotten "free fonts" website.
The only tool that I had at hand and proved able to do the above tasks was WordPerfect’s Presentations X3 software, essentially Corel’s version of PowerPoint that is distributed with Word Perfect. Although certainly not perfect for this job, I found a way to use it, and it eventually made the slips more easily than I had initially expected. It let me drew the graphic elements of the slip template, adjust the thickness of each line, and accurately placed the table values in each cell. Although it handily made the table slips, it has no graphic capabilities, and so only the blank table outline was available for the mask slips.
To make the mask slips a blank table image has to be moved into a graphics editor, a troublesome task. My technique for producing the mask strips is a bit convoluted, but it worked almost flawlessly most of the time. I use PaintShopPro for graphic editing, but most other similar graphic editors can probably be used for this task.
Making a Mask Slip
The overall purpose of this part of the exercise is the equivalent of printing out the slip, then scanning it back in to be edited as an image, an approach that severly degrades any high resolution image. The following directions are as plain as I can make them. If you are using different software, may the force be with you; it took hours and hours to find this one procedural solution. If you are using different software, I bet you’ll be spending some quality time with your computer as well.
Step 1. While in Presentations X3 , I took a blank table slip (one that wasn’t filled out with a table yet), then redrew the diagonals to effectively rotate the table by 90°. This is necessary because the mask slips are placed horizontally. I then edited the diagonals so that only every third diagonal was thickened to .020" thick and thinned the others as much as possible. The intermediate diagonals have to be left in place so the photo editor can pour color into the individual cells as a part of the editing process. The thickened diagonals (see the Napier slip drawing above) make it easier to see the diagonal columns. This file was then saved as the master mask file.Editing the Mask Slip
This operation takes the high resolution .tif file just generated, trims it, fills out the mask and gives it a nice label. Almost any graphics editor that has similar functions (such as Adobe’s Photoshop) can be used, but instructions here are directed toward the command style of PaintShopPro. This process isn’t rocket science, but it can send you to new heights of Compulsive Computer Disorder.
The work outlined here is for the mask slips, although I also ran the table slips through this program as indicated in the steps to ensure that all slips are trimmed to the same size.
Perform the following steps:
Step 1. If you are working with a table slip, go directly to Step 4. Else, before starting, select and copy the slip number at the top of the mask to the clipboard. This saves a positive image of the label which will be used shortly.Printing
The table image files were processed by PaintShopPro in the same way, by cropping each table and resizing it. I used the PaintShopPro Print Layout and fitted five slips to a page, ending up with two pages for the table slips 0 through 9, and two for the corresponding mask slips. The mask slips should be printed on overhead transparency stock, which is generally available at office supply stores.
Stiffer stock for the mask slips would be better, but I couldn’t find another film that could be run through the laser printer. You could take the mask sets to an offset print shop and have them make film copies, but the cost would be prohibitive.
All slips are laser printed at 600dpi to avoid "the jaggies," especially apparent on the fine table lines. It also dramatically improves the appearance of the numbers. Inkjet printers are not recommended because they require a special kind of transparency, and even that doesn't work particularly. The masks use an incredible amount of toner (or ink). Make sure you have additional supplies at hand before starting to print your slips.
Making Your Slip Collection
The question of how many slips you should make is an interesting one. The Promptuary is designed to multiply numbers up to 10 by 10 digits in length. Napier stipulated that 10 of each slip should be made so that a 10-place figure consisting of a single number, such as 5555555555, could be used.
Given that his slips were made of wood, if all 200 slips were put in a single pile, it’d be a little over 31in high, or almost a yard! This seems a bit excessive to me, especially since I still have my electronic calculator available as a backup. I decided to print five sets of slips for my Promptuary because its primary use is as an educational tool rather than a “practical” calculator.
Although producing the slips is an easy, repetitious mechanical process, making a complete set of slips is long, tedious and tiring. Plus it is incredibly easy to make mistakes. The penalty for doing so is great: start over and do it right this time! It takes at least a weekend, maybe two, to make a perfect set of slips from scratch. Even then you’ll probably find something later that you’d like to change. Then you have to start all over.
Cutting the Slips
The individual slips were cut apart using a rotary paper cutter. I get better control and much nicer, more consistently-sized slips with it than a standard paper cutter. If you have to use a regular paper cutter, consider mounting a small light under the cutter area so you can better see the edges to be cut. Once the slips are cut apart, they are ready for use or storage in your Promptuary case.
For those of you willing to accept the challenge of making your own Promptuary, my advice is to plan it out in as much detail as possible before you start. The careful layout of the slips cannot be stressed enough. I went through four or five revisions before I was satisfied. Or just make a gentleman’s copy of what I’ve done and use that as your starting place. I have placed copies of my slip masters in the download area of this section for anyone who would like to see or use them, and they'll save a ton of work if used.
Enjoy using them and please tell me if you find any errors.
Jim