GM Andrews calculating instrument

Description

I'm unaware of this slide rule having been manufactured. Also, I have been unable to find any biographical info on the inventor.

This slide rule has a 10 turn Archimedean spiral scale, and a linear scale on the circumference. Respectively, they comprise the equivalent of a 'C' and 'L' scale on a traditional linear slide rule.

As with almost all spiral models, 2 cursors are used, like dividers, to hold a constant angle during computations.

Each cursor has an index pointer that can be moved radially; these work as placeholders for keeping a record of which turns are in play, and to help compute which turn of the spiral the answer is on. A rotary turn counter (look for K, L, M, J in the image above) is also included on the face of the slide rule.

Because Mr. Andrews chose a 10 turn model, the logarithm of any number is very easy to obtain, which means computations involving powers and roots are also easy to execute (see "L scales on spiral models"). The slide rule has no other scales; the patent suggested that the reverse side of the slide rule might have tables of values for common trigonometric functions.

The patent indicates no model was provided. Although the inventor included a good drawing, I suspect he built no models to test the drawing as some of the features of this instrument don't appear to be practical as drawn. I complain about them further on.

The index pointers appear to me to be redundant. The turn counter is the mechanism for determining the turn that an answer would be found, especially in the case of a chain calculation. Really what you need are the indices on the cursors, those can be read directly.

Cursor design

The cursors on the design look quite slim. I expect that these were planned to be brass or other metal since other materials would be lack strength or flex a lot. This is not an issue with the design, but really a problem for me as a modern re-interpreter.

Based on an 8-inch outer circumference, the entire turn counter would be less than 1 inch in diameter. In the model I've made so far, this means the holes are separated by about 1 mm, and therefore pretty small.

Perhaps you could operate the dial with a pin, or a mighty fine-pointed pencil.

If the turn counter is to remain on the face of the calculator as shown, it would need to be larger than the drawing seems to imply.

One way to do this is to make the disk larger. A 20-cm or 8-inch diameter to be a 'large' disk. However, if we enlarge the disk the turn counter likewise increases in size.

Another way is to start the scale farther out from the center. This actually makes the scale a bit longer, so could be beneficial. The turn counter can then occupy the space freed by the larger area. I'll try a couple of iterations of this.

Make your own Andrews Spiral Calculator

Below, I uploaded PostScript files of my interpretation of the GM Andrews instrument. I believe the slide rule to be reasonably close to the inventor's design, but I had to make some modifications to make it workable for a home build.

I found that it was not feasible to fit a turn counter on the disk, at least if I wanted to use a normal A4 or letter-sized paper. I enlarged the turn counter and shrunk the disk a little so that both could fit a page. Based on my iterated prototypes, I think the current turn counter is almost as small as it can be. Moreover, to fit on a disk, then the disk would need to be about 12 inches in diameter.

Other differences are:

• I rendered the numbers to be radially oriented. The patent has the scale numbers horizontal to the page. I've never seen that in a production rule, and suppose it's perhaps a thing done on patents to make them more readable.

• I made the cursors wider than the patent drawing suggests. More surface area helps keep homemade cursors rigid and improves the friction between them.

• I reshaped the turn counter; these appear to be intended for screws and I'm using glue. I added wings for tabs. You pin the inner part of the turn counter to provide an axis of rotation, and just tack the faceplate over top.

• I used simple paper rings to slide over the cursors for my indicators. These will prevent the cursors from completely closing but should work well enough for a working demo.

Build and Operating Instructions are in the PDF.