The Nystrom Calculator

Front page: "Description and Key to the Nystrom Calculator", JW Nystrom.

This slide rule was invented by John W. Nystrom, and there are very few examples of it known to exist. This slide rule is considered the first to be patented in the U.S.

Overview

The slide rule was machine engraved on a 9.5 inch brass disk. It could perform computations to 4 decimal places.

I first learned of it from the excellent JOS article by Conrad Schure (V16 no. 2), available on the JOS site. The original patent model is now at the Smithsonian. There is also one at the British Naval museum, and I think another at the British Science Museum.

History-Computer.com has a copy of the original manual, available from this page.

How it works

Basically, this is a Gunter style circular calculator; the two arms act as dividers and allow you to add or subtract logarithms.

What is novel is that the you only obtain the 1st 2 significant figures of the computation from the outer circular part of the scale. You must find the intersection of the cursor with the appropriate curved line to obtain the next 2 figures for a 4 digit computation.

First, there are three kinds of locking mechanisms on the Nystrom Calculator. At the end of each arm is a thumbscrew so you can lock that arm into position while working with the other arm.

There is some form of spring lock underneath the disk that helps you lock a cursor in the 'home' position at 1.000 - The Nystrom calls this '0'. And in order to make sure that your dividers are held steady, the knob can be turned to lock the cursors together. The locking mechanisms were essential to making accurate readings. I would expect that bright light and magnification were desirable as well.

Suppose you are computing 1.51 x 3. On a a "standard" Gunter rule, you set one the pointer ( I'll call it "B") against '1.000' and the other pointer "A" to '1.51'. That gives you a log of 1.51. The pointers normally lock together by friction, and form a divider. Then you rotate the dividers with so that the pointer "B" at 1.000 is now at 1.51 and take your reading at the other end as 4.53.

With the Nystrom, you first LOCK the B cursor at 1.000. Next you move the A cursor to 1.51. Then you turn the knob to lock the arc between the two cursors. After that you unlock the B cursor and rotate the cursors so that B is over 3.000. You take the reading on the A cursor, by looking along the cursor for the intersection cursor with a curved line.

There are other of curved lines on this thing; On the log scale, with the log curves, there are also antilog curves going in the opposite direction. Further inward is a sine/cosine scale, and a points scale (points as in the compass rose used for navigation .

Observations

This must have been a difficult calculator to use, based on my experience with the models I've been working on.

What you are expected to do is take your reading from a curved hair line that is often nearly parallel with the actual cursor itself. The cursor ticks are very close together (akin to vernier scale), and because the curved lines are very steep, the angle of intersection with the cursor can be very small. The slightest miss could make a large difference in the answer.

I do expect that the original Nystrom Calculator's must have been marvels of precision machining, but even so, it could not have been easy to operate without magnification and great care at reading.

I am of the opinion that this calculator would be much less precise at the top ends of the scales, because the curves are so nearly radial that it'd be nearly impossible to get the 4th, let alone the 3rd digit reliably.

I expect that was offset just by the fact that whoever owned one of them had serious bragging rights, and would very much not mind the work.

Above, one of the trial versions I've made. I decided to try a 3D printed approach to get decent cursors. In the end, I came to the conclusion that the only viable approach was to have the cursor markings laid flat against the surface of the slide rule, to eliminate parallax. On the original calculator, the cursor scales were engraved on an inclined plane, like a wedge, with the scales sitting on the 'sharp' end of the wedge.

Nystrom10inch11x17.pdf

File : Nystrom10inch10x18.pdf August 1, 2020

The above file contains PostScript images of a Nystrom replica. This version requires a printer capable of printing 11x17 inches or A3. I kept a build diary here

NYSTROM-PATENT.pdf

J. W. Nystrom, "Calculating-Machine" (U.S. Patent 7,961 issued March 4, 1851, extracted in PDF format from the US patent search engine.