# What is the highest level of accuracy in motion control a Victorian society could achieve?

In my late-Victorian world high-precision clockwork is highly available, but I am having trouble finding out exactly how precise their work could be.

I have done some research on the subject, but cannot discover how people make more precise tools with less precise tools.

If, for example, one simply translates large movements into small movements by gears or levers there is the irregularity of the parts themselves, let alone the movement, that would cause defects in the final product if my thinking is correct.

This is how I am left with the question what is the highest mechanical precision achievable in a late-Victorian setting?

I am aware that clockwork was already very precise, but I could imagine that it would be possible to have even higher precision, even though it may have been impractical at the time (e.g. watchmaker using pincers to place a dust-speck-sized cog on a shaft the breadth of a hair, missing and damaging the entire apparatus).

EDIT: With precision I mean the smallest distance I can move a tool in a controlled and measurable fashion, e.g. a saw that lets me cut a groove x wide and y deep, x being the width of the saw and y being the 'precision' of the tool.

• The watchmaker example you give seems to suggesting that you are looking at the smallest manufacturable feature, not at precision. Can you clarify?
– L.Dutch
Jul 3, 2019 at 8:56
• Your use of precision may be imprecise in this context ;-) You should clearly distinguish this question from your previous, related one. Jul 3, 2019 at 9:05
• Just to be clear with my request: making a steel bar with a length of 1 meter and controlling the length to the tenth of millimeter is more precise than making a 1 mm bar controlling the length to the tenth of millimeter.
– L.Dutch
Jul 3, 2019 at 9:18
• To kinda wave toward the broadest "how can I make a more-precise tool with a less-precise tool", you can connect a big gear to a small gear by the teeth, connected to a small gear by the axle, connected to a big gear by the teeth, etc. until the final gear drives a belt. Turning the first, biggest gear by some distance should move the belt at the end by some fraction of that distance, so you can (for example) measure how far to crank the gear to move the belt 1 meter, and then just do 1/1000 that many cranks to move the belt 1 mm.... Jul 4, 2019 at 0:40
• @JesseAmano backash, belt stretch (and other structural movement), thermal issues and frictional losses will limit your ability to get arbitrarily fine control over the grabber. Your approach only scales so far. Jul 4, 2019 at 14:00

TL;DR: you almost certainly can't manage better than a ten-thousandth of an inch (~2.5 μm).

The length and depth of the cut of your hypothetical saw could conceivably be accurate to this scale. Making a saw that could produce a width of cut this fine is probably impractical for your Victorians, if only for material issues. It is theoretically possible that diamond or ruby engraving tips could be up to the job, though.

Your question is still slightly ill-specified, but the general issue of victorian precison and mechanical tolerances should still be answerable.

Exhibit 1: gauge blocks, specifically those by Carl Johannson. He apparently invented them in about 1896, and was granted a Swedish patent in 1901 a few months after Victoria's death (just sneaking out of the victorian era proper). His combination gauge block set included 49 blocks with thicknesses from 1.01mm to 1.49mm (source, PDF). These don't represent the pinnacle of dimensional accuracy, but they are things that could be repeatably and reliably manufactured and sold as a practical and popular commercial product.

Exhibit 2: micrometers. The mechanical principles of these had been around for a long time before Victoria appeared, but micrometers for measuring the size of objects rather than the angles between stars appeared around the time of her reign or slightly before. Henry Maudslay, who gave us screw-cutting lathes, had a micrometer that could measure down to a ten-thousandth of an inch (~2.54 microns). Joseph Whitworth had a device of similar capabilities in 1844, but built so that it was a bit less delicate and more practical for general workshop use.

(You may also recognise the name Whitworth from the British Standard Whitworth, a specification for screw threads. Not so important for ultra-fine machining, but repeatably being able to make high quality parts is also important and Whitworth threads were a part of how this was done in the Victorian era)

Exhibit 3: Whitworth had also devised a technique around 1830 for getting surface plates (a particular kind of reference plane) to a flatness of under a ten-thousandth of an inch. Surface plates are extremely important for the production of high-precision tools, because (amongst other things) they give you a way to create high-quality right-angle gauges.

With careful use of these three items, you should be able to make very precise mechanical movements with your hypothetical saw. The issue of making a saw that's up to the job of making cuts this fine is left as an exercise to the reader!

Victorian material science simply wasn't nearly as good as ours. Without our fancy metallurgy and ceramics technology, making tough cutting tools at this scale would be extremely difficult. Engraving features at this scale might be possible with a diamond or ruby tip, as for anything else material wear under use would ruin your precision very quickly. I can't find enough detail about Victorian micro engraving to say any more on what may or may not have been possible in this regard, though.

For further reading on the issue in general, rather than victorian engineering in particular, have a read of The Foundations of Mechanical Accuracy (PDF, original book printed in the 70s).

• "you almost certainly can't manage better than a ten-thousandth of an inch." How much is that in milimeters? :P Jul 4, 2019 at 12:31
• @jo1storm a conversion is given in microns for those who read the answer, but no-one victorian would have been using those. Jul 4, 2019 at 13:56
• @StarfishPrime: While it's true that while Englishmen lived in the Victorian Age, Americans lived in the Gilded Age and Frenchmen lived in the Belle Époque; but behind the names the worldview, scientific environment and technological ability were pretty much the same. Moreover, in those days people, capital, goods and ideas moved freely between civilized countries. Jul 4, 2019 at 14:50
• @AlexP why is that relevant to the choice of units? British used imperial units. I gave imperial units. I included a conversion to metric units. By all means discuss other units and other nations on other answers. Jul 5, 2019 at 13:22
• @StarfishPrime: The answer already has my upvote. And it is a very good answer. The comment was just in reply to your throwaway remark that no-one Victorian would be using millimeters. Jul 5, 2019 at 13:29

Millimeter and possibly sub-millimeter accuracy was possible in normal manufacture.

In scientific experiments far more precise measurement was made, but that does not equate to manufacturing and particularly to milling and machine processes.

Here would be my candidates for common high precision manufacturing processes of that era.

The Janvier Reduction Machine

One of the most accurate instruments I've heard of (in common manufacturing, as opposed to special one-off scientific experiments) would be a device used in coin making (and some other fields) which controls a high precision lathe to generate a true size coin from mechanically scanning a much larger design form.

Here's a link to a page on these devices : http://www.1881o.com/reduction.html

These would reduce a template about the size of a dinner plate (perhaps a large dinner plate) to a standard coin size. The resulting coin would be used to stamp out coins. These machine were in daily use in the same role until relatively recently (and may still be in use somewhere for all I know :-) ).

They allowed intricate coin designs (hard to fake by crooks) to be made by your beloved governments and make counterfeit coinage harder to pass.

Vernier Caliper/Scale

These are lovely (and still used) devices which existed before the Victorian era and allow high precision (and more importantly consistent) measurements to be made of object sizes. Wikipedia can explain more about them. These gadgets are simultaneously loved and hated by engineers everywhere, loved because of their precision and hated because they sometimes bring bad news :-) .

The Common Screw

As odd as it may seem the Industrial Revolution depended as much on the accurate and consistent manufacture of well size screws (including their threads) as it did on any of the more glamorous engines and devices.Wikipedia has a page on these devices.

• "possibly sub-millimetre"?? I can get sub-millimetre accuracy on a block of wood with a sharp chisel. Victorian engineers could do much better than that! Jul 4, 2019 at 8:40
• Also see: Whitworth Three Plates Method, Pantograph, and transmission with gears making very precise movements.
– data
Jul 4, 2019 at 12:03
• Agree with @MartinBonner machining could be done to the thou (thousandthsof an inch ) back then - obvisly we would use thou as at that time Britain was the world leader Jul 4, 2019 at 18:58

It depends on how you define precision, and also whether you place more importance on what would be commercially viable technology for mass production in the Victorian era, or what would be the best cutting edge fabrication processes available to the era's top scientists and instrumentmakers. For example, would the best precision of our era be represented by computer chips, or by LIGO?

In the latter case, the answer would probably be "remarkably good precision".

I think the best I can do is to cherry pick the era's most advanced instruments to serve as examples. So:

1. Diffraction grating ruling engines.

These are a classic example of machines that push the limits of mechanical precision, and they also directly match your definition of "move a tool in a controlled and measurable fashion, e.g. a saw that lets me cut a groove x wide and y deep". By the end of the Victorian era, Henry Joseph Grayson had constructed ruling engines that could scribe gratings with 4700 lines per mm (ie, 212 nm pitch; each groove can roughly be assumed to be about 100 nm deep). Previous ruling engines were already pretty good, too.

1. Michelson interferometer

The Michelson-Morley experiment was conducted in the 1880s, and represents one of the first and most important applications of the interferometer, which is still among the most sensitive measuring instruments in existence today. Their white-light interferometer was built on a sandstone block floating on mercury, which would compare well with setups in today's top academic labs (for precision if not for safety). Although they were looking for optical path length changes due to aether wind with fixed mirrors, their interferometer would have been sensitive enough to detect the mirrors moving by as little as 2-3 nm.

1. Whitworth's comparator

Accurate micrometers for use in machine shops were already being commonly made in the Victorian era, but undoubtedly the king of this category of instrument would be Whitworth's comparator, built in 1871 and which could measure differences in the lengths of objects to submicron accuracy.

1. Chemical etching

The smallest scale parts might be made by chemical rather than purely machining techniques. For example, platinum wire of about 1.5 micron diameter, known as Wollaston wire, was produced by the early 19th century. It is first embedded in silver, then drawn down, then the silver is chemically dissolved. If you wanted to make gears the size of specks of dust in the Victorian era, you could try to do it this way. (By the way, microscopic clockwork will make your clocks smaller, but probably not better at keeping time...)

1. Coating processes

Although this isn't directly motion control related, it's also relevant to fabrication abilities. Electroplating became a mature technology during the Victorian era, and other thin-film deposition techniques such as vacuum sputtering were invented during that period. Electroforming was invented by 1840. These additive-manufacturing techniques allow the creation of extremely thin and uniform films and delicate thin-walled structures. A coating of silver on a glass substrate could be made less than a micron thick. Electroformed thin-walled metal objects could be tens of microns thick.

1. Bonus: Division of the circle

In addition to length, another important thing is accuracy of angles. For example, if you have gear teeth, how evenly-spaced are they. The Victorians would have had little difficulty here. Already in the pre-Victorian 18th century, Jesse Ramsden had built division engines accurate to one arc-second.

How many zeros in your check book and how much time do we have?

How do people make more precise tools with less precise tools? Precisely how you said: 'people' did it by hand (sometimes literally, polishing it with their fingers). "You" specifically, probably can't, which is why clockwork has always been a respected profession, and why gunsmithing still is.

All well-made firearms are finished by hand to achieve the tolerances required. Which is done by dragging a file across the part, and then checking it against its mate. Over and over and over, until the smallest grit 'file' is simply a flat piece of a harder metal; abrasive number: +3000. That's why you're supposed to check that all the serial numbers of the parts match, because each one of them has been custom fit to the specific weapon.

It becomes a question of how fine you can hone an edge on your cutting tool, which is well beyond the limit of human dexterity to employ completely no matter how good you are. To keep it realistic, I'd be looking for the smallest tolerances ever achieved in production, not what would have been possible, because that's determined by skill, dexterity, time, and 'number of zeros' until we're past the microscopic level.

And then all sorts of problems start to crop up, like having a duty cycle of half a second, or being susceptible to even minor fluctuations in temperature and pressure or humidity, and the oxidation of materials commonly thought not to (the only one is gold, which is too soft to make parts). And it abrading itself. If you have to start worrying about the Casimir effect; you've gone way too far.

Motion control is easy: gear reduction. But wanting to be able to wear it on your wrist and have it actually still work (accurately!) longer than half a second, (aka, miniaturization) is the problem, because even if you can make it, that doesn't mean it will work. At some point it gets small enough that the governor isn't reliable anymore due to the size of air molecules.

For analog clocks it's ultimately a question of how small you can make a balance wheel (invented in the 14th century, the crucial advance that "finally made accurate pocket watches possible"), until the 1960s when electronics (tuning fork and quartz movement) became available.

TL;DR: as small and accurate as you're willing to pay and wait for, up until the point that physics or material science says no. If you're Britain trying to solve the longitude problem at sea, that's yesterday so here's three million pounds to anyone who can. That's in adjusted dollars and it was John Harrison, inventor of the marine chronometer: "a timepiece that is precise and accurate enough to be used as a portable time standard".

Have a demand, be willing to pay for it, and you can have your cake and eat it too... within reason, as dictated by the laws of the cosmos. Just don't forget to wind your watch and 'always dial one number higher'.