Waves of chance amplitude are measured typically in MilliHawtons (mH). According to Professor Hawton's recovered notebooks, one Hawton, or 1,000 MilliHawtons, is "enough to make one or more six-sided wooden dice momentarily show a result of seven, when cast among a set of one hundred similar dice in the presence of a single human observer."
The unit is not particularly accurate or reproducible because the observer, the dice, and the method of casting can have an effect on the probability of a seven occuring, along with a host of other factors. Of course, this doesn't really matter outside of academia - to this day, five countries still quote temperatures in a scale at which zero is the coldest day that Daniel Gabriel Fahrenheit had ever seen, and 100 degrees is the inside of Daniel Gabriel Fahrenheit on a day when he had a cold,
and they're doing just fine so don't let it worry you too much, it's probably fine.
Potential for interaction with a Hawton field is measured in Rands. It takes a lot of Hawtons to change the behaviour of a thing that is low in Rands, and vice versa. The Rand value of a given object seems to have a large cultural component. A coin has more Rands than an identically-sized disc of metal.
Acrylic, stone, metal or bone dice have different Rand values than wooden dice. Freshly-manufactured dice have a lower Rand value than older ones. A pineapple has more Rands than an orange, and nobody knows why. White mice have more Rands than grey mice, and nobody knows why. Transistors have a Rand value high enough to prevent the use of solid-state computers on Improbable Island, but diodes and other passive components do not. Transistors inside the Island's Robot citizens apparently work well enough for the Robots to function, and nobody knows why. The Rand value of humans varies enormously; the Rand values of other species on Improbable Island also vary enormously, but are almost always higher than that of humans. Nobody knows why.
A Hawton Meter makes use of an artifact of enormous Rand value, stored inside a vacuum chamber and attached via a long lever to a coil and some circuitry which measures the artefact of Chance upon the artifact of chance. The meter does not work when observed directly, nor does it work unless someone has confidently used the words artefact and artifact in its presence without quite understanding the difference between the two. The meter uses an analogue needle, as digital displays do not work (nobody knows why). To take a measurement, turn the device on, avert your gaze and wave the device around randomly, and then turn it off while quickly glancing at the needle - a large capacitor stops the needle from falling to zero immediately, and your frantic flailing creates enough additional bounce in the needle to give you an impression vague enough to not violate conservation of ignorance.
If you observe the device directly while it's activated, the principle of conservation of ignorance will cause a Hawton spike of sufficient magnitude to destroy the device, which will quickly become the least of your concerns. Weirdly, observing a manufactured artifact in conjuction with the meter has the opposite effect. Nobody knows why. Yet.
Turn the meter on from your Inventory anywhere outside of combat, at which point it'll make sense to put it into your Bandolier. Once it's turned on, you can add an artifact to improve the meter's resilience - you have two minutes' grace in case you activate a meter inside a Chance field high enough to immediately destroy it, but it's a good idea to ask in chat if it's safe to turn the meter on. The meter will constantly display ambient milliHawtons (amH) under the Game State heading in the stats area, until it is destroyed.
The ambient chance amplitude affects combat - the higher the amH, the greater a role Chance plays in the fight. If you're all but certain to lose a fight against a strong monster, adding some degree of randomness might give you a chance, however slim - observe the meter directly in combat to destroy it and create an enormous Hawton spike. Conversely, if a fight is going well and you don't want your opponent to get in any lucky strikes, you can observe an attached Manufactured Artifact to suck the chance out of the encounter.
Manufactured artifacts are specially-designed artifacts of Chance that are made to act as capacitors. Charging one will temporarily suck the Chance energy out of an unfriendly encounter. Caution: once the artifact is fully charged, it'll discharge spectacularly at the slightest provocation, and if it's overcharged it can discharge spectacularly with no provocation at all, creating a huge Chance spike and destroying the attached meter.
Even outside of combat, Manufactured Artifacts are useful in absorbing some Chance energy, improving the meter's resilience. Hawton Meters start taking damage when they measure more than 680 ambient milliHawtons, but a Manufactured Artifact added to the meter stops it from taking damage until the needle reaches 700amH, and a Purified Manufactured Artifact can keep things safe right up to 720amH.
To use the Manufactured Artifact in combat, it must be attached to an activated meter stored in your Bandolier, whereupon you'll see the option to open the observation shutter. Opening the shutter causes the local amH to immediately drop to almost nothing as the artifact charges, making combat much more predictable. Pay attention to messages shown in combat as they'll reveal the status of the artifact. Close the observation shutter to allow the artifact to discharge safely - remember that it takes time (or, rather, interactions with Chance) for the artifact to discharge, so leave it alone for a few combat rounds before you observe it again. The artifact discharges into the local area, so amH will be higher than usual after closing the shutter over a highly-charged artifact - if you're in the middle of a big Hawton wave, closing the shutter can occasionally end up destroying the meter.
Remember, the higher the amH, the faster the artifact will charge. The more it's charged, the longer it'll take to discharge.
Following a significant Hawton spike such as may occur when a meter explodes, the individual nearby will be temporarily (and enormously) higher in Rand than usual, causing a feedback effect which manifests in a personal Hawton field around the subject. The effects can stick around for a while, so it's a bad idea to turn on a Hawton meter immediately after you've just had one explode in your face. Regardless of how many meters you blow up, the effects will be dispelled following a good night's sleep. Nobody knows why.