## The Zen of Weighing and Running

A 10 millilitre gas bottle within the weighing enclosure.

The technology of weighing is simple in principle: we determine an unknown mass by comparing the force of gravity on the unknown object with the force of gravity on objects of known mass. The basic simplicity of this process is at the heart of its power.

Astonishingly, this simple procedure underpins essentially every result in analytical chemistry, because the validation of almost every technique of analysis (e.g. mass spectrometry or chromatography) can eventually  be traced back to a weighing.

At the moment I am involved in two ‘projects’ in which weighing is the key technology.

Argon Isotopes

The first project involves preparation of a mixture of two gases to create samples of known composition that can be used to  calibrate a special mass spectrometer.

To do this I just need to:

• Weigh some empty gas bottles
• Fill them with gas of one of two types.
• Weigh them again

The difference should give me the mass of gas in each bottle. I then ‘just’ need to connect the bottles together and let the gases mix. Then I should have samples of gas with a known ratio of the amount of two types of gas molecules.

Although simple in principle, the project is difficult in practice.

To contain 10 millilitres of gas requires an object (see illustration at the top) which weighs around 300 grams. The most gas I can put into this container (the gas is crazily expensive – around £3000 per gram!) is around 0.2 grams.

To achieve my target uncertainty in the calibration of the mass spectrometer, I need to weigh that gas with an uncertainty of around 0.2 milligrams. So overall I need to compare objects weighing 300 grams and detect differences with an uncertainty of less than 1 part in a million.

In fact weighing technology can achieve this!

The display of the Mettler AT1005 Mass Comparator. On this 200 g to 300 g range, it is possible to read results with a resolution of 0.01 milligrams – 1 part in 30 million of the object’s mass!

But sadly things are not as simple as just using a great weighing machine.

One aspect of weighing that is often not appreciated is that objects being weighed are constantly being ‘buoyed’ upwards by the air they displace. The extent of this buoyancy is related to the difference in density between the object being weighed and air. For steel objects this typically affects the results in the fourth decimal place e.g. 300.x grams.

And since air density changes from day to day by as much as 10% – the results of a weighing can vary from day to day by parts in 100,000. In other words the y figure in 300.0y grams changes with the weather from day to day. Unfortunately, this is 100 times larger than the changes I am hoping to detect 😦

To counteract this, instead of trying to work out the absolute mass of the bottles, I simply compare them with a standard object – called a tare – which has a similar weight and volume and so experiences similar uplift to the object I am trying to weigh. In this experiment I simply use another stainless steel bottle that I don’t fill with gas.

To determine the difference from the tare requires three weighing.

• First I weigh the tare and wait for a stable reading.
• I then weigh the object of interest,
• and finally re-weigh the tare.

The key result is the difference in the reading from the  object and the average of the two tare readings. This gives me one result. I acquire 5 such results to allow me to assess the stability of the result and estimate the random component of its uncertainty.

In the NPL weighing room. The gas bottles I am weighing can be seen in the foreground.

The weighings need to be repeated prior to doing anything interesting – such as filling a bottle – in order to establish that the weights of the bottles are suitably stable when left alone.

Weighing the set of 10 bottles takes about two and half hours and while weighing I achieve a kind of meditative bliss. The activity requires attention and patience, and hurrying simply results in errors. While weighing, time passes slowly, but when I have finished – it seems like the time has disappeared.

My weight

My second ‘weighing project’ is myself.

Long term readers will know that my weight goes up and down. I am currently in a phase of losing weight and, of course, I record my weight each day, at the same time of day and wearing the same clothes.

This particular bout of weight loss was sparked by being invited to the NPL awards dinner in January – I was being rewarded with food for having been at NPL for 15 years.

As I went to put on my suit, I found it hard to fasten the waistband of my trousers. On weighing myself I was confronted with a number larger than any I had ever seen on these scales, and I resolved that immediately after I had eaten this next excellent meal, I would begin to lose weight. And I have.

My weight since the end of January 2016

My strategy for losing weight combines modest calorie restriction with running.

Running serves the dual purposes of burning up fat, while allowing me to enter a second meditative state: at a certain heart rate I am able only to concentrate on putting my feet on the ground safely and I become temporarily unable to release the mental resources to worry.

Long term readers readers will be relieved to know that this effect is transitory: my capacity to worry quickly returns after I stop running.

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