Tag Archives: standard

Vienna Standard Mean Ocean Water

Vienna Standard Mean Ocean Water (VSMOW) is the standard water used for calibrating instruments such as thermometers. Water will freeze and boil at different temperatures depending on the mix of isotopes it contains, and VSMOW standardises these ratios so that all experiments achieve the same results. (If you want to buy some VSMOW, it’ll cost you €180 for twenty millilitres, about twenty times more expensive than inkjet printer ink.)



The hydrogen in water is one of three isotopes: hydrogen-1 (one proton), hydrogen-2 (one proton, one neutron, also known as deuterium) and hydrogen-3 (one proton, two neutrons, also known as tritium). Hydrogen-1 and deuterium are stable, but tritium is radioactive but has a long half-life (12.32 years). VSMOW contains one deuterium atom for every 6420 atoms of hydrogen-1, and one tritium atom for every 54.05 billion atoms of hydrogen-1. (The amount of tritium in VSMOW is so small that it is ignored for all but the most precise work.)

I tried really hard to come up diagrams to represent these ratios, but the amount of tritium is so small in comparison to the amount of hydrogen-1 and deuterium that it just disappeared every time.


The oxygen in water is also one of three isotopes, all of which are radioactively stable: oxygen-16 (eight protons, eight neutrons), oxygen-17 (eight protons, nine neutrons) and oxygen-18 (eight protons, ten neutrons). VSMOW contains one oxygen-17 atom for every 2632 atoms of oxygen-16, and one atom of oxygen-18 for every 498.7 atoms of oxygen-16.

My attempt at a diagram for the oxygen ratios was a bit more successful. If you enlarge the thumbnail below the blue square shows the amount of oxygen-18, and if you look really closely you can see a single green pixel in the bottom left-hand corner that represents oxygen-17.


Stop Putting Commas In Your Numbers

or Why you need to read Le Système international d’unités (8e édition)

How do you write very large or very small numbers? How, for example, would you write the speed of light out in full?

If you would write c = 299,792,458 m/s then please stop, because you’re doing it wrong. You can argue all you want about tradition, and “the way things have always been done” but you are still totally, absolutely, unequivocally wrong. There is a right way, an official, standardised way, to write very large and very small numbers, and it’s not with commas in them.

“Following the 9th CGPM (1948, Resolution 7) and the 22nd CGPM (2003, Resolution 10), for numbers with many digits the digits may be divided into groups of three by a thin space, in order to facilitate reading. Neither dots nor commas are inserted in the spaces between groups of three.”

The correct way to write the speed of light is c = 299 792 458 m/s. Ideally you’d use a special Unicode character, known as “NARROW NO-BREAK SPACE (U+202F)”, which stops text from wrapping around half-way through a number, but this isn’t very well supported, so the better-supported “THIN SPACE (U+2009)” or even just a normal space will do.

The reason for this is that the decimal point isn’t always a decimal point. Only 60% of countries use a full stop, whereas other countries use other marks. For example, a number that would traditionally be written in the UK as 123,456,789.01 would be written in France, Germany, Spain and many other countries as 123.456.789,01 and in Canada as either, depending on whether you’re working in English or French. This confusion (see this for example) was deemed undesirable and as such the scientific community declared in 2003 that:

The 22nd General Conference [of the BIPM],
considering that a principal purpose of the International System of Units is to enable values of quantities to be expressed in a manner that can be readily understood throughout the world …
reaffirms that “Numbers may be divided in groups of three in order to facilitate reading; neither dots nor commas are ever inserted in the spaces between groups”, as stated in Resolution 7 of the 9th CGPM, 1948.

Remember that thousand separators are also used when dealing with very small numbers. I’ve provided some examples below if you’re struggling to get your head around them.

Incorrect Correct Incorrect Correct
123 123 0.123 0.123
1234 1234 0.1234 0.1234
12,345 12 345 0.12345 0.123 45
123,456 123 456 0.123456 0.123 456
1,234,567 1 234 567 0.1234567 0.123 456 7
12,345,678 12 345 678 0.12345678 0.123 456 78

A-series paper

There are not many things in this world that I hate more than Letter Size paper.

Just look at it. Isn’t it horrible? Sitting there being based on outdated imperial units, looking all wonky and fat.

But instead of explaining in great detail why I hate Letter Size paper I’m going to explain why I love its main competitor: A4 size paper.

A4 is the fourth size in the metric International Standard (ISO 216) A-series of paper which runs from A0 (the largest) to A10 (the smallest). The A-series is constructed so that the longer side is 1.414 (√2) times the length of the shorter side, which makes each size in the series composed of two copies of the next-smallest size.

If x is the length of the shortest side then the area of an A-series sheet of paper is 1.414x2. Given that the first size in the series, A0, has an area of 1m2, that means that the short side of Ao is 841 millimetres and the long side 1189 mm. From this, the dimensions of all the remaining sizes in the series can be found.