# Why isn't a meter defined from a kilogram of water?

Why are there different official definitions for a kilogram and for a meter when a meter can be defined by the volume of a kilogram of water? For instance, using the triple point or some other state where the volume is well defined.

• Contrary to the comments so far, this is a very good question. We could have defined a kilogram as the standard mass of so-and-so many hydrogen atoms, and then the definition of the meter could have followed as the linear dimension of one cubic megagram of water at 4 degrees celsius. The density of water would have been 1.000 by definition. Instead, we have to determine the density of water by experiment, from the standard meter and the standard kilogram. So how close is it to 1.00 anyways? – Marty Green Nov 21 '15 at 15:15
• Except you'd have to worry about how much deuterium was in the water. That's a complication. – Marty Green Nov 21 '15 at 15:36

When we pick standards for units it's important to pick standards that are as percisely defined as possible and measureable to very high precision in the lab.

So for example the second is defined as 9192631770 times the period of the radiation emitted from a specific transition of the caesium atom. This is easily measured and indeed thousands of atomic clocks all around the world are currently measuring it. So if you're in a lab doing an experiment and you need a very precise measurement of time you can easily get one.

The metre is defined as the distance light moves one second divided by 299792458. The speed of light is a universal constant that is the same for every experimental scientist in the universe, and the speed of light is easily measured interferometrically. And as we saw in the previous paragraph the second is also well defined. That makes the metre a well defined and easily measured quantity as well.

The kilogram however is a bit of a thorn as it's currently defined as the weight of a specific lump of platinum. This isn't based on any constant of nature and it's not easy to measure precisely unless you can borrow the lump of platinum, which the International Bureau of Weights and Measures aren't particularly keen on.

So using the kilogram to define the metre would be ignoring a precise and convenient measure for a vague and inconvenient one. Worse still, the density of water is strongly temperature dependant so you also need a standard for temperature otherwise your value for the metre will depend on the weather. So now you're basing your metre on two vague and inconvenient standards.

There might be an argument for defining the kilogram from the metre i.e. the weight of 1 dm$^3$ of water at some reference temperature $T$. The trouble is you still have to measure the temperature and that can't be done to the required precision.

I believe there is a plan to define the kilogram using Planck's constant $h$. The units of $h$ are joule seconds or kilogram metres squared per second. Since we have good definitions for the metre and second this allows us to use $h$ to define the kilogram. However I don't know how far this plan has got.

There are various reasons why water isn't a good basis for length measurements.

In the long term, the most important is that water evaporates. To appreciate this, keep in mind that you can't just weigh out a kilogram of water and then somehow make a perfect cube container, then measure the sides. At the very least, dealing with the meniscus at the top would be a nightmare. What you need is a reference sample of fixed length, and liquid (or triple-point) water is, by its nature, not a fixed length. Even if you were to go for ice at a fixed temperature and pressure, ice sublimates, so the length would change over time. It's worth noting that even a platinum-iridium alloy, such as that used in the kilogram standard, appears to suffer some sort of mass loss over time. It's true that you might posit a hermitically sealed container for the water sample, but this has two strikes against it. Long-term hermitic seals are not a trivial business, and such a sealed container would make comparison measurements extremely different if not impossible.

• Water was used to define the kg for a few years. The idea of the OP was probably not to have an artefact made of water as a reference, but to define the kilogram as the mass of a dm³ of the substance called water (Vienna Standard Mean Ocean Water ?). Your objections are off topic – Frédéric Grosshans Nov 28 '15 at 15:33
• Although this answer isn't optimal, it is good. My question is about defining the kilogram as the mass of a dm³ of a substance, but if we define it this way, we would have to measure it somehow to compare it with other units, and that is the hard part that this answer answers. (At least that's my point of view. I'm new to this forum; I may be wrong.) – Nic Szerman Nov 29 '15 at 16:19