# Standard Units: why 'cgs' and 'mks' not 'mgs'?

It always annoyed me (albeit slightly - certainly not pit worthy) when at school and university that SI units were based on meters, kilograms and seconds. That Kg always got in the way - millimeters make sense, millikilograms don’t. Similarly in the cgs world a microcentimeter doesn’t quite cut it. Why not use meters, grams and seconds?

Because a kilogram is a more useful mass for ordinary, day-to-day measurements?

Much as in the English system, the basic weight is a pound and not an ounce.

OK, so the unit of mass that’s convenient is the thing that weighs about two pounds on Earth. But then the question just becomes, why is that called a kilogram? Why not give that unit the base name (I’ve heard grave was proposed for it), and call the thing the size of a small grape the “milligrave”, or whatever?

Personally, I favor using the meter-ton-second system. That way, none of your base units has a prefix on it, and you also get to keep the useful relationship that one cubic length-unit of water has a mass of one mass-unit.

I’l go out on a limb here and point out that the system was invented by the French, therefore neither efficiency nor internal logic was ever a consideration.

(If I ever used smilies, one would appear here.)

It must be me but I honestly have no idea what you are talking about. Of course millikilograms don’t make sense - they’re called milligrams or kilograms; similarly, there’s centimeters and micrometers. You can’t have two prefixes.

Now since this is on the dope and people here are generally smart I’m going to assume that the problem that the OP is getting at is is more profound, but if it is, it is so profound that I don’t see what it is - so will someone fight my ignorance and explain the OP to me?

The OP is pointing out that seconds, grams and meters are the base units. Kilograms and centimeters are derived units.

So it is a little strange (and I agree) that the convention is to use either cgs – two base units and one derived unit-- or mks – two base units and one derived unit-- rather than meter/gram/second, which would be the three base units.

Now the answer is that for the kinds of things we measure frequently, things of roughly gram mass are roughly centimeter in length, while things of roughly kilogram mass are roughly meter in length, so it’s more natural to measure in grams and centimeters or kilograms and meters; that way the order of magitudes of mass and length are about the same.

Which leads to the question of why the inventors of the metric system didn’t make the units of mass and length more similar. And I’m no historian of science, but I suspect they just didn’t realize at the time that it would be useful to do so.

Read the wikipedia article on the grave. All is explained.

a gram is a good base unit. in usage going up and down by 6 orders a magnitude covers most situations.

I think you misunderstand. You know that thing that weighs 2.2 lbs? He wants that to be called a gram. You know that thing that’s roughly a teaspoon of sugar? He wants that to be a milligram. That way, the base units would all work in one system, mgs.

It’s only nomenclature though. Coming from a country that (mostly) uses metric for domestic weights and measures, I think of e.g. a “centimetre” or a “kilo” as a unit all by itself. Doesn’t really matter what the word derivation is.

This seems unfair, considering how sensible the metric/SI system is compared to the system it replaced (in most of the world). Are you a “freedom fries” type of person?

Anyway, from the Wikipedia article provided by The Hamster King, the answer appears to be that the word ‘gram’ was felt to be too short - I guess base units need at least two syllables…

I’m not sure how you got that from the link.

According to wikipedia the inventors of the metric system quickly realized that the gram was too small for a base unit and switched to the kilogram, calling it the “grave”. Unfortunately, however, the word “grave” was too close to the German noble title “graf” and so in the revolutionary fervor of the time, “grave” never caught on. As a result even though the kilogram was the new base unit, it kept its old name.

On a second look I see that I misinterpreted this statement (the italics threw me off):

So I guess it was just history and politics that led to mks rather than mgs.

You can read an interesting account of the origins of the metric system amidst the turmoil of the French Revolution in “The Measure of All Things” by Ken Alder. It is mostly about the meter, which was originally defined as 1 ten millionth of the distance from the equator to the north pole along the meridian going through Paris. Thomas Jefferson was a big advocate of the metric system when they were discussing defining the meter in terms of the length of a pendulum with a period of one second. This made the definition something that could be measured in any laboratory (assuming you had a good clock), with corrections needed to account for latitude. Jefferson lost considerable interest when the definition depended on measurements that could only be made in France.

Not really just nomenclature. Derived units are defined as products and quotients of powers of base units. One force-unit, for instance, is the force needed to accelerate an object of 1 mass-unit by 1 length-unit per time-unit-squared. Thus in mks, you get the Newton, the force needed to accelerate an object of 1 kg by 1 m/s^2. In cgs, you have the dyne, the force needed to accelerate an object of 1 g by 1 cm/s^2. One Newton equals 100,000 dyne.

Thus the choice of base units cascades down to determine the theoretically derived units of your system.

Truth is that the gram is the rotten unit. And so is the liter. Think about it, you have a meter, and you should have a cubic meter of water be based as the unit of mass and a cubit meter be the unit of volume.

Of course, your basic unit of weight would be over a ton, and your basic unit of volume would be about 250 gallons. Too big? Make the damn meter smaller! Make it 1/10 the size, and your standard volume would be the liter and standard weight would be equal to a kilogram. If you’re going to create logical units, you might as well go all the way.

Getting back to the original question. The gram/centimeter/second scale was originally chosen because it was good at measuring things. Units based on the cgs system usually ended up being pretty rational sizes. The problem is that the gram and centimeter were not officially defined.

The real unit of measures that sit in Paris under special lock and key are the official meter stick and the official kilogram mass. Therefore, it simply makes more logical sense to define official measurements with official units of measure. Thus the SI system.

The problem with the SI system is that you end up with some really screwy measurements. Take the unit of pressure, pascals, which are measured as newtons per square meter. A newton is the unit of weight which is mass times acceleration, so a 1 kilogram mass at sea level weighs about 9.8 newtons. Spread a single newton (about 1/10 of a kilogram at sea level) over a square meter, and you have a single pascal.

So, regular atmospheric pressure is about 100,000 pascals. Fill up a bike tire, and you’re talking about putting in 200 to 600 kilopascals. So, the Pascal is impractically small. On the scale of impartially big is the Farad which is the unit of capacitance. I don’t think power plants have capacitors as big as a single farad.

Why is the kilogram mass sitting there in Paris and not the gram mass? After all, it is the gram that was officially defined as the mass of a cubic inch of pure water? Because it is a lousy way to define measurement of mass! What pressure shall this pure square centimeter of water be at? You can’t define pressure until you define mass, and you can’t define mass based upon the amount of water until you define pressure!

I say to hell with it, and let’s go with the Portzebie System of Weights and Measures. It makes about as much sense.

I’m really not understanding the question either. Which prefix you use for measurement is up to what you happen to be using at the time. It doesn’t really matter much though, because there is no case where you can go working without prefixes 75% of the time…you’re always going to have to factor in powers of ten somewhere.

I think the SI system is fine, because it has enough reference to the world around us (1 dm^2 of water == 1kg mass == 1 liter volume) to be useful in everyday life, but is regular enough to be used in science.

Anyway, there are plenty of conversions from SI units to common units, 1 bar = 100 kPa is a typical example. They come up wherever there is a use for them.

I think you missed the word “domestic” in my post.

While I agree with your post both in fact and in attitude, you’re a bit behind the times with the bit I quoted above.

See http://www.illinoiscapacitor.com/search/main/SuperCapDetails.asp?PARTNUMBERID=700022 for information on standard 400 Farad (not a typo) capacitors. They come in a can-style package 1-3/8" in diameter and 2.5" long. Again not a typo.

Švejk said:

Actually, a “millikilogram” is just a gram.