Newsletter #1

The basic units of measurement are length, mass and time. All physical quantities can be expressed in terms of these units. Velocity is length/time, acceleration is length/time squared and force is mass times length/time squared. Even such obscure quantities as electric charge and magnetic field strength can ultimately be expressed in terms of length, mass and time.

Standard lengths, masses and time intervals are essential for verification and communication of physical phenomena. Up to about the end of the 18^th century length and mass standards, the standards of commerce, were established locally, usually by the reigning sovereign.

The first system of international units was established in 1791 by the Paris Academy of Sciences. The length standard, the meter, was defined as one ten-millionth of the distance from the North Pole to the equator along a great circle passing through Paris (of course!). The mass standard, the kilogram, was defined as the mass of a particular platinum-iridium alloy cylinder. The time standard, the second, was defined as a specific fraction, one over the number of seconds in a day, of a mean solar day. A mean solar day is the average (over one year) length of a day as measured from high-noon (sun directly over head) to high noon. Length and time measurements are now tied to microwave (time) and light (length) radiation.

The length standard is related to an astronomical measurement of the dimensions of the earth. The time standard is related to an average length day. This mass standard, however, seems to be tied to nothing. A cylinder of a very stable material kept in a vault doesn't seem to fit with the other standards.

The size, amount of matter, in the standard mass is not arbitrary. The explanation of how this particular cylinder got to be the standard kilogram is a bit round about. It is somewhat like one of those James Burke stories Connections popular on PBS and the Discovery channel.

The mass of something is loosely defined as its "quantity of matter." The mass of an individual atom is the quantity of matter in the atom with nearly all the mass being contained within the nucleus, specifically the resident protons and neutrons. Remember, an atom of aluminum is the smallest quantity of aluminum that has the property of being aluminum.

The atomic masses in the periodic chart are based on carbon having 12 nuclear residents (6 protons and 6 neutrons). If 12 grams of carbon are allowed to react with 16 grams of oxygen to make carbon monoxide, all the carbon and oxygen combine with nothing left over. This means that there are the same number of atoms in 16 grams of oxygen as there are in 12 grams of carbon. The relative masses of carbon and oxygen are in the ration of 12 to 16. If carbon is atomic mass 12, then oxygen is atomic mass 16. This comparison scheme carried out over and over for all the elements provides the relative masses of the elements and was historically important in the arrangement known as the periodic chart of the elements. Now we have relative masses, but how do we get to kilograms?

A certain number of atoms of platinum (mass 195) and iridium (mass 192) make one kilogram (a kilogram is a thousand grams) and this certain number is traceable to pressure, volume and temperature measurements determining Avogadro's number which is the number of atoms of iridium in 192 grams of iridium.

Ultimately the kilogram is related to carbon having an atomic mass of 12 and the Avogadro's number, the number of carbon atoms in 12 grams of carbon.

Antoine Lavoisier, the French chemist and acknowledged proponent of modern chemistry with its reliance on accurate measurement, literally lost his head in the revolution (1794), purportedly in part because of his chastisement of his colleagues for their lack of measurement and the use of standards in their work. He, like his father, studied law early in his career but later turned to chemistry. His major contributions were in demolishing the notion of "phlogiston," a substance thought essential to combustion and the introduction of accurate measurement to chemistry.

His wife, Marie-Anne, who worked as Lavoisier's assistant, later married Count Rumford, another controversial physicist. In one of those interesting twists of history Marie-Ann was married to Lavoisier when he demolished the concept of "phlogiston," and to Count Rumford when he demolished the idea that heat was a substance called "caloric" that passes from one material to another as they are heated. Rumford discovered this while supervising the boring of cannons. Boring the cannons with a dull drill produced a seemingly inexhaustible supply of heat. Weapons research was popular even then!

Operationally, length and mass standards are available from scientific supply houses or national bureaus of standards (more expensive), or the International Bureau of Standards (even more expensive), still located in a Paris suburb. Time intervals are broadcast on several radio stations throughout the world.

There are three main systems of units plus a myriad of units peculiar to specific trades or fields. The fundamental system of units, and the one on which all the others are based, is the SI (Standard International) system. The SI system is based on the meter, kilogram and second as described above.

The cgs system (centimeter-gram-second) system was popular forty plus years ago and is still used in certain areas. Heat is often described in cgs terms. For example, a cube of water 1 cm on a side, called a cubic centimeter or cc for short, has mass of 1 gram. The calorie (the popular food calorie is 1000 of these real calories) is the amount of heat energy needed to raise 1 gram, or 1 cc, of water one Centigrade degree. A centrigrade degree is one-hundredth of the temperature range between the freezing and boiling points of water.

A cubic centimeter of water with mass of 1 gram provides a very convenient laboratory standard mass. One thousand cc of water has mass of 1000 grams or 1 kilogram.

The British system (foot-slug-second) is used for commerce in English speaking countries. The foot is a specified fraction of a meter and the slug is a specified fraction of the kilogram. These three systems are illustrated in the following table.

In very rough terms a meter stick is comparable in length to a yardstick and a kilogram has about the mass of a two-pound bag of coffee.

The really odd unit here is the slug, the British standard mass. This little oddity will be cleared up in next quarter's newsletter in the article on Weight and Mass.

If you have questions or comments on this article, or would like to suggest a future topic please let me know. My snail, e-mail, FAX, and telephone information is on my personal page accessible from the home page.