I have never been entirely pleased with the Metric System. The meter is the basic unit of length and provides the units of area and volume. Combined with water the liter, as the unit of volume, provides the unit of mass. A liter of water has a mass of one kilogram. The units operate as multiples of ten so that a kilogram, for example, is a thousand grams and a kilometer is a thousand meters.
But the meter is an arbitrary unit. That doesn't mean we can't use it but it would be more useful to have a natural unit that accomplished something. Examples of natural units are days, because that is how long it takes for the earth to rotate, and years, because that is how long it takes the earth to revolve around the sun. Divisions of time, such as hours, minutes and, seconds, are partially arbitrary but they are divisions of a natural unit.
Water does add a natural element to the Metric units of mass but the meter itself remains an arbitrary unit. A 360 degree circle is somewhat arbitrary but an angular degree is a convenient unit of angular distance and 360 is a round, easily divisible number. The Fahrenheit scale of temperature is entirely arbitrary. The Celsius and Kelvin scales have some naturalness as they are based on the freezing point of water and absolute zero. Latitude, based on the Equator and the poles, is natural but longitude, based on the Prime Meridian, is arbitrary.
There actually could be a natural unit of angular distance. Both the sun and moon have an angular diameter of about half a degree. The sun has an actual diameter about 400 times that of the moon but it is about 400 times as far away as the moon, so that the two appear as about the same size in the sky. We cannot be too precise about the angular diameters of the sun and moon, since the distances to both vary, but the two are very close to the same size in the sky at about half an angular degree.
What if we divided an angular degree in half? Then there would be 720 degrees in a circle, instead of 360. But this would be a very natural unit of measurement since both the sun and moon would then have an angular diameter of one degree.
We could make the measurement of time into more of a natural unit by measuring it in degrees of the earth's rotation. With a 360 degree circle, the earth rotates one degree every four minutes. If there was a 720 degree circle, it would be a degree every two minutes. This would make it more useful in dealing with space and such things as satellites and launches.
Coming up with a natural unit of linear measure is not as readily obvious. A meter was originally intended to be one-ten millionth of the distance from the north pole to the equator, although it has since been redefined in terms of wavelengths of light and this multiple of ten still wouldn't fit well with the 360 degree circle used with latitude and longitude. A mile was originally a natural unit based on a thousand paces, the left foot touching the ground a thousand times, of marching soldiers. The prefix "mil" means one-thousandth.
The Metric System was introduced during the French Revolution and Napoleon's enthusiasm for it is the reason we are using it. I have wondered what would have resulted if sailors had developed the Metric System.
There actually are two natural units of linear distance, both based on the earth. The circumference of the earth has long been important to navigation and now to satellites and radio communication. If we consider a circle as 360 degrees then this brings the possibility of a unit of length based on the earth's circumference. A degree is divided into 60 minutes. These are minutes of arc and are not the same thing as minutes of time, which are based on the rotation of the earth.
One minute of arc, on the circumference of the earth, is defined as a nautical mile and has long been used by sailors because it is a natural unit and is useful for determining position, based on latitude and longitude. A nautical mile is about 1.16 statue miles, which were commonly used on land before the Metric System became widespread. The U.S. still prefers miles.
A natural nautical mile cannot be too precisely defined simply because the earth is not a perfect sphere.
The other natural unit of linear distance involves the acceleration, due to gravity, of a falling object. The acceleration, due to gravity, of a weighty compact object, so that it has minimal air resistance, is 32 feet, or 4.74 meters, per second squared.
This means that the velocity of the falling object is 32 feet per second at the end of the first second and 64 feet per second at the end of the second second, and so on. Since the object starts with a velocity of zero and steadily increases to the 32 feet per second during the first second of fall, that means that the average velocity during the first second is 16 feet per second so that the object falls 16 feet during the first second.
The falling object starts the second second at 32 feet per second and finishes the second at 64 feet per second. That means it's average velocity during the second second is 48 feet per second so that it falls 48 feet during the second second.
Notice that 48 is 3 x 16. This reveals the pattern that the object, neglecting air resistance, falls 1 x 16 feet during the first second and 3 x 16 feet during the second second. Continuing with the math, it would fall 5 x 16 feet during the third second and 7 x 16 feet during the fourth second.
Thus we see that, if we are going to measure time in seconds which are a division of the rotation of the earth, 16 feet is an important distance with regard to gravity and this makes it a natural unit of linear measurement. The Metric System was developed during the French Revolution, before tall buildings and aircraft so that this was less of a factor. I have written about this before and refer to 16 feet as a grav, for gravity.
Now let's go back to the other natural unit of linear measurement, the nautical mile. Remember that there is no precise definition of a nautical mile, which is 1/60 of a degree of the earth's circumference, simply because the earth is not quite a perfect sphere. The British version of a nautical mile was called the Admiralty Mile, and was defined as 6,080 feet. This was very useful when used with the system of latitude and longitude.
Notice that 6,080 feet is evenly divisible by 16 feet. 380 x 16= 6,080. So why don't we make the 16 foot grav into our basic linear measurement and define 380 gravs as a grav mile? Unlike the arbitrary units of the Metric System or the obsolete definition of the statue mile, these are two natural units that accomplish something that is important to us. This is gravity and the circumference of the earth, which we use with our system of latitude and longitude. I think that this is as close as we are going to get to making the most out of natural units.
This has been added to the compound posting "Measurement", September 2021.
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