Units of Measure, Historical Progression• Historical Units, “pre-science” measurement

– Human, plants, and animals as standards

– No tape measure … so use what’s readily available

• Introduction of Metric System

– Eliminate inconsistencies, odd multiples, inconvenient units

– Towards a global system, international acceptance

• Deployment of “Universal” natural constants

– Speed of Light available to anybody, anywhere … including E.T.

• Combinations of units

– Area, Volume, Speed

Units of Measure• Mass

– Historical definitions & difficulties

– Mass versus Weight, Planetary influence

• Length

– Historical definitions & difficulties

– Modern Definition

• Time

– Historical Definitions & difficulties

– Modern definitions

• Combination Measurements

– Area and volume from lengths (2500 sqft home, 1 acre-foot)

– Density (grams/cm^3) from mass and volume

– Speed (miles/hour) from distance and time

Definition of Mass, “grains”

• First “standard”

• Easy access

• Consistent weight ?

• What variety to use?

• Inconveniently small

• Persists to this day

– Pharmacy

– Ammunition

• 7000 gr. ≡ 1 pound

Mass• “Grain” originated from a Barley grain (now defined as 64.8

milligrams), and still used in pharmacy ( 5 grains of Aspirin) and firearms (M-16 rifle bullet weighs 55 grains)

• “Carat” is a unit of mass still used for gems (equals 200 milligrams). The word is based on Greek keration (fruit of the carob). Carob seeds were once used as weights on scales due to a reputation for having uniform weight.

• “Avoirdupois pound” invented by London merchants in 1303 equals 7000 grains. 16 ounce/pound, 1 ounce = 28.3495 grams

• “Troy Pound” and “Troy Ounces” (12 per pound) still used in precious metals trade. One Troy Ounce = 31.1035 grams

• “Stone” is a unit of mass formerly used in parts of the United Kingdom. It is equal to 14 pounds avoirdupois, and 8 stone make a hundredweight in the Imperial system

• “Apothecary” or Pharmacy system of units, mostly phased out. Still used for shotgun shells. One dram= 3.888 grams

Grain used in pharmacy, but being phased out

• Standard dose for aspirin is 5 grains, 325mg

Which pound was it ?…• Avoirdupois Pound, from England

– 16 ounces per pound, still in use … mostly USA

– 1 pound ≡ 7,000 grains of Barley (originally)• Troy Pound, from Troyes in France

– 12 Troy ounces per Troy pound

– 1 Troy Pound ≡ 5,760 grains of Barley

– At least the grains were the same kind!• Tower Pound

– Tower Pound = 7200 grains of Wheat … not Barley

– 7200 grains of wheat ≈ 5400 grains of Barley

Mass was a mess!• >12 variations on the pound• Other units of measure add to confusion

– Drams, pennyweights, Stones, tons …

• International trade a problem

– A “pound” is not always the same

• Standardization difficult

– Same names for different metrics (ounce)

• A better method was needed ….

– And helped give rise to the “metric system”

Definitions of Time

• Arbitrary units

– Earth cycles reference

– 12 or 24 hour basis, but 24 is less confusing and avoids AM/PM notation

• Depends on location

– “Zulu” time = “GMT” Greenwich Mean Time based on one longitude.

– “UTC” = universal coord. Time, broadcast by NIST, used by “atomic” clocks.

Time … is also arbitrary• “Year” is defined as earth’s circumnavigation time around the sun, NOT

an integer multiple of any other measurement. All planets are different.

• “Day” defined by earth’s Rotation on its own axis. There are 365.25 days per year, leading to “leap years” every 4th year to keep seasons as they are.

• “Hour” was defined by the ancient Egyptians as either 1/12 of daytime or 1/12 of nighttime, hence both day and night hours varied with the seasons (must have been confusing), but the sum was always 24 hours per day.

• “Minutes” per hour multiple of 60 comes from the Babylonians who used factors of 60 in their counting system

• “Seconds” originally referred to Babylonian subdivision of a minute called the “second minute”, later simplified to the “second”… also a factor of 60

• “Leap Seconds” accommodate the Earth's rotation slowing down due to tidal action.. The length of a solar day increased from an exactly defined 86,400 seconds per day (60 sec/min*60min/hr*24hr/day=86,400sec/day) in 1820 to 86,400.002 seconds per day in 1999, The difference amounts to nearly one second per year (365 days * 0.002 sec/day = 0.73 sec) which is handled by inserting a leap second into reference clocks about once a year.

Early measurements a mess!• Length based on King’s foot

– What happens when we change Kings? (save the foot!)

– The King’s foot might change with age …

• Mass depends on bits of something natural

– Inconsistent by location, time, plant variety, humidity …

• Nonsensical multiples abound over time

– 4 quarts/gallon, 32 ounces/quart, barrels, cords …

– 12 inch/foot, 3 feet/yard, 5280 ft/mile, leagues, fathom …

– 7000 grains/pound, 14 pounds/stone

– 20 schillings per currency “pound”, reams of paper, …

• France attacked the problem

– Defined new measurements (no plants or people)

– Based values using powers of 10, became the “metric” system

Length

Where did the meter come from?

• Objective was to dispense with artifacts

• Use something “universal” to measure

• Why not the earth itself?

– Everybody has access

– Easy to understand

– Conceptually simple

– Reproducible result

Basis of Metric SystemNorth pole to equator ≡ 10^7 meters

Original Meter Definition• Early measurement systems were problematic, so a new

definition of length was desired NOT to be tied to human or animal-centric artifacts.

• In 1791, the French Academy of Sciences adopted a meridional definition to establish a universally accepted definition of the metre. The Bureau des Longitudes commissioned an expedition, from 1792 to 1799, to measure length of the meridian between Dunkerque and Barcelona. This portion of the meridian, which also passes through Paris, was to serve as the basis for the length of the quarter meridian, connecting the North Pole with the Equator.

• in 1793, France adopted provisional results from the expedition, but it was later determined that the first definition was short by 1/5 millimetre from miscalculation of flattening of Earth. The length of this quarter-circumference divided by 10,000,000 became the standard meter. This measurement was transferred to scribed lines on a metal bar kept in Paris.

Historical International Prototype Metre bar, made of an alloy of

platinum and iridium, which was the standard from 1889 to 1960

SI system of units• Employ a Decimal System, of powers of 10

– Defined kilometer, meter, centimeter, millimeter, nanometer

• Replacing feet, fathoms, knots, cubits, furlongs, etc.

• Volume defined as 1 liter = 10 x 10 x 10 cm = 1000cm^3

– Kilogram, gram, metric ton (1000 Kg)

• Replacing pounds, stones, grains, ounces, drams

• Related to water (1 liter = 1000 cm^3 = 1 kilogram)

– Second, millisecond, microsecond

• Preserved historical units, impractical to change all clocks

• Tied old units to more precise standards

Basic CGS metric schemePreceded SI / ISO system of units (cm vs meter)

1 cm^3 = 1 milliliter = 1 gram H2O

A thought experiment …

• Assume we establish radio & TV communication with intelligent life from another galaxy. After sharing pictures of our families and technical data, the questions begin.

• When asked “how tall are you”, the response of 6 feet 2 inches is met with an obvious question: “What is a foot?” Same issue with measurement in meters.

• Advice for our friends in the other world to come to Paris for a copy of meter bar is not too practical.

• A more universal solution is required ….

Light to the rescue!

• In 1893, the standard metre was first measured with an interferometer by Albert A. Michelson, the inventor of the device and an advocate of using wavelength of light as a standard of distance.

• By 1925, interferometry was in regular use by standards organizations, although the International metal bar Metre remained the primary standard until 1960.

• In 1960 the metre was redefined as equal to 1,650,763.73 wavelengths of the orange-red emission line of the krypton-86 atom in a vacuum. The original international prototype of the metre metal bar is still kept in Paris under the conditions specified in 1889.

“Universal” ISO dimensions

• The Meter was redefined again in 1983 as the path length traveled by light during a time of 1/(299,792,458) second. This fixes speed of light at exactly 299,792,458 meters per second. Definitions based on light are more precise and reproducible because properties of light are believed to be universally constant. … E.T. would agree.

• Length and time are related by the speed of light, a universal constant, so time can be similarly defined.

• The “Second” is currently defined as the duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium-133 atom. This definition eliminates any relationship to time variations of planetary motion.

Seven Basic SI Measurements

• Mass = Kilogram

• Length = Meter

• Time = Second

• Temperature = degrees Kelvin

• Quantity of matter = mole

• Energy Rate = Ampere

• Light Energy = Candela

Why are we still using inches?• Reluctance to Change

– Relearning, converting old values to new

• Economic Impact (a BIG deal)

– Cost to make the switch is significant

• Tools & tooling, lost inventory, packaging resizing, construction, etc.

– Marketing trend to reduce cost by giving less (cereal, candy bars)

• Metric units often larger (500 gram vs 1 pound, 1 liter is 1.06 quart)

– UK currency metrification in 1971

• Needed to change ALL cash registers, vending machines

• A gradual shift towards metric IS in progress

– Global economy drives standards

• Ford owns Volvo and Mazda, 2 standards more costly to maintain

• All wine now in 750 ml bottles (same as 1/5 gallon), sodas are 2 liters

• NASA crashed a mars landing due to metric/English mix-up

Chem 32A, Fall 2010

• Stop here for measurements

• Density is for week 4

Table 3-3, p. 75

Derived Units• Area is a 2-dimensional multiplication of lengths. An

acre was defined by length of one furlong (220 yards) and breadth of one chain (22 yards), or 4,840 square yards per acre. Square feet still common in US

• Volume a 3-Dimensional concept, based on (length)3 Early definitions were arbitrary (quart, gallon), “metric” system is based on 1 Liter = 1000 cm3

• Density is mass per unit volume. The initial metric system “CGS” (Centimeter, Gram, Second) used water defined as 1.0 gram per cubic centimeter. CGS evolved to MKS (Meter, Kilogram, Second), now called SI (System Internationale) or ISO (International Standards Organization) units system.

Density

• Water all around us, a useful reference

– Easy to obtain, purify, & measure

• Density is temperature sensitive

– Usually expand with rising temperature

– Water has a maximum density at 4oC

• Water at < 0oC forms ice, which floats

• Density defined as 1.0000 gm/cm^3 at 4oC

Ice and Water

Density• Mass/Volume defined by water

– Grams/cm^3 =1 (also defined as 1 milliliter)

– Kilograms/liter = 1 (1000x gm and ml)

– 1000 kilogram/meter^3 (1000 liter/meter^3)

• Density is important on a “water planet”

– Objects >1 gm/ml sink in water, <1 gm/ml float

– Ships float due to mass < water displacement

– Ice floats due to expansion <4oC

• If not, ice would sink … life on planet changes

Density TriangleMass=D*V, Density=M/V, Volume=M/D

Utility of Density• Does it Float in Water? … Density < 1.0

– water covers >70% earth surface

• 1.3 billion cubic kilometers of ice & water

– Density an important feature for ships

• Also works for balloons in air

• Does it Sink in water? … Density > 1.0

– Conventional material property

– Helps identify elements and compounds

• Is your gift of “gold” for real? (better be 19.3 gm/ml)

Density of Water

Density of material groups(water is 1000 kg/m^3)

Table 3-4, p. 82

Helium and/or Hot AirDensity difference provides the lift

Proposed new “cruise ship” dirigible

Dimensions  (feet): 165' H x 244' W x 647'  L

14  million cubic feet of helium hoist only two-thirds of the craft's  weight. The  aerodynamic body is driven by huge rear-ward  propellers, with enough lift to keep the aircraft

and its  400-ton payload aloft while cruising.

UNofficial dimensions• Ratio of igloo's circumference / diameter = Eskimo Pi

• Time between slipping on a peel and smacking the pavement = 1 bananosecond

• Time to sail 220 yards at 1 nautical mph = Knotfurlong

• 365.25 days drinking low calorie beer = 1 Lite year

• Half a large intestine = 1 semicolon

• 1,000,000 aches = 1 megahurtz

• Basic unit of laryngitis = 1 hoarsepower

• Shortest distance between two jokes = a straight line

• 1 million microphones = 1 megaphone

More UNofficial dimensions

• 2000 mockingbirds = two kilomockingbirds• 52 cards = 1 deckacard• 1000 grams of wet socks = 1 literhosen• 1 millionth of a fish = 1 microfiche• 1 trillion pins = 1 terrapin• 10 rations = 1 decaration• 100 rations = 1 C-Ration• 2 monograms = 1 diagram• 8 nickels = 2 paradigms

Last Slide

• Now to the experiment !

Problems with Artifact based Standards

• Only ONE “master” or “gold” standard (meter bar in Paris).• Copies made of master become “secondary” or “silver”

standards (sent to USA, England, Germany, etc.)• “Silver” standards (our National Secondary standards)

used to create “Reference standards” for science and industry, and “Working Standards” are made from those.

• Errors are cumulative as copies are made from copies, and defects propagate through the system. Consider a 10th generation Xerox copy … quality degradation obvious.

• Users must have access to the standards for calibration, risk of damage to the standard and measurement error.

• Complex schemes evolve, groups of objects whose average value is “the standard”, etc. Disk Drive example, NBS used 20 pieces of media to define a “gold average”.