## Greek Lead Weights - History

**The ancient Olympic Games were initially a one-day event until 684 BC, when they were extended to three days. In the 5th century B.C., the Games were extended again to cover five days. The ancient Games included running, long jump, shot put, javelin, boxing, pankration and equestrian events.**

##### Pentathlon

The Pentathlon became an Olympic sport with the addition of wrestling in 708 B.C., and included the following:

##### Running / Jumping / Discus Throw

Running contests included:

the stade race, which was the pre-eminent test of speed, covering the Olympia track from one end to the other (200m foot race),

the diaulos (two stades - 400m foot race),

dolichos (ranging between 7 and 24 stades).

##### Jumping

Athletes used stone or lead weights called halteres to increase the distance of a jump. They held onto the weights until the end of their flight, and then jettisoned them backwards.

##### Discus throw

The discus was originally made of stone and later of iron, lead or bronze. The technique was very similar to today's freestyle discus throw.

##### Wrestling

This was highly valued as a form of military exercise without weapons. It ended only when one of the contestants admitted defeat.

##### Boxing

Boxers wrapped straps (himantes) around their hands to strengthen their wrists and steady their fingers. Initially, these straps were soft but, as time progressed, boxers started using hard leather straps, often causing disfigurement of their opponent's face.

##### Pankration

This was a primitive form of martial art combining wrestling and boxing, and was considered to be one of the toughest sports. Greeks believed that it was founded by Theseus when he defeated the fierce Minotaur in the labyrinth.

##### Equestrian events

These included horse races and chariot races and took place in the Hippodrome, a wide, flat, open space.

## Greek Lead Weights - History

Archimedes, A Gold Thief and Buoyancy

This is an electronic reprint and expansion of an article that appeared in SOURCES (July/Aug. 1993, p. 27-30). This material is copyrighted and all rights retained by the author. This article is made available as a service to the diving community by the author and may be distributed for any non-commercial or Not-For-Profit use.

** All rights reserved.**

Once upon a time (the 3 rd century B.C.) there was a very wealthy king. Like most kings, Hiero of Syracuse (on the island of modern day Sicily) wore a crown as a symbol of his authority. Over the years, Hiero was made aware that his Royal Goldsmith (who made his crown from Hiero's treasury) was living a lifestyle that was beyond his means. Hiero suspected that the Royal Goldsmith was using royal gold, intended for the royal crown, to augment his personal wealth. The goldsmith was rumored to be preparing the crowns with a cheaper alloy (using a silver-gold mix) than pure gold. No one using 3 rd century B.C. technology knew how to prove or disprove the speculation that the Royal Goldsmith was "stealing from the crown."

The problem of determining the gold content of the royal crown was given to Archimedes, a noted Greek mathematician and natural philosopher. Needles to say, this was not a trivial problem! Archimedes knew that silver was less dense than gold, but did not know any way of determining the relative the density (mass/volume) of an irregularly shaped crown, The weight could be determined using a balance or scale, but the only way known to determine volume, using the geometry of the day, was to beat the crown into a solid sphere or cube. Since Hiero had specified that damage to the crown would be viewed with less than enthusiasm, Archimedes did not wish to risk the king's wrath by pounding the crown into a cube and hoping that post-analysis it could be made all better again.

While in the public baths, Archimedes observed that the level of water rose in the tub when he entered the bath. He realized this was the solution to his problem and supposedly, in his excitement, he leaped up and ran naked through the streets back to his laboratory screaming "Eureka, Eureka!" (I've got it!).

Later, he demonstrated to Hiero and his court how the amount of water overflowing a tub could be used to measure a volume. His calculations indicated the goldsmith was, indeed, an embezzler. History does not record the fate of the unscrupulous artisan.

Archimedes observation has been formalized into Archimedes Principle:

"An object partially or wholly immersed in a fluid, is buoyed up by a force equal to the weight of the fluid displaced by the object."

Translation: objects more dense than water (like lead) will sink objects less dense than water (like cork) will float objects of the same density will remain at the same level (hover) and neither sink nor float. Objects that sink are frequently termed negatively buoyant. Objects that float are termed positively buoyant. Objects that stay stationary at depth are said to be neutrally buoyant.

Buoyancy is easiest understood by the application of "force arrow" principles or vectors. Vectors are mathematical constructs that have magnitude (like mass) and direction (towards or away from the surface). Weight is a downward force (gravity acting on mass) buoyancy is an upward force. If these two forces are balanced, then so-called neutral buoyancy (object hovers) is achieved. If they are not balanced, the object immersed will either sink (weight greater than upward buoyant force) or float (weight less than upward buoyant force).

NOTE: As with weight and mass, divers commonly are imprecise in the use of the term buoyancy. Rigorously, buoyancy is defined as ONLY an upward force directed against the force of weight. Although commonly used in the diving community, the terms "neutrally buoyant" and "negatively buoyant" are rigorously improper the term "positively buoyant" is redundant. Buoyancy is much easier to understand if one only considers balancing an upward force (buoyancy) and a downward force (weight). In this scheme, there is no positive or negative. We will use the term "hover" to refer to the so-called "neutrally buoyant" state. Thus, an object will float, hover or sink. If weight is greater than buoyancy, the object sinks. If buoyancy is greater than weight, the object rises. If weight and buoyancy are identical, then the object hovers ("is weightless")

EXAMPLE: When a helicopter "hovers." (Remains stationary and neither rises or sinks) the helicopter has exactly balanced the downward force of weight with the upward force of lift supplied by the turning rotor. A diver "hovers" by balancing the downward force of weight with the upward force of buoyancy.

For the diver, the force of buoyancy (yellow arrow, below) ALWAYS acts to move the diver (immersed object) towards the surface. Weight (red arrow, below) ALWAYS acts to move the diver (immersed object) towards the bottom. These forces are either balanced (identical) or unbalanced. If they are NOT balanced (the ideal "hovering" or weightless condition), then the diver MUST expend energy to maintain a horizontal steady state.

**Buoyancy Largest = Ascend**

**Forces Balanced = Hover**

Most buoyancy issues (either solving buoyancy physics problems or in-water diving) can be understood by simply determining the relationship between forces acting either up or down.

Buoyancy-type problems involve three factors: the weight of the object being submerged, the volume of the object submerged, and the density of the liquid involved in the problem. Any two of these factors can be used to determine the third. Let's study some representative numeric examples.

**ENGLISH EXAMPLE** : What is the buoyancy in seawater of a piece of wood that weighs 2000 pounds & measures 6 ft x 2 ft x 3 ft?

**ANSWER:** Determine forces involved:

a. The weight of wood = 2000 pounds

b. The volume of wood = 6 ft x 2 ft x 3 ft = 36 ft 3

c. The corresponding weight of an equal volume of seawater

36 ft 3 x 64 lb / ft 3 = 2304 lb

At this point, we know that the wood object weighs less than the corresponding volume of water (the volume of seawater that would be displaced if the entire object were to be submerged), thus it will float.

The object will float with a buoyant force of 304 pounds. In order to sink the object, the object would have to weigh more than an additional 304 pounds (without changing volume.) This is the amount of "push" you would have to exert on this log for it to sink. Although the object is buoyant (i.e., there is a net force of 304 pounds pushing up on this log), it will not be completely out of the water. The density of the log can then be used to determine how much of the log will be submerged.

Since this log is less dense than seawater, it will float. The amount of the volume that is submerged will be determined by the ratio of the density of the log and the density of the seawater. In general:

Ratio: Volume Submerged = Density Object / Density Liquid

Substituting the value of this log & seawater:

So, about 87% of the log's volume will be submerged.

**ENGLISH EXAMPLE:** A fully suited diver weighs 200 pounds. This diver displaces a volume of 3.0 cubic feet of seawater. Will the diver float or sink?

**ANSWER:** Determine forces involved:

a. weight of equal volume of seawater:

3.0 ft 3 x 64 lb / ft 3 . = 192 lb.

The diver will sink. This diver weighs 8 pounds in the water and is severely over-weighted. Removal of eight pounds will allow the diver to hover (which means the diver will have to do less work while diving see the trim discussion.) Since the object of recreational diving is to enjoy the environment, less work translates into more bottom time and more fun!

**ENGLISH EXAMPLE** : A fully geared diver in a wet suit weighs 210 pounds. In fresh water, this diver with a scuba cylinder containing 500 psig needs 18 pounds of lead to hover. How much lead will this diver need when diving in a wet suit in seawater?

**ANSWER:** Using Force Arrows:

To hover, the volume of water displaced by the diver must exert a buoyant force upward equal the total weight of the diver plus gear (downward force). This is the buoyant force exerted by a volume of fresh water (density = 62.4 lb./cubic foot) that weighs 228 pounds.

Determine Volume of diver:

Now that we know the volume of the diver, we can determine (with the assumption the volume of the weight belt is negligible) the buoyant force from the seawater (density 64 lb./ cubic foot) the diver would displace:

3.65 ft 3 x 64 lb / ft 3 = 233.6 lb.

So, the diver that was comfortable with eighteen pounds of lead on the weight belt in fresh water must add 6 more pounds (for a total of 24 lb.) on the weight belt to dive in seawater.

**ENGLISH EXAMPLE** : A fully geared diver in a wet suit weighs 210 pounds. In seawater, this diver needs 18 pounds of lead to hover. How much lead will this diver need when diving in a wet suit in fresh water?

**ANSWER:** Using Force Arrows:

To hover, the volume of water displaced by the diver must exert an upward buoyant force equal the total weight of the diver plus gear (downward force). This is the upward buoyant force exerted by the displaced volume of seawater (density = 64 lb./cubic foot) that weighs 228 pounds.

Determine Volume of diver: (Divers use weight and mass as equivalent terms)

Now that we know the volume of the diver, we can determine the upward buoyant force from fresh water (density 62.4 lb./ cubic foot) the diver would displace:

3.56 ft 3 x 62.4 lb / ft 3 = 222.1 lb.

So, the diver that was comfortable with eighteen pounds of lead on the weight belt in seawater must remove 6 pounds (for a total of 12 lb.) from the weight belt to dive in fresh water. The difference in density between fresh and seawater is the reason why different amounts of weight must be used when diving in different environments. When moving from fresh to seawater (with the same equipment configuration), divers must add weight. When moving from seawater to less dense fresh water, divers should remove weight.

**METRIC EXAMPLE** : A log weighing 6000 kg measures 1 m x 3 m x 2 m. Will this object sink or float in seawater (density = 1.0256 kg/l)?

**ANSWER:** Determine volume of object:

Volume = 1 m x 3 m x 2 m = 6 m 3

Convert cubic meters to liters:

Determine weight of the displaced water:

6,000 l x 1.0256 kg/ l = 6,154 kg

Now we know that this object will float

**METRIC EXAMPLE:** How much of the log will be submerged?

**ANSWER** : Determine density of object:

The amount that will be submerged is the ratio of densities:

So, about 98% of this object will be submerged in seawater.

**METRIC EXAMPLE** : A wet suited diver weighs 74 kg with gear. The diver has a volume of 80 l. How much lead should the diver wear for diving in seawater (density = 1.026 kg/l)?

**ANSWER** : Determine weight of seawater displaced:

80 l x 1.026 kg / l = 82.1 kg

Since there is a resultant buoyant force of 8 kg, the diver will have to wear 8 kg to compensate.

Divers wearing wet or dry suits have an additional factor to consider. Within the wet suit are trapped bubbles of gas a dry suit diver has air spaces between the diver and the suit. This gas (in fact, all air spaces) is subject to changes in volume as a result of changes in pressure (See Boyle's Law). This means that as the diver moves up or down in the water column, the volume of these gas spaces changes. This change in gas volume affects the diver's buoyancy. As a diver descends, the volume of the gas decreases. Thus, less water is displaced. The diver is less buoyant and sinks. On ascent, the pressure on the diver decreases. The gas expands and occupies a larger volume. This displaces more water and increases the buoyant (upward) force.

Archimedes principle points out that if we are not hovering, we MUST be either floating (moving up) or sinking. So, unless our buoyancy and weight are equal, we must expend energy to hover in the water column. However, if the buoyant force exactly matches the downward force contributed by the weight of the object submerged, then a "weightless" state is achieved. This is why NASA uses underwater training for its astronauts. By finely tuning the buoyancy of a space-suited astronaut underwater, the weightless environment of space can be simulated. This allows astronauts the opportunity to practice (using the philosophy that "Perfect Practice and Prior Planning Precedes Perfect Performance!) their mission on earth to insure success in space.

### LIFTING

The lift associated with air spaces can be used to raise objects from the bottom. Since air weighs very little compared to the weight of the displaced water, it can be assumed that the lifting capacity is equal to the weight of the volume of water that is displaced by the air volume of the lifting device.

**ENGLISH EXAMPLE** : You wish to lift a 300-pound anchor from the bottom of a lake bed. The bottom is hard and flat (so no excess lift will be needed to overcome the suction associated with being immersed in the bottom muck). You have access to 55 gal drums (weighing 20 pounds each) that have been fitted with over-expansion vents. How many 55 gal drums will it take to lift the anchor?

**ANSWER:** Determine forces involved:

a. Determine weight of water displaced:

Lake implies fresh water: density = 62.4 lbs/ft 3

Since the object to be lifted weighs less than the 440-pound lifting capacity of a 55 gal drum, a single 55 gallon drum should be sufficient to lift the 300 pound anchor. In practice, large lifting objects (like a 55 gal drum) have a large surface area and will generate considerable drag (which decreases lifting capacity). Without getting mathematically rigorous and calculating drag coefficients, a safe rule of thumb is to assume about 0.75 of the calculated lifting capacity for the lifting device in an actual lifting operation.

**PROBLEM** : Which weighs more underwater: a pound of lead or a pound of concrete?

**ANSWER:** Although both weigh the same on the surface, lead will weigh more while totally submerged. Rationale: Lead is more dense than concrete, thus an equal weight will displace less volume of water. Lead will therefore have less buoyancy counteracting its weight and thus its underwater weight will be greater.

As a diver moves in the water column, the diver is subject to a number of forces. In the vertical plane, gravity (weight) tends to make the diver descend and buoyancy (from too little weight or too much air in the b.c.d.) makes the diver ascend. In the horizontal plane, the diver moves forward propelled by the force of the kick. The thrust, or forward motion, must overcome drag (or friction) that the diver and equipment present to the water. A good diver tries to adjust diving style to balance the forces involved.

Part of the unique exhilaration of diving is the ability to glide, weightless, under the surface of the water. It is the most efficient and enjoyable way to dive. If the diver is over weighted (a too common occurrence), then s/he must continually expend energy to overcome gravity and remain at constant depth. If the diver is under weighted, s/he must also continually expend energy in an attempt to overcome buoyancy with leg power. (In battles with the forces of buoyancy and weight, these forces always overcome leg power and fatigue is certain.) The way to maximize efficiency (decrease work load and thus increase enjoyment) in the water is to balance weight and buoyancy so that the thrust from the fins can be directed towards forward movement, not towards overcoming buoyancy errors.

Assuming a horizontal position in the water can reduce drag. The more horizontal the diver, the less drag (resistance to movement caused by friction between the diver and the dense water environment) will occur and the easier underwater swimming will be! In general, cutting the cross-sectional area by a factor of two requires four times less energy to go the same distance. A more horizontal position presents a smaller area to the path of movement and thus lessens resistance.

Understanding the interaction of the forces of weight and buoyancy will help a diver achieve weightless diving. The concepts associated with buoyancy control are a superb example of the Easy Diver's principle of "Dive with your brains, not your back!"

Portions of this article were used in my chapter on Dive Physics appearing in:

Bove and Davis' Diving Medicine (4 th Edition), published by Saunders (Elsevier)

Larry "Harris" Taylor, Ph.D. is a biochemist and Diving Safety Coordinator at the University of Michigan. He has authored more than 100 scuba related articles. His personal dive library (See Alert Diver, Mar/Apr, 1997, p. 54) is considered one of the best recreational sources of information In North America.

Copyright 2001-2020 by Larry "Harris" Taylor

Use of these articles for personal or organizational profit is specifically denied.

## Leaders

The United States and Europe have dominated the men’s Olympic long jump throughout modern history 5. The most well-known of the American long jumpers included Jesse Owens, who took the gold in Berlin in 1936. At the Los Angeles Olympics in 1984, Carl Lewis burst onto the Olympic scene, taking the gold in the long jump 35. He held the gold in the long jump for the next three Olympics, in 1988, 1992 and 1996. The Soviet Union and East Germany were the top countries in the women’s long jump Olympic events until Jackie Joyner-Kersee took the gold in 1988 5.

## Greek Lead Weights - History

Greek Numbers and Arithmetic

The earliest numerical notation used by the Greeks was the Attic system. It employed the vertical stroke for a one, and symbols for ``5", ``10", ``100", ``1000", and ``10,000". Though there was some steamlining of its use, these symbols were used in a similar way to the Egyptian system, being that symbols were used repeatedly as needed and the system was non positional. By the Alexandrian Age, the Greek Attic system of enumeration was being replaced by the Ionian or alphabetic numerals. This is the system we discuss.

The (Ionian) Greek system of enumeration was a little more sophisticated than the Egyptian though it was non-positional. Like the Attic and Egyptian systems it was also decimal. Its distinguishing feature is that it was alphabetical and required the use of more than 27 different symbols for numbers plus a couple of other symbols for meaning. This made the system somewhat cumbersome to use. However, calculation lends itself to a great deal of skill within almost any system, the Greek system being no exception.

Greek Enumeration

and

Basic Number Formation

First, we note that the number symbols were the same as the letters of the Greek alphabet.

where three additional characters, the (digamma), the (koppa), and the (sampi) are used. Hence,

Larger numbers were also available. The thousands, 1000 to 9000, were represented by placing and apostrophe ' before a unit. Thus

The letter *M* was used to represent numbers from 10,000 on up. Thus

Alternatively, depending on the history one reads

As should be evident this system does not allow very large numbers to be expressed. Archimedes extended the system in his book The Sand Reckoner where he computed the number of grains of sand to fill the universe (of Aristarchus).

The Greeks used fractions, as did earlier civilizations. Their notation, however, was ambiguous and context was crucial for the correct reading a fraction. A diacritical mark was placed after the denominator of the (unit) fraction. So,

but this latter example could also mean .

More complex fractions could be written as well, with context again being important. The numerator was written with an overbar, the denominator with the diacritical mark. Thus,

Numerous, similar, representations also have been used, with increasing sophistication with time. Indeed, Diophantus (who came along very late in Greek mathematics) uses a fractional form identical to ours but with the numerator and denominator in reversed positions.

The arithmetic operations are complex in that so many symbols are used. Multiplication was carried out using the distributive law. For example:

Remarkably, division was performed in essentially the same way as we do it today.

## Lead poisoning and the fall of Rome

How bad is lead for human health? The answer is not encouraging: The Centers for Disease Control and Prevention states flatly that no lead level is safe for children. As we've been reminded by the ongoing water crisis in Flint, Mich., lead can irreversibly harm brain development in children, causing learning disabilities, behavioral issues and other problems. At high levels, it can lead to kidney damage, seizures and even death.

But could lead poisoning bring down an entire empire? Some researchers have questioned whether it contributed to the fall of Rome.

Back in 1983, a Canadian research scientist, Jerome Nriagu, examined evidence of the diets of 30 Roman emperors and "usurpers" who reigned between 30 B.C. and 220 A.D. Nriagu concluded that 19 "had a predilection to the lead-tainted" food and wine popular then and probably suffered from lead poisoning, as well as a form of gout.

We're not talking about small amounts of lead. To sweeten their wines and other foods, the Romans would boil down grapes into a variety of syrups, all of which had one thing in common, according to Nriagu's article in the New England Journal of Medicine: They were simmered slowly in lead pots or lead-lined copper kettles.

When the recipes were tested in modern days, they produced syrups with lead concentrations of 240 to 1000 milligrams per liter. "One teaspoon (5ml) of such syrup would have been more than enough to cause chronic lead poisoning," Nriagu wrote.

Given the gluttonous habits of Roman aristocrats, it would be no surprise if they showed the impact of lead in their diets, Nriagu believed. Here's how he described "the dull-witted and absent-minded Claudius," whom he considered most likely to have suffered lead poisoning: "He had disturbed speech, weak limbs, an ungainly gait, tremor, fits of excessive and inappropriate laughter and unseemly anger, and he often slobbered." However, the researcher admitted that the cause of these maladies was "a matter of longstanding debate."

## The Talent of Money

In the New Testament, the term "talent" meant something very different than it does today. The talents Jesus Christ spoke of in the Parable of the Unforgiving Servant (Matthew 18:21-35) and the Parable of the Talents (Matthew 25:14-30) referred to the largest unit of currency at the time. For example, the ten thousand talents owed by the unforgiving servant would come to at least 204 metric tons of silver, reflecting an astronomical sum of 60 million denarii.

Thus, a talent represented a rather large sum of money. According to *New Nave's Topical Bible*, one who possessed five talents of gold or silver was a multimillionaire by today's standards. Some calculate the talent in the parables to be equivalent to 20 years of wages for the common worker. Other scholars estimate more conservatively, valuing the New Testament talent somewhere between $1,000 to $30,000 dollars today.

Needless to say (but let's say it anyway), knowing the actual meaning, weight, and value of a term like talent can help give context, deeper understanding, and better perspective when studying the Scriptures.

## 6) Honorius

Honorius was born on 9 September 384 AD and died on 15 August 423 AD. His reign was chaotic and unsystematic. Honorius was greatly influenced by the popes of Rome whose influence increased during his lifetime.

Honorius was extravagant and jealous. He alienated his most loyal subjects due to his envy and even had Stilicho, one of Rome’s most skillful and adept generals, hung because of this. His political weakness and subbornness led to the rise in power of the Goths, who became a significant threat to the Roman Empire.

## Who Invented the Arch?

**It is believed that the Sumerians invented the arch somewhere around 6000 B.C.** The Romans, however, receive much of the credit for perfecting the design.

Arches have been used in the architecture of ancient societies for thousands of years, so it is difficult to know exactly who invented arches. Sumerians receive the credit based on the appearance of arches in ancient aqueduct ruins. Romans figured out to reinforce the arch so that weight placed on it could be more evenly distributed. They reinforced the midsection by adding concrete, a Roman invention and that is primarily credited with the durability of Roman structures. The foundation of the arch is the keystone, which acts as the pivotal stone that distributes weight throughout the structure based on the pressure placed on top of it. Because the stones of an arch need to fit together tightly, concrete helped seal the seams between them. The Romans also figured out that repeating arches at regular intervals support the construction of large structures, such as the Colosseum of Rome. Romans also flattened the design of arches from those originally designed by earlier civilizations. They used Greek column design and spacing to calculate the ideal width of an arch to optimize weight distribution.

## Lead in Air

Lead in the air is regulated two ways under the Clean Air Act:

- As one of six common pollutants for which EPA has issued national ambient air quality standards (NAAQS), and
- As a toxic air pollutant (also called a hazardous air pollutant) for which industrial facility emissions are regulated.

Under the lead NAAQS, EPA limits how much lead there can be in the ambient (outdoor) air. EPA specifies requirements for the siting of monitoring stations to ensure compliance with the NAAQS. EPA also publishes guidelines for state, local and tribal permitting authorities to guide development of NAAQS state implementation plans (SIPs). In addition, EPA’s New Source Review permitting programs require any large new or modified stationary source to get a permit before it begins construction.

EPA also regulates lead as a toxic air pollutant by limiting the emissions that come from some industrial sources. The regulations that limit toxic air pollutant emissions are called National Emission Standards for Hazardous Air Pollutants, or NESHAPs. Two regulations that focus on limiting lead emissions are the NESHAPs for Primary Lead Smelting and Secondary Lead Smelting. Other NESHAPs control lead that is emitted along with other toxic air pollutants.