# Intro to Classical Arithmetic, Lesson 04. Weight Measure

by William C. Michael

You must complete the following assignments for this lesson:

- Study your Lesson.

- Complete your Memory Work.

- Complete the Lesson Exercises.

- Complete the Lesson Examination.

Lesson

Study the following lesson carefully, reading it aloud and making any notes that help you. You must know all of the content to pass your lesson examination.

We have learned that to measure any quantity, we must begin with some known quantity, which we call Unity. When we measure, we count how many times a unity or unit is contained in the quantity we wish to measure. We discussed how our everyday tasks do not usually need exact measurements — we can estimate — but in many cases exact measurements are needed. We learned that men have worked together to set these units so that all men everywhere can use the same units and share measurements. In the last lesson, we studied the units that men have established for measuring distance or length: the inch, the foot, the yard and the mile. In this lesson, we will learn the units established for measuring weight or the heaviness of an object.

UNITS OF WEIGHT MEASURE

We learned in measuring length or distance that Americans use a different system of units than other countries in the world — and the same is true in measuring weight. If you see the weight of items measured in milligrams, grams and kilograms, that is the Metric System. We will learn about the Metric System later in Arithmetic. Before the metric system was developed, there were three basic systems used for measuring weight. The weight of all goods sold in large quantities (seed, grain, fruits, vegetables, household supplies, etc..) were measured by Avoirdupois Weight, which is simply a French word meaning “goods of weight”. In English, we pronounce this ĂV-ur-du-POIZ and if correctly said, it rhymes with “gather the toys”. Troy Weight, was used for weighing precious metals like silver and gold, and the Apothecaries’ Weight, was used for weighing medicines. (We call apothecaries “pharmacists” today.). Troy Weight and Apothecaries’ Weight are no longer used.

When we measure with Avoirdupois Weight, we use four basic units: the grain, the ounce, the pound and the ton. The Avoirdupois system is based on the weight of a grain of dried barley. If we put seven-thousand barley grains into a pot, we would have one pound. If we divided the pound into sixteen parts, each of those parts would be one ounce. Thinking again of the grain, the ounce is equal to four-hundred, thirty-seven and one-half grains. If we had a weight of two-thousand pounds, that would equal one ton. So, in summary:

Avoirdupois Weights437 1/2 grains. equals 1 ounce7,000 grains or 16 ounces equals 1 pound2,000 pounds equals 1 ton.

In simpler terms, one ounce is equal to the weight of five quarters in money and is about the weight of one slice of white sandwich bread bought from the store. A can of soda weighs 12 ounces. Most canned foods weigh about one pound and 4 sticks of butter will also give you a pound. A gallon of milk weighs about 7 pounds. Two horses weigh about one ton and a normal American car weighs about two tons or four-thousand pounds. Remember these everyday weights because they will help you to quickly think of these units in the future.

We will often see these weights written in their shorter forms. The ounce is written as “oz.”, so 1oz. means “one ounce” and 12oz. means “twelve ounces”. The abbreviation “oz.” comes from the Italian word for ounce: onza.

The pound is written as “lb.” That looks strange — but not if you know Latin! The Latin word for pound is libra, and is the source of the shorter form used to write pound. The plural form of “lb” is “lbs.” Therefore, 1 lb. is “one pound” and 7 lbs. is “seven pounds”. Since the word ton is so small, no shorter form is used.

Now, you may look at the word ounce and ask, “Where in the world does that come from?” The answer is pretty confusing. In Rome, the libra (one pound) was equal to twelve unciae. This word unciae should be familiar to you. It’s the same Latin word from which the word inch comes. If you remember back to your last lesson, we learned that the word uncia means “one twelfth-part” and that there were twelve inches in a foot. Well, in Rome, there were twelve uncia in a pound. However, as time went on, units of measurement were changed and men continued to use the name “ounce” even though it wasn’t equal to the Roman uncia in weight. As we said, there are sixteen ounces in a pound, not twelve.

WEIGHTS & BALANCES

Throughout history, weights have been measured using a balance. As shown on the right, a balance consists of two pans hung from a balance beam. These balances were made of all different sizes — even enormous ones that could hold hundreds of pounds.

Measuring weight on a balance is pretty simple. If you wanted to buy 50 lbs. of grain, the seller would put 50 lbs. of weights (see below) in one of the pans. These known weights would serve as unity. Then, you would add grain to the other pan until the two pans balanced. That would prove that the weights and the grain were equal in measure.

If you wanted to measure the weight of an item, you would place the item in one pan and then add known weights in the other pan until they balanced. Then, you add up all the weights added and that would equal the weight of the item.

This leads us to a very important lesson in living a holy life. Wicked men in the ancient world would create false weights to cheat their customers out of money. If a customer wanted to buy 50 lbs. of grain, a seller might use a weight that said “50 lbs.”, while it only weighed 45 lbs. This would allow the seller to get more money for his grain. However, God warned men who did this that they would be punished for it:

“The voice of the Lord crieth to the city, “Hear O ye tribes, and who shall approve it” Shall I justify wicked balances, and the deceitful weights of the bag? By which her rich men were filled with iniquity, and the inhabitants thereof have spoken lies, and their tongue was deceitful in their mouth. And I therefore began to strike thee with desolation for thy sins. Thou shalt eat, but shalt not be filled: and thy humiliation shall be in the midst of thee: and thou shalt take hold, but shalt not save: and those whom thou shalt save, I will give up to the sword.”

God warns men that any kind of dishonesty by which we cheat other men will be punished. How do you know that when you buy a pound of sugar, it really weighs one pound? How do you know the store is not cheating you? It is because the government checks the weights and measures used by stores and if they are found to be false, the store will pay very great penalties. This keeps the sellers honest.

MODERN MEASURING TOOLS

Spring Scales

In addition to the ancient balance, weights are measured with spring scales. In a spring scale, the strength of a spring is used as unity, since the makers know how much weight is required to stretch the spring a certain distance. This strength is then shown in ounces and pounds on the face of the scale (see right). One simply places objects in the pan of the spring scale and reads the weight from the scale — the spring is inside. You may see a spring scale in the fruit and vegetable section of your grocery store. You may also find one in your bathroom, if your family’s scale uses a spring for weight and not electricity.

Electronic Scales

Computers allow us to measure weight without needing to balance weights or use springs. The computer is designed to know how much an ounce or a pound weighs and then measure how many ounces and pounds are contained in an object being weighed. Scientists use electronic balances like the one below. You simply place an object to be weighed on the metal plate and the scale measures the weight.

Electronic scales sometimes need to be adjusted to make sure the units are just right. To do this, one has to go back to old fashioned known weights. The user will place a 1 oz. weight on the scale and adjust the scale so that it reads exactly 1 oz.. This process of adjusting scales so that their units are accurate is known as Calibration. What we are really doing when we calibrate a scale is making sure unity is what it should be. After all, if we do not begin with a known quantity, we cannot measure at anything at all!

Large Scales

To measure tons, we need larger scales than those above. As your family is driving on a road trip, you will likely pass a Truck Weigh Station. At a weigh station, large trucks drive over a scale (right), which measures the weight of the truck in tons and pounds. It is also possible to place scales under each wheel of a car or truck and then add the weight measured by each scale to get the total weight of the vehicle.

SUMMARY

As we learned in Lesson 02, we cannot measure any quantity unless we find some known quantity to measure it with. The “known quantity” we use is called a “unit”, and we may use any quantity we wish as unity. However, so that men can measure more exactly and share their measurements with others, units of measurement have been established for all. For measuring length using the American system, these units include the inch, the foot, the yard and the mile. For measuring weight using the Avoirdupois system, these units include the ounce, the pound and the ton.

Remember that in addition to the Avoirdupois, Troy and Apothecaries’ systems, is the modern Metric System, which you will learn is much easier to use. We will learn about the Metric System later in Arithmetic.

Memory Work

Directions: The following questions help you to memorize the most important points of this lesson. Commit them perfectly to memory and have a parent or praeceptor quiz you to test your mastery before taking your lesson exam.

- (Review) What is Unity, or a Unit? Unity, or a Unit, is a known quantity we refer to as One.

- What is a Weight Measure? A Weight Measure is a measure used to measure the heaviness of an object.

- What are the four systems of weight measurement? The four systems used are the Avoirdupois system, Troy system, the Apothecaries’ system and the Metric system.

- Are all these systems used today?No. Only the Avoirdupois and Metric systems are used today.

- What are the four basic units of weight measure in the Avoirdupois system?In the Avoirdupois system, the four basic units of weight measure are the grain, the ounce, the pound and the ton.

- How great is the grain?The grain is the weight of a barley grain. It is not used in measuring, only as the known quantity by which the ounce and the pound are measured.

- How great is the pound and how is it written?The pound contains 7,000 grains. It is written “lb.” from the Latin word libra as in 100 lbs., that is one-hundred pounds.

- How great is the ounce and how is it written?The ounce is one sixteenth-part of a pound, which contains 16 ounces. It is written “oz.” from the Italian word onza as in 8 oz., that is eight ounces.

- How great is the ton and how is it written? The ton is 2,000 lbs. It has no short form.

- What is Calibration? Calibration is the process by which scales are adjusted to measure units accurately.