8.8: Planning Firm Actions to Implement Strategies
- How and why do managers plan? Why are goals important in the planning process?
When managers create strategies, they are making plans for how their firm will compete in the marketplace and what actions the firm will have to undertake to compete. A plan is a decision to carry out a particular action to achieve a specific goal. A plan includes decisions about when and how actions should be accomplished and what resources will be required to complete the actions. Because planning is one of the basic functions of management, a good manager should have good goal-setting skills, technical knowledge about the tasks necessary to reach goals, time-management skills, and the organizational skills required to arrange company resources to be available to complete the planned tasks. Planning is a combination of deciding what needs to be done, figuring out how to do it, assigning roles to people and providing them the resources to complete their tasks, and overseeing the work to make sure it gets done correctly and in a timely manner.
Technology and Innovation: Amazon Puts Brick-and-Mortar Retailers on the Defensive
Amazon.com has become the place everyone buys from. It wasn’t always that way, though. In 1995, Jeff Bezos founded Amazon in the garage of his house as an online book-selling company. Even then, however, he had a bigger mission: he wanted Amazon to be "an everything store." In a little over two decades, Bezos achieved his vision by growing Amazon in almost every possible way. Amazon reaches across international borders, with 14 country-specific websites, and has expanded product offerings to include almost anything a shopper might be looking for. They have developed their own products, such as the Kindle reader and Echo/Alexa digital home assistant, and now, with the acquisition of Whole Foods grocery stores, Amazon operates physical “brick-and-mortar” stores. Amazon uses the expertise it has developed along the way to serve other online retailers by hosting its stores and also by offering other tech services.
Amazon’s online business model has transformed how people shop, which has impacted the retail industry. Malls and brick-and-mortar stores have struggled to match Amazon’s prices, selection, and convenience. Exhibit 8.8 shows the stock market’s reaction to retail’s struggles: Amazon’s share price has soared even as shares of stores such as Macy’s and Best Buy have lost value.
Exhibit 8.8 Share Price Comparison: Amazon, Best Buy, and Macy’s (Attribution: Copyright Rice University, OpenStax, under CC-BY 4.0 license)
How have traditional brick-and-mortar retailers adjusted their strategies and objectives in response to changing customer shopping habits? Clothing retailers such as Macy’s have had to adopt defensive strategies by lowering prices, reducing the number of locations, and expanding their own online sales capabilities. Big-box stores such as Best Buy, in an effort to sustain their business, have fought back against “showrooming,” the process that occurs when a customer visits a brick-and-mortar store to check out a product in person and then goes home to order it online. To combat this practice, big-box stores offer installation services and price-match the online retailers.
The transformation of the retail industry has hurt some stores, such as Macy’s, whose share price has declined as they shrink their operations to try to survive. Best Buy, on the other hand, is trying to adapt by choosing defensive actions that will maintain its operations. Best Buy has had some success in figuring out how to attract buyers in the era of online retail, and market investors have approved their actions, as shown in their share price increases. Will these retailers survive over the long term? It’s hard to say. Macy’s and JCPenney announced that they were closing stores, and Sears filed for bankruptcy in 2018. Analysts predicted the death of Best Buy for years and still think that over the long term, physical retail stores are going to have to become service providers to differentiate themselves from product retailers such as Amazon. For example, in 2002, Best Buy acquired Geek Squad, a computer repair company, to provide in-home computer repair services.
Critical Thinking Questions
- What PESTEL forces have contributed to the transformation of the retail industry?
- Amazon has entered into the brick-and-mortar store business with the acquisition of Whole Foods. Do you think this is a good move or a bad move for Amazon? Why?
- What strategic actions do you think a store like Macy’s can undertake to survive in the current retail industry?
Exhibit 8.9 Amazon’s aggressive strategy has forced retailers such as Macy’s to shutter some of their underperforming stores, like this one in downtown Miami. (Credit: Phillip Pessar/ Flickr/ Attribution 2.0 Generic (CC BY 2.0))
Goal Setting
To examine the planning process, we need to start by understanding what the planning is for. A goal is something that you are trying to accomplish, and any firm will have many items on its list of things to accomplish. Consider the situation of a Walmart store in a college town. When it’s time for students to arrive back to school in the fall, the store needs to be ready with all the products students need when they move in. The Walmart store manager will plan months in advance and use information learned from the previous year’s sales to decide what products to order and how many, and when to have extra staff in the store to efficiently check out increased numbers of shoppers. Note that because Walmart is a global firm, goals will likely be prescribed from a higher level and the store manager’s responsibility would be to functional strategy response.
The manager’s plans will take into account the lead time for ordering products to make sure that mini refrigerators and twin XL sheets arrive and can be stocked in the store in time for the back-to-school rush. Preparing for the back-to-school season may involve reducing prices on other items to get them out of the way to make room for all those small refrigerators, and hiring and training additional employees so that there will be enough associates to help students and their parents. The manager’s ultimate goal is to have a successful back-to-school sales season, but achieving that goal will involve completing tasks such as making product-selection decisions, meeting ordering deadlines, and setting intermediate goals for hiring and training additional employees.
Setting Good Goals: The SMART Framework
Good goals have a few common characteristics and Exhibit 8.10 presents a framework for creating good goals.
Exhibit 8.10 SMART Goals (Attribution: Copyright Rice University, OpenStax, under CC-BY 4.0 license)
The SMART framework can be applied to business or personal goals. A good goal should be specific, measurable, achievable, relevant, and time bound.
Say you want to do well in this class. You need to turn that into a specific goal, because “doing well” is a little vague. Make the goal more specific by stating that your goal is to get an A in this course. Is this goal measurable ? Well, yes: grades are good examples of performance measures. Is your goal achievable ? That’s something you have to think about yourself: Do you usually get good grades? Are you able to put in the time to study the course material? Is the goal relevant to the achievement of a larger objective such as graduating with a good overall grade point average? If so, then getting an A in this class would contribute to that larger goal. Will you have time to accomplish your goal? Class-grade goals are inherently time-bound because the class ends on a certain date. So it’s possible that getting an A in this class is an overall SMART goal. To achieve it, however, you have to set some shorter-term goals. For example, you should set a SMART goal for getting an A on the next exam.
The Planning Process
Exhibit 8.11 illustrates the planning cycle. It looks a lot like the strategy cycle shown in Exhibit 8.3 because they have a lot in common. In fact, the planning process is an integral part of the strategy cycle because developing objectives, creating strategies, and implementing firm-wide activities all require extensive planning.
The first step in planning is to set a goal to be accomplished. Making sure that the goal checks off all of the SMART criteria will help make the planning process easier and more likely to be successful, so be sure to spend some time developing a good goal.
Exhibit 8.11 The Planning Cycle (Attribution: Copyright Rice University, OpenStax, under CC-BY 4.0 license)
Once you’ve figured out your goal, the next step is to design the plan. “Designing the plan” involves several distinct activities, so let’s break it down into what needs to happen. Think of planning as a problem-solving exercise. A plan is a set of actions developed to accomplish a goal, and planning is essentially figuring out what those actions should be. The goal is the endpoint, and the plan answers the question, “How do we get there?”
When designing a plan, a manager may think of many ways to achieve a goal. He or she can have a group of employees brainstorm to come up with ideas. Not all of the potential ideas are likely to be feasible, however. Part of the manager’s task in designing a plan is to coordinate various ideas with a firm’s resources and capabilities and its time constraints (see Exhibit 8.12). When does the goal need to be accomplished? What other resources does the firm need to complete the project?
Exhibit 8.12 Planning Requires Coordination (Attribution: Copyright Rice University, OpenStax, under CC-BY 4.0 license)
Designing the plan becomes a puzzle of figuring out what is the best way to reach a goal with the resources the firm has or can reasonably get in the time available. There is no prescription for this, and the best way to learn how to plan is to practice. Fortunately, you probably have a pretty good amount of practice already because you’ve been planning in one form or another for a long time. You have planned study time, team practices, club events, and even meals. Strategic planning uses the same skills in a new context. Planning a product launch may sound complicated, but so is planning a wedding. The scale and scope of the things a manager must coordinate to reach company goals may be larger than what you are used to, but the specific skills are likely not new at all.
For example, let’s take a look at the challenge Tesla is facing.
Tesla has developed a mass-market car and has a line of about half a million customers waiting to buy one. Until now, Tesla has been more of a boutique car maker, manufacturing small numbers of cars that they are able to sell at high prices. The Model 3, however, has been specifically conceived as an affordable car that almost anyone can buy. The brand and reputation Tesla has built with its premium cars have generated a lot of enthusiasm and demand for this new model. So, Elon Musk, CEO of Tesla, is planning to make cars in larger numbers and more quickly than ever before.
What’s Tesla’s goal?
Manufacture cars at a rate of 500,000 per year to meet demand. Is this a SMART goal? Analysts around the world are arguing over this (is it achievable?), but it’s the goal that Tesla is focusing on, so Musk has to design a plan to reach that goal. What resources does Tesla need to reach this level of production? They developed a car that was easy to manufacture because they knew that they would want to build it in large numbers. Still, they need manufacturing facilities, parts, and production employees. To get these resources, they need money. Elon Musk is a spectacular fundraiser, but they need billions of dollars to develop manufacturing capabilities on this scale. So while Tesla builds the world’s largest factory in Nevada, called the Gigafactory, Musk continues to raise funds.
Components (specifically the batteries) are also an issue for the Model 3, and Musk has built his giant factory in part to manufacture the hundreds of thousands of batteries needed to power the Model 3. Tesla’s planning involves many interrelated activities, and figuring out what the activities are, what resources Tesla needs to perform the activities, and how to obtain resources that they need but don’t have yet are the challenges Elon Musk is tackling. Tesla is a fascinating company that is multifaceted. Serious questions have been raised about their ability to produce enough cars, and an examination of more recent commentary is encouraged.
Implementing Plans for Different Levels of Firm Activity and Time Horizons
Developing plans happens simultaneously at multiple levels in any company. Plans, as in our earlier grade example, often require different steps to achieve a large-scale objective. If a firm decides on growth as a grand strategy, actions at every level of firm activity should contribute to firm growth, and managers at all of those levels should develop plans so that their part of the firm is working to implement the growth strategy. A grand strategy cascades throughout the company, becoming more and more specific until front-line employees are working on specific tasks that support the grand strategy.
Time is an important consideration when top managers develop company goals and the plans to achieve them. In general, firms have two timespans that they plan for: short term and long term. A short-term strategic plan is one that can be accomplished in a year or sooner. A long-term strategic plan is developed when an objective cannot be accomplished in less than a year. Companies generally have both scales of plans in place at any given time: short-term plans might involve quarterly sales goals, for example, but a firm might have a longer-term goal of establishing operations in another country or building a new facility. Tesla’s Gigafactory and Apple’s new headquarters at Apple Park in Cupertino, California, are both multiyear, multibillion-dollar projects, and so would be good examples of long-term plans. In Tesla’s case, the Gigafactory was initially planned many years ago when the company knew that it wanted to mass-produce cars at the scale required for the Model 3 (Tesla, 2017).
Scale Levels of Planning
Another dimension that impacts strategic planning is scale. We have already looked at some large-scale planning concepts, such as business-level and grand strategies. However, the day-to-day planning that managers do to take steps toward those bigger objectives is key to achieving success. Exhibit 8.13 shows the typical levels of planning going on in a company at any given time.
Exhibit 8.13 Levels of Strategic Planning (Attribution: Copyright Rice University, OpenStax, under CC-BY 4.0 license)
Note that if you compare Exhibit 8.13 to Exhibit 8.6, the “what” and “how” are switched. The switch is a scale switch. Vision and mission are both conceived at the broadest scale, and so even the “how” of the mission is a large-scale idea. In contrast, when managers are planning, the “how” of operational planning lays out precise actions and steps to follow to achieve a specific objective.
Let’s look at the levels one by one. Strategic planning is what we’ve been discussing so far. It’s the high-level planning performed by company executives to set the overall direction of the company. Grand strategies are part of strategic planning, as are business-level strategies such as cost leadership. Strategic planning connects the company’s actions back to its vision and mission statements (the “why does this company exist” question).
Tactical planning is mid-level planning that consists of broad ideas of what the company should do to pursue its mission. This is the sort of planning done by division managers. For example, Walmart division managers carry out the company’s growth and cost-leadership strategies by finding ways for the company to grow and continue to be able to offer low prices. They may decide where to locate distribution centers to maximize store-stocking efficiency, which manufacturers of goods they can buy inventory from at low prices, and where to build new stores to attract more customers.
Operational planning lays out the front-line activities that each employee in the company will do to advance the tactical plans. A McDonald’s restaurant manager develops operational plans, but you might recognize them more as employee schedules or promotional plans. Operational plans are the daily activities required for the company to function, including ordering inventory or supplies, scheduling workers and defining their work tasks, and developing sales goals and promotions to help achieve those goals. At McDonald’s, as at other companies that pursue a cost-leadership strategy, scheduling enough employees to work in the restaurant at specific times to keep the store functioning smoothly without scheduling more than you need (and incurring excess labor costs) is a critical task for the manager, and doing that task successfully is how the manager contributes to the company’s larger cost-leadership strategy.
Implementing Planned Strategies
Implementation of planned strategies refers to the execution of a strategy by assigning tasks for people to carry out to accomplish the company’s strategic goals. Although a manager may talk about “implementing a differentiation strategy,” the real implementation of a strategy happens at the bottom of not just the strategy hierarchy, but the organizational hierarchy, in the actions of operational employees who carry out planned tasks that add value to the company’s product. Such tasks include research and development to add unique features, monitoring manufacturing to ensure company products meet high-quality standards, and marketing the product to add brand value in the eyes of consumers.
- What are the three levels of planning, and what kinds of plans do managers develop at each level?
- Why is strategic implementation most commonly carried out at the operational level?


3.3: Unit 3 Summary
At the end of this unit, the learners will be conversant with Low-level programming, which is about machine and Assembly programming. It also looked at the language support offered.
Unit Assessment
The following section will test the learners understanding of this unit which is on low and high-level programming and its architecture
Instructions
Answer the following questions
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Differentiate between low-level and high-level programming
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Give 3 limitations of low-level architecture
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Explain machine code
- Grading Scheme
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The marks will be awarded as shown below
question sub-question marks awarded 1 Any difference award 2 mark maximum 4 8 2 any limitation listed award 2 mark, maximum 4 8 3 explanation (maximum marks 4) 4 Total 20
Feedback
1. A low-level programming language is a programming language that provides little or no abstraction from a computer’s instruction set architecture—commands or functions in the language map closely to processor instructions. it refers to either machine code or assembly language. while high-level programming languages are those closer to human languages and further from machine languages.
2. Very hard to read or learn for the uninitiated.
- Not very self-documenting like higher level languages.
- Harder to modify and maintain.
- Less support, than high level languages, in development and debug environments.
3. Is a set of instructions executed directly by a computer’s central processing unit (CPU). Each instruction performs a very specific task, such as a load, a jump, or an Arithmetic logic unit (ALU) operation on a unit of data in a CPU register or memory.


9.4: Complement, union, and intersection
First, it is often convenient to restrict the scope of the discussion.
a set that contains all objects currently under consideration
We will consider all of the following set operations to be performed within a universal set \(U\text{.}\) In particular, suppose \(A,B\subseteq U\text{.}\)
9.4.1: Universal and relative complement
the set of elements of \(U\) which are not in \(A\)
the complement of \(A\) (in \(U\)), so that
\begin{equation*} A^{C} = \{ x \in U \vert x \notin A \} \end{equation*}
if \(A,B \subseteq U\text{,}\) the complement of \(A\) in \(B\) is the set of elements of \(B\) which are not in \(A\)
the complement of \(A\) in \(B\text{,}\) so that
\begin{equation*} B \setminus A = \{ x \in B \vert x \notin A \} \end{equation*}
Another common notation for relative complement is \(B - A\text{.}\) However, this conflicts with the notation for the algebraic operation of subtraction in certain contexts, so we will prefer the notation \(B \setminus A\text{.}\)
- Suppose \(B = \{ 1, 2, 3, 4, 5, 6 \}\) and \(A = \{ 1, 3, 5 \}\text{.}\) Then \(B \setminus A = \{ 2, 4, 6 \}\text{.}\)
- The complement of the set of rational numbers \(\mathbb{Q}\) inside the set of real numbers \(\mathbb{R}\) is called the set of irrational numbers, and we write \(\mathbb{I} = \mathbb{R} \setminus \mathbb{Q} \) for this set. If you are thinking of real numbers in terms of their decimal expanions, the irrational numbers are precisely those that have nonterminating, nonrepeating decimal expansions.
9.4.2: Union, intersection, and disjoint sets
the combined collection of all elements in a pair of sets
the union of sets \(A\) and \(B\text{,}\) so that
\begin{equation*} A \cup B = \{ x\in U \vert x\in A \text{ or } x\in B \text{ (or both)}\} \end{equation*}
the collection of only those elements common to a pair of sets
the intersection of \(A\) and \(B\text{,}\) so that
\begin{equation*} A \cap B = \{x\in U \vert x\in A \text{ and } x\in B \} \end{equation*}
A union contains every element from both sets, so it contains both sets as subsets:
\begin{equation*} A, B \subseteq A \cup B \text{.} \end{equation*}
On the other hand, every element in an intersection is in both sets, so the intersection is a subset of both sets:
\begin{equation*} A \cap B \subseteq A, B \text{.} \end{equation*}
For subsets \(A = \{1,2,3,4\}\) and \(B = \{3,4,5,6\}\) of \(\mathbb{N}\text{,}\) we have
\begin{align*} A \cup B & = \{1,2,3,4,5,6\}, & A \cap B & = \{3,4\}. \end{align*}
Consider the following subsets of \(\mathbb{N}\text{.}\)
\begin{align*} \scr{E} & = \{ n\in\mathbb{N} \vert n\text{ even}\} & \scr{P} & = \{n\in\mathbb{N} \vert n\text{ prime, } n\mathbb{N}e 0\} \\ \scr{O} & = \{ n\in\mathbb{N} \vert n\text{ odd} \} & \scr{T} & = \{3n \vert n\in\mathbb{N} \} = \{ 0,\, 3,\, 6,\, 9,\, \ldots \} \end{align*}
Then,
\begin{align*} \scr{E} \cup\scr{O} & = \mathbb{N}, & \scr{E} \cap \scr{P} & = \{2\}, & \scr{E} \cap \scr{T} & = \{6n \vert n\in\mathbb{N} \}, \\ \scr{E} \cap \scr{O} & = \emptyset, & \scr{O} \cap \scr{P} & = \scr{P} \setminus \{2\}, & \scr{O} \cap \scr{T} & = \{6n+3 \vert n\in\mathbb{N}\}. \end{align*}
sets that have no elements in common, i.e. sets \(A,B\) such that \(A\cap B = \emptyset\)
a union \(A \cup B\) where \(A\) and \(B\) are disjoint
the disjoint union of sets \(A\) and \(B\)
Sets \(\scr{E},\scr{O}\) from Example \(\PageIndex{3}\) are disjoint, and \(\mathbb{N} = \scr{E} \sqcup \scr{O}\text{.}\)
If \(A \subseteq U\text{,}\) then we can express \(U\) as a disjoint union \(U = A \sqcup A^{C}\text{.}\) Similarly, if \(U = A \sqcup B\text{,}\) then we must have \(B = A^{C}\text{.}\)
9.4.3: Rules for set operations
Suppose \(A,B,C\) are subsets of a universal set \(U\text{.}\) Then the following set equalities hold.
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Properties of the universal set.
- \(\displaystyle A \cup U = U \)
- \(\displaystyle A \cap U = A \)
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Properties of the empty set.
- \(\displaystyle A \cup \emptyset = A \)
- \(\displaystyle A \cap \emptyset = \emptyset \)
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Duality of universal and empty sets.
- \(\displaystyle U^{C} = \emptyset \)
- \(\displaystyle \emptyset ^{C} = U \)
- \(\displaystyle (A^{C})^C = A \)
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Idempotence.
- \(\displaystyle A \cup A = A \)
- \(\displaystyle A \cap A = A \)
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Commutativity.
- \(\displaystyle A \cup B = B \cup A \)
- \(\displaystyle A \cap B = B \cap A \)
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Associativity.
- \(\displaystyle (A \cup B) \cup C = A \cup (B \cup C) \)
- \(\displaystyle (A \cap B) \cap C = A \cap (B \cap C) \)
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Distributivity.
- \(\displaystyle A \cap (B \cup C) = (A \cap B) \cup (A \cap C) \)
- \(\displaystyle A \cup (B \cap C) = (A \cup B) \cap (A \cup C) \)
- \(\displaystyle (A \cup B) \cap C = (A \cap C) \cup (B \cap C) \)
- \(\displaystyle (A \cap B) \cup C = (A \cup C) \cap (B \cup C) \)
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DeMorgan's Laws.
- \(\displaystyle (A \cup B)^C = A^{C} \cap B^C \)
- \(\displaystyle (A \cap B)^C = A^{C} \cup B^C \)
- Proof of Rule 9.a.
-
Recall that to prove this set equality, we need to show both
\begin{align*} (A \cup B)^C & \subseteq A^{C} \cap B^C \text{,} & A^{C} \cap B^C & \subseteq (A \cup B)^C \text{.} \end{align*}
Show \((A \cup B)^C \subseteq A^{C} \cap B^C\).
We need to show\begin{equation*} x \in (A \cup B)^C \Rightarrow x \in A^{C} \cap B^C \text{.} \end{equation*}
If \(x \in (A \cup B)^C\) then by definition of complement, \(x\in U\) but \(x \notin A \cup B\text{.}\) Then \(x \notin A\) must be true, since if \(x\) were in \(A\) then it would also be in \(A \cup B\text{.}\) Similarly, \(x \notin B\) must also be true. So \(x \in A^{C}\) and \(x\in B^C\text{;}\) i.e. \(x\in A^{C} \cap B^C\text{.}\)
Show \(A^{C} \cap B^C \subseteq (A \cup B)^C \). We need to show
\begin{equation*} x \in A^{C} \cap B^C \Rightarrow x \in (A \cup B)^C \text{.} \end{equation*}
If \(x \in A^{C} \cap B^C\) then by definition of intersection, both \(x \in A^{C}\) and \(x \in B^C\) are true.; i.e. \(x \notin A\) and \(x \notin B\text{.}\) Since \(A \cup B\) is all elements of \(U\) which are in one (or both) of \(A,B\text{,}\) we must have \(x \notin A \cup B\text{.}\) Thus \(x \in (A \cup B)^C\text{.}\)
- Proofs of the other rules.
-
These are left to you, the reader, in the Exercise 9.9.1 .
Compare the set operation rules of the proposition above with the Rules of Propositional Calculus.


2.3: Evaluating Expressions
In the Water Industry, we use many formulas to make calculations. As a result, we need to know how to evaluate expressions, that is, substitute known values for variables, and simplify the expression using the order of operations.
If \(x=4\) and \(y=3\) evaluate \(3xy^2+2\sqrt{x}\).
Solution
First, substitute the given values for \(x\) and \(y\):
\[3(4)(3)^2 + 2 \sqrt{4} \nonumber\]
Next, perform order of operations to simplify:
\[3\left(4\right){\left(3\right)}^2+2\sqrt{4}=3\left(4\right)\left(9\right)+2\left(2\right)=108+4=112 \nonumber\]
If \(a=9\ and\ b=7\), evaluate \(\frac{2\sqrt{a}+3}{b-5}\).
Solution
First, substitute the given values for a and b:
\( \frac{2\sqrt{9}+3}{7-5}\)
Next, simplify using order of operations:
\(\frac{2\cdot 3+3}{7-5}=\frac{6+3}{7-5}=\frac{9}{2}\)
Recall from Unit 1, we could convert this fraction to a decimal to obtain 4.5, however, the general rule of thumb is to use decimals only when you start with decimals, or the directions states to use decimals.
A water plant has a rectangular basin with a base that is in the shape of a square with sides of length x and the height of the basin is y. As a result, the volume is calculated using the following expression: \(x^2y\). If the length of the base of the basin is 50 feet and the height of the basin is 20 feet, calculate the volume of the basin.
Solution
First, we substitute the values for x and y: \(x^2y={\left(50\ feet\right)}^2\cdot \left(20\ feet\right)\)
Next, we simplify the expression using order of operations to obtain:
\[\left(2500\ ft^2\right)\left(20\ ft\right)=50,000\ ft^3\]
To estimate the extra water a town needs to store for emergencies, we must multiply the population by 45 gallons, then add 42,000 gallons to account for what the fire fighters would need in case of a fire, and then multiply the result by a safety factor of 1.8.
a. Write an expression for calculating the amount of extra water a town needs to store in case of an emergency.
b. Use the expression to calculate the amount of extra water a town needs to store in case of an emergency if the population of the town is 48,000.
Solution
a. We begin by converting the English to math:
Multiply the population, let’s call the population P, by 45 gallons: \(45P\)
Then add 42,000 gallons: \(45P+42,000\)
Then multiply by 1.8: \(1.8(45P+42,000)\)
Hence, the amount of extra water needed is \(1.8(45P+42,000)\)
b. If the population is 48,000, we will replace P in the above expression with 48,000 to obtain: \(1.8\left(45\cdot 48,000+42,000\right)=1.8\left(2,160,000+42,000\right)=1.8\left(2,202,000\right)=3,963,600\)
Hence, the town needs to reserve 3,963,600 gallons of water in case of an emergency.


3.6.10: THE THEOGONY
*Spellings have been updated to American English
(ll. 1-25) From the Heliconian Muses let us begin to sing, who hold the great and holy mount of Helicon, and dance on soft feet about the deep-blue spring and the altar of the almighty son of Cronos, and, when they have washed their tender bodies in Permessus or in the Horse’s Spring or Olmeius, make their fair, lovely dances upon highest Helicon and move with vigorous feet. Thence they arise and go abroad by night, veiled in thick mist, and utter their song with lovely voice, praising Zeus the aegis-holder and queenly Hera of Argos who walks on golden sandals and the daughter of Zeus the aegis-holder bright-eyed Athene, and Phoebus Apollo, and Artemis who delights in arrows, and Poseidon the earth-holder who shakes the earth, and reverend Themis and quick-glancing Aphrodite, and Hebe with the crown of gold, and fair Dione, Leto, Iapetus, and Cronos the crafty counselor, Eos and great Helius and bright Selene, Earth too, and great Oceanus, and dark Night, and the holy race of all the other deathless ones that are for ever. And one day they taught Hesiod glorious song while he was shepherding his lambs under holy Helicon, and this word first the goddesses said to me—the Muses of Olympus, daughters of Zeus who holds the aegis:
(ll. 26-28) ‘Shepherds of the wilderness, wretched things of shame, mere bellies, we know how to speak many false things as though they were true; but we know, when we will, to utter true things.’
(ll. 29-35) So said the ready-voiced daughters of great Zeus, and they plucked and gave me a rod, a shoot of sturdy laurel, a marvelous thing, and breathed into me a divine voice to celebrate things that shall be and things there were aforetime; and they bade me sing of the race of the blessed gods that are eternally, but ever to sing of themselves both first and last. But why all this about oak or stone?
(ll. 36-52) Come thou, let us begin with the Muses who gladden the great spirit of their father Zeus in Olympus with their songs, telling of things that are and that shall be and that were aforetime with consenting voice. Unwearying flows the sweet sound from their lips, and the house of their father Zeus the loud-thunderer is glad at the lily-like voice of the goddesses as it spread abroad, and the peaks of snowy Olympus resound, and the homes of the immortals. And they uttering their immortal voice, celebrate in song first of all the reverend race of the gods from the beginning, those whom Earth and wide Heaven begot, and the gods sprung of these, givers of good things. Then, next, the goddesses sing of Zeus, the father of gods and men, as they begin and end their strain, how much he is the most excellent among the gods and supreme in power. And again, they chant the race of men and strong giants, and gladden the heart of Zeus within Olympus,—the Olympian Muses, daughters of Zeus the aegis-holder.
(ll. 53-74) Them in Pieria did Mnemosyne (Memory), who reigns over the hills of Eleuther, bear of union with the father, the son of Cronos, a forgetting of ills and a rest from sorrow. For nine nights did wise Zeus lie with her, entering her holy bed remote from the immortals. And when a year was passed and the seasons came round as the months waned, and many days were accomplished, she bare nine daughters, all of one mind, whose hearts are set upon song and their spirit free from care, a little way from the topmost peak of snowy Olympus. There are their bright dancing-places and beautiful homes, and beside them the Graces and Himerus (Desire) live in delight. And they, uttering through their lips a lovely voice, sing the laws of all and the goodly ways of the immortals, uttering their lovely voice. Then went they to Olympus, delighting in their sweet voice, with heavenly song, and the dark earth resounded about them as they chanted, and a lovely sound rose up beneath their feet as they went to their father. And he was reigning in heaven, himself holding the lightning and glowing thunderbolt, when he had overcome by might his father Cronos; and he distributed fairly to the immortals their portions and declared their privileges.
(ll. 75-103) These things, then, the Muses sang who dwell on Olympus, nine daughters begotten by great Zeus, Cleio and Euterpe, Thaleia, Melpomene and Terpsichore, and Erato and Polyhymnia and Urania and Calliope, who is the chiefest of them all, for she attends on worshipful princes: whomsoever of heaven-nourished princes the daughters of great Zeus honor, and behold him at his birth, they pour sweet dew upon his tongue, and from his lips flow gracious words. All the people look towards him while he settles causes with true judgements: and he, speaking surely, would soon make wise end even of a great quarrel; for therefore are there princes wise in heart, because when the people are being misguided in their assembly, they set right the matter again with ease, persuading them with gentle words. And when he passes through a gathering, they greet him as a god with gentle reverence, and he is conspicuous amongst the assembled: such is the holy gift of the Muses to men. For it is through the Muses and far-shooting Apollo that there are singers and harpers upon the earth; but princes are of Zeus, and happy is he whom the Muses love: sweet flows speech from his mouth. For though a man have sorrow and grief in his newly-troubled soul and live in dread because his heart is distressed, yet, when a singer, the servant of the Muses, chants the glorious deeds of men of old and the blessed gods who inhabit Olympus, at once he forgets his heaviness and remembers not his sorrows at all; but the gifts of the goddesses soon turn him away from these.
(ll. 104-115) Hail, children of Zeus! Grant lovely song and celebrate the holy race of the deathless gods who are for ever, those that were born of Earth and starry Heaven and gloomy Night and them that briny Sea did rear. Tell how at the first gods and earth came to be, and rivers, and the boundless sea with its raging swell, and the gleaming stars, and the wide heaven above, and the gods who were born of them, givers of good things, and how they divided their wealth, and how they shared their honors amongst them, and also how at the first they took many-folded Olympus. These things declare to me from the beginning, ye Muses who dwell in the house of Olympus, and tell me which of them first came to be.
(ll. 116-138) Verily at the first Chaos came to be, but next wide-bosomed Earth, the ever-sure foundations of all the deathless ones who hold the peaks of snowy Olympus, and dim Tartarus in the depth of the wide-pathed Earth, and Eros (Love), fairest among the deathless gods, who unnerves the limbs and overcomes the mind and wise counsels of all gods and all men within them. From Chaos came forth Erebus and black Night; but of Night were born Aether and Day, whom she conceived and bare from union in love with Erebus. And Earth first bare starry Heaven, equal to herself, to cover her on every side, and to be an ever-sure abiding-place for the blessed gods. And she brought forth long Hills, graceful haunts of the goddess-Nymphs who dwell amongst the glens of the hills. She bare also the fruitless deep with his raging swell, Pontus, without sweet union of love. But afterwards she lay with Heaven and bare deep-swirling Oceanus, Coeus and Crius and Hyperion and Iapetus, Theia and Rhea, Themis and Mnemosyne and gold-crowned Phoebe and lovely Tethys. After them was born Cronos the wily, youngest and most terrible of her children, and he hated his lusty sire.
(ll. 139-146) And again, she bare the Cyclopes, overbearing in spirit, Brontes, and Steropes and stubborn-hearted Arges, who gave Zeus the thunder and made the thunderbolt: in all else they were like the gods, but one eye only was set in the midst of their fore-heads. And they were surnamed Cyclopes (Orb-eyed) because one orbed eye was set in their foreheads. Strength and might and craft were in their works.
(ll. 147-163) And again, three other sons were born of Earth and Heaven, great and doughty beyond telling, Cottus and Briareos and Gyes, presumptuous children. From their shoulders sprang an hundred arms, not to be approached, and each had fifty heads upon his shoulders on their strong limbs, and irresistible was the stubborn strength that was in their great forms. For of all the children that were born of Earth and Heaven, these were the most terrible, and they were hated by their own father from the first.
And he used to hide them all away in a secret place of Earth so soon as each was born, and would not suffer them to come up into the light: and Heaven rejoiced in his evil doing. But vast Earth groaned within, being straitened, and she made the element of gray flint and shaped a great sickle, and told her plan to her dear sons. And she spoke, cheering them, while she was vexed in her dear heart:
(ll. 164-166) ‘My children, gotten of a sinful father, if you will obey me, we should punish the vile outrage of your father; for he first thought of doing shameful things.’
(ll. 167-169) So she said; but fear seized them all, and none of them uttered a word. But great Cronos the wily took courage and answered his dear mother:
(ll. 170-172) ‘Mother, I will undertake to do this deed, for I reverence not our father of evil name, for he first thought of doing shameful things.’
(ll. 173-175) So he said: and vast Earth rejoiced greatly in spirit, and set and hid him in an ambush, and put in his hands a jagged sickle, and revealed to him the whole plot.
(ll. 176-206) And Heaven came, bringing on night and longing for love, and he lay about Earth spreading himself full upon her.
Then the son from his ambush stretched forth his left hand and in his right took the great long sickle with jagged teeth, and swiftly lopped off his own father’s members and cast them away to fall behind him.  And so soon as he had cut off the members with flint and cast them from the land into the surging sea, they were swept away over the main a long time: and a white foam spread around them from the immortal flesh, and in it there grew a maiden. First she drew near holy Cythera, and from there, afterwards, she came to sea-girt Cyprus, and came forth an awful and lovely goddess, and grass grew up about her beneath her shapely feet. Her gods and men call Aphrodite, and the foam-born goddess and rich-crowned Cytherea, because she grew amid the foam, and Cytherea because she reached Cythera, and Cyprogenes because she was born in billowy Cyprus, and Philommedes because sprang from the members. And with her went Eros, and comely Desire followed her at her birth at the first and as she went into the assembly of the gods. This honor she has from the beginning, and this is the portion allotted to her amongst men and undying gods,—the whisperings of maidens and smiles and deceits with sweet delight and love and graciousness.
(ll. 207-210) But these sons whom he begot himself great Heaven used to call Titans (Strainers) in reproach, for he said that they strained and did presumptuously a fearful deed, and that vengeance for it would come afterwards.
(ll. 211-225) And Night bare hateful Doom and black Fate and Death, and she bare Sleep and the tribe of Dreams. And again the goddess murky Night, though she lay with none, bare Blame and painful Woe, and the Hesperides who guard the rich, golden apples and the trees bearing fruit beyond glorious Ocean. Also she bare the Destinies and ruthless avenging Fates, Clotho and Lachesis and Atropos, who give men at their birth both evil and good to have, and they pursue the transgressions of men and of gods: and these goddesses never cease from their dread anger until they punish the sinner with a sore penalty. Also deadly Night bare Nemesis (Indignation) to afflict mortal men, and after her, Deceit and Friendship and hateful Age and hard-hearted Strife.
(ll. 226-232) But abhorred Strife bare painful Toil and Forgetfulness and Famine and tearful Sorrows, Fightings also, Battles, Murders, Manslaughters, Quarrels, Lying Words, Disputes, Lawlessness and Ruin, all of one nature, and Oath who most troubles men upon earth when anyone wilfully swears a false oath.
(ll. 233-239) And Sea begat Nereus, the eldest of his children, who is true and lies not: and men call him the Old Man because he is trusty and gentle and does not forget the laws of righteousness, but thinks just and kindly thoughts. And yet again he got great Thaumas and proud Phorcys, being mated with Earth, and fair-cheeked Ceto and Eurybia who has a heart of flint within her.
(ll. 240-264) And of Nereus and rich-haired Doris, daughter of Ocean the perfect river, were born children, passing lovely amongst goddesses, Ploto, Eucrante, Sao, and Amphitrite, and Eudora, and Thetis, Galene and Glauce, Cymothoe, Speo, Thoe and lovely Halie, and Pasithea, and Erato, and rosy-armed Eunice, and gracious Melite, and Eulimene, and Agaue, Doto, Proto, Pherusa, and Dynamene, and Nisaea, and Actaea, and Protomedea, Doris, Panopea, and comely Galatea, and lovely Hippothoe, and rosy-armed Hipponoe, and Cymodoce who with Cymatolege and Amphitrite easily calms the waves upon the misty sea and the blasts of raging winds, and Cymo, and Eione, and rich-crowned Alimede, and Glauconome, fond of laughter, and Pontoporea, Leagore, Euagore, and Laomedea, and Polynoe, and Autonoe, and Lysianassa, and Euarne, lovely of shape and without blemish of form, and Psamathe of charming figure and divine Menippe, Neso, Eupompe, Themisto, Pronoe, and Nemertes who has the nature of her deathless father. These fifty daughters sprang from blameless Nereus, skilled in excellent crafts.
(ll. 265-269) And Thaumas wedded Electra the daughter of deep-flowing Ocean, and she bare him swift Iris and the long-haired Harpies, Aello (Storm-swift) and Ocypetes (Swift-flier) who on their swift wings keep pace with the blasts of the winds and the birds; for quick as time they dart along.
(ll 270-294) And again, Ceto bare to Phorcys the fair-cheeked Graiae, sisters gray from their birth: and both deathless gods and men who walk on earth call them Graiae, Pemphredo well-clad, and saffron-robed Enyo, and the Gorgons who dwell beyond glorious Ocean in the frontier land towards Night where are the clear-voiced Hesperides, Sthenno, and Euryale, and Medusa who suffered a woeful fate: she was mortal, but the two were undying and grew not old. With her lay the Dark-haired One in a soft meadow amid spring flowers. And when Perseus cut off her head, there sprang forth great Chrysaor and the horse Pegasus who is so called because he was born near the springs ( pegae ) of Ocean; and that other, because he held a golden blade ( aor ) in his hands. Now Pegasus flew away and left the earth, the mother of flocks, and came to the deathless gods: and he dwells in the house of Zeus and brings to wise Zeus the thunder and lightning. But Chrysaor was joined in love to Callirrhoe, the daughter of glorious Ocean, and begot three-headed Geryones. Him mighty Heracles slew in sea-girt Erythea by his shambling oxen on that day when he drove the wide-browed oxen to holy Tiryns, and had crossed the ford of Ocean and killed Orthus and Eurytion the herdsman in the dim stead out beyond glorious Ocean.
(ll. 295-305) And in a hollow cave she bare another monster, irresistible, in no wise like either to mortal men or to the undying gods, even the goddess fierce Echidna who is half a nymph with glancing eyes and fair cheeks, and half again a huge snake, great and awful, with speckled skin, eating raw flesh beneath the secret parts of the holy earth. And there she has a cave deep down under a hollow rock far from the deathless gods and mortal men. There, then, did the gods appoint her a glorious house to dwell in: and she keeps guard in Arima beneath the earth, grim Echidna, a nymph who dies not nor grows old all her days.
(ll. 306-332) Men say that Typhaon the terrible, outrageous and lawless, was joined in love to her, the maid with glancing eyes. So she conceived and brought forth fierce offspring; first she bare Orthus the hound of Geryones, and then again she bare a second, a monster not to be overcome and that may not be described, Cerberus who eats raw flesh, the brazen-voiced hound of Hades, fifty-headed, relentless and strong. And again she bore a third, the evil-minded Hydra of Lerna, whom the goddess, white-armed Hera nourished, being angry beyond measure with the mighty Heracles. And her Heracles, the son of Zeus, of the house of Amphitryon, together with warlike Iolaus, destroyed with the unpitying sword through the plans of Athene the spoil-driver.  Her did Pegasus and noble Bellerophon slay; but Echidna was subject in love to Orthus and brought forth the deadly Sphinx which destroyed the Cadmeans, and the Nemean lion, which Hera, the good wife of Zeus, brought up and made to haunt the hills of Nemea, a plague to men. There he preyed upon the tribes of her own people and had power over Tretus of Nemea and Apesas: yet the strength of stout Heracles overcame him.
(ll. 333-336) And Ceto was joined in love to Phorcys and bare her youngest, the awful snake who guards the apples all of gold in the secret places of the dark earth at its great bounds. This is the offspring of Ceto and Phorcys.
(ll. 334-345) And Tethys bare to Ocean eddying rivers, Nilus, and Alpheus, and deep-swirling Eridanus, Strymon, and Meander, and the fair stream of Ister, and Phasis, and Rhesus, and the silver eddies of Achelous, Nessus, and Rhodius, Haliacmon, and Heptaporus, Granicus, and Aesepus, and holy Simois, and Peneus, and Hermus, and Caicus fair stream, and great Sangarius, Ladon, Parthenius, Euenus, Ardescus, and divine Scamander.
(ll. 346-370) Also she brought forth a holy company of daughters who with the lord Apollo and the Rivers have youths in their keeping—to this charge Zeus appointed them—Peitho, and Admete, and Ianthe, and Electra, and Doris, and Prymno, and Urania divine in form, Hippo, Clymene, Rhodea, and Callirrhoe, Zeuxo and Clytie, and Idyia, and Pasithoe, Plexaura, and Galaxaura, and lovely Dione, Melobosis and Thoe and handsome Polydora, Cerceis lovely of form, and soft eyed Pluto, Perseis, Ianeira, Acaste, Xanthe, Petraea the fair, Menestho, and Europa, Metis, and Eurynome, and Telesto saffron-clad, Chryseis and Asia and charming Calypso, Eudora, and Tyche, Amphirho, and Ocyrrhoe, and Styx who is the chiefest of them all. These are the eldest daughters that sprang from Ocean and Tethys; but there are many besides. For there are three thousand neat-ankled daughters of Ocean who are dispersed far and wide, and in every place alike serve the earth and the deep waters, children who are glorious among goddesses. And as many other rivers are there, babbling as they flow, sons of Ocean, whom queenly Tethys bare, but their names it is hard for a mortal man to tell, but people know those by which they severally dwell.
(ll. 371-374) And Theia was subject in love to Hyperion and bare great Helius (Sun) and clear Selene (Moon) and Eos (Dawn) who shines upon all that are on earth and upon the deathless Gods who live in the wide heaven.
(ll. 375-377) And Eurybia, bright goddess, was joined in love to Crius and bare great Astraeus, and Pallas, and Perses who also was eminent among all men in wisdom.
(ll. 378-382) And Eos bare to Astraeus the strong-hearted winds, brightening Zephyrus, and Boreas, headlong in his course, and Notus,—a goddess mating in love with a god. And after these Erigenia bare the star Eosphorus (Dawn-bringer), and the gleaming stars with which heaven is crowned.
(ll. 383-403) And Styx the daughter of Ocean was joined to Pallas and bare Zelus (Emulation) and trim-ankled Nike (Victory) in the house. Also she brought forth Cratos (Strength) and Bia (Force), wonderful children. These have no house apart from Zeus, nor any dwelling nor path except that wherein God leads them, but they dwell always with Zeus the loud-thunderer. For so did Styx the deathless daughter of Ocean plan on that day when the Olympian Lightener called all the deathless gods to great Olympus, and said that whosoever of the gods would fight with him against the Titans, he would not cast him out from his rights, but each should have the office which he had before amongst the deathless gods. And he declared that he who was without office and rights under Cronos, should be raised to both office and rights as is just. So deathless Styx came first to Olympus with her children through the wit of her dear father. And Zeus honored her, and gave her very great gifts, for her he appointed to be the great oath of the gods, and her children to live with him always. And as he promised, so he performed fully unto them all. But he himself mightily reigns and rules.
(ll. 404-452) Again, Phoebe came to the desired embrace of Coeus.
Then the goddess through the love of the god conceived and brought forth dark-gowned Leto, always mild, kind to men and to the deathless gods, mild from the beginning, gentlest in all Olympus. Also she bare Asteria of happy name, whom Perses once led to his great house to be called his dear wife. And she conceived and bare Hecate whom Zeus the son of Cronos honored above all. He gave her splendid gifts, to have a share of the earth and the unfruitful sea. She. received honor also in starry heaven, and is honored exceedingly by the deathless gods. For to this day, whenever any one of men on earth offers rich sacrifices and prays for favor according to custom, he calls upon Hecate. Great honor comes full easily to him whose prayers the goddess receives favorably, and she bestows wealth upon him; for the power surely is with her. For as many as were born of Earth and Ocean amongst all these she has her due portion. The son of Cronos did her no wrong nor took anything away of all that was her portion among the former Titan gods: but she holds, as the division was at the first from the beginning, privilege both in earth, and in heaven, and in sea. Also, because she is an only child, the goddess receives not less honor, but much more still, for Zeus honors her. Whom she will she greatly aids and advances: she sits by worshipful kings in judgment, and in the assembly whom she will is distinguished among the people. And when men arm themselves for the battle that destroys men, then the goddess is at hand to give victory and grant glory readily to whom she will. Good is she also when men contend at the games, for there too the goddess is with them and profits them: and he who by might and strength gets the victory wins the rich prize easily with joy, and brings glory to his parents. And she is good to stand by horsemen, whom she will: and to those whose business is in the gray discomfortable sea, and who pray to Hecate and the loud-crashing Earth-Shaker, easily the glorious goddess gives great catch, and easily she takes it away as soon as seen, if so she will. She is good in the byre with Hermes to increase the stock. The droves of kine and wide herds of goats and flocks of fleecy sheep, if she will, she increases from a few, or makes many to be less. So, then. albeit her mother’s only child, she is honored amongst all the deathless gods. And the son of Cronos made her a nurse of the young who after that day saw with their eyes the light of all-seeing Dawn. So from the beginning she is a nurse of the young, and these are her honors.
(ll. 453-491) But Rhea was subject in love to Cronos and bare splendid children, Hestia, Demeter, and gold-shod Hera and strong Hades, pitiless in heart, who dwells under the earth, and the loud-crashing Earth-Shaker, and wise Zeus, father of gods and men, by whose thunder the wide earth is shaken. These great Cronos swallowed as each came forth from the womb to his mother’s knees with this intent, that no other of the proud sons of Heaven should hold the kingly office amongst the deathless gods. For he learned from Earth and starry Heaven that he was destined to be overcome by his own son, strong though he was, through the contriving of great Zeus. Therefore he kept no blind outlook, but watched and swallowed down his children: and unceasing grief seized Rhea. But when she was about to bear Zeus, the father of gods and men, then she besought her own dear parents, Earth and starry Heaven, to devise some plan with her that the birth of her dear child might be concealed, and that retribution might overtake great, crafty Cronos for his own father and also for the children whom he had swallowed down. And they readily heard and obeyed their dear daughter, and told her all that was destined to happen touching Cronos the king and his stout-hearted son. So they sent her to Lyetus, to the rich land of Crete, when she was ready to bear great Zeus, the youngest of her children. Him did vast Earth receive from Rhea in wide Crete to nourish and to bring up. Thither came Earth carrying him swiftly through the black night to Lyctus first, and took him in her arms and hid him in a remote cave beneath the secret places of the holy earth on thick-wooded Mount Aegeum; but to the mightily ruling son of Heaven, the earlier king of the gods, she gave a great stone wrapped in swaddling clothes. Then he took it in his hands and thrust it down into his belly: wretch! he knew not in his heart that in place of the stone his son was left behind, unconquered and untroubled, and that he was soon to overcome him by force and might and drive him from his honors, himself to reign over the deathless gods.
(ll. 492-506) After that, the strength and glorious limbs of the prince increased quickly, and as the years rolled on, great Cronos the wily was beguiled by the deep suggestions of Earth, and brought up again his offspring, vanquished by the arts and might of his own son, and he vomited up first the stone which he had swallowed last. And Zeus set it fast in the wide-pathed earth at goodly Pytho under the glens of Parnassus, to be a sign thenceforth and a marvel to mortal men. And he set free from their deadly bonds the brothers of his father, sons of Heaven whom his father in his foolishness had bound. And they remembered to be grateful to him for his kindness, and gave him thunder and the glowing thunderbolt and lightening: for before that, huge Earth had hidden these. In them he trusts and rules over mortals and immortals.
(ll. 507-543) Now Iapetus took to wife the neat-ankled maid Clymene, daughter of Ocean, and went up with her into one bed. And she bare him a stout-hearted son, Atlas: also she bare very glorious Menoetius and clever Prometheus, full of various wiles, and scatter-brained Epimetheus who from the first was a mischief to men who eat bread; for it was he who first took of Zeus the woman, the maiden whom he had formed. But Menoetius was outrageous, and far-seeing Zeus struck him with a lurid thunderbolt and sent him down to Erebus because of his mad presumption and exceeding pride. And Atlas through hard constraint upholds the wide heaven with unwearying head and arms, standing at the borders of the earth before the clear-voiced Hesperides; for this lot wise Zeus assigned to him. And ready-witted Prometheus he bound with inextricable bonds, cruel chains, and drove a shaft through his middle, and set on him a long-winged eagle, which used to eat his immortal liver; but by night the liver grew as much again everyway as the long-winged bird devoured in the whole day. That bird Heracles, the valiant son of shapely-ankled Alcmene, slew; and delivered the son of Iapetus from the cruel plague, and released him from his affliction—not without the will of Olympian Zeus who reigns on high, that the glory of Heracles the Theban-born might be yet greater than it was before over the plenteous earth. This, then, he regarded, and honored his famous son; though he was angry, he ceased from the wrath which he had before because Prometheus matched himself in wit with the almighty son of Cronos. For when the gods and mortal men had a dispute at Mecone, even then Prometheus was forward to cut up a great ox and set portions before them, trying to befool the mind of Zeus. Before the rest he set flesh and inner parts thick with fat upon the hide, covering them with an ox paunch; but for Zeus he put the white bones dressed up with cunning art and covered with shining fat. Then the father of men and of gods said to him:
(ll. 543-544) ‘Son of Iapetus, most glorious of all lords, good sir, how unfairly you have divided the portions!’
(ll. 545-547) So said Zeus whose wisdom is everlasting, rebuking him. But wily Prometheus answered him, smiling softly and not forgetting his cunning trick:
(ll. 548-558) ‘Zeus, most glorious and greatest of the eternal gods, take whichever of these portions your heart within you bids.’ So he said, thinking trickery. But Zeus, whose wisdom is everlasting, saw and failed not to perceive the trick, and in his heart he thought mischief against mortal men which also was to be fulfilled.  But Zeus who drives the clouds was greatly vexed and said to him:
(ll. 559-560) ‘Son of Iapetus, clever above all! So, sir, you have not yet forgotten your cunning arts!’
(ll. 561-584) So spake Zeus in anger, whose wisdom is everlasting; and from that time he was always mindful of the trick, and would not give the power of unwearying fire to the Melian race of mortal men who live on the earth. But the noble son of Iapetus outwitted him and stole the far-seen gleam of unwearying fire in a hollow fennel stalk. And Zeus who thunders on high was stung in spirit, and his dear heart was angered when he saw amongst men the far-seen ray of fire. Forthwith he made an evil thing for men as the price of fire; for the very famous Limping God formed of earth the likeness of a shy maiden as the son of Cronos willed. And the goddess bright-eyed Athene girded and clothed her with silvery raiment, and down from her head she spread with her hands a broidered veil, a wonder to see; and she, Pallas Athene, put about her head lovely garlands, flowers of new-grown herbs. Also she put upon her head a crown of gold which the very famous Limping God made himself and worked with his own hands as a favor to Zeus his father. On it was much curious work, wonderful to see; for of the many creatures which the land and sea rear up, he put most upon it, wonderful things, like living beings with voices: and great beauty shone out from it.
(ll. 585-589) But when he had made the beautiful evil to be the price for the blessing, he brought her out, delighting in the finery which the bright-eyed daughter of a mighty father had given her, to the place where the other gods and men were. And wonder took hold of the deathless gods and mortal men when they saw that which was sheer guile, not to be withstood by men.
(ll. 590-612) For from her is the race of women and female kind: of her is the deadly race and tribe of women who live amongst mortal men to their great trouble, no helpmeets in hateful poverty, but only in wealth. And as in thatched hives bees feed the drones whose nature is to do mischief—by day and throughout the day until the sun goes down the bees are busy and lay the white combs, while the drones stay at home in the covered skeps and reap the toil of others into their own bellies—even so Zeus who thunders on high made women to be an evil to mortal men, with a nature to do evil. And he gave them a second evil to be the price for the good they had: whoever avoids marriage and the sorrows that women cause, and will not wed, reaches deadly old age without anyone to tend his years, and though he at least has no lack of livelihood while he lives, yet, when he is dead, his kinsfolk divide his possessions amongst them. And as for the man who chooses the lot of marriage and takes a good wife suited to his mind, evil continually contends with good; for whoever happens to have mischievous children, lives always with unceasing grief in his spirit and heart within him; and this evil cannot be healed.
(ll. 613-616) So it is not possible to deceive or go beyond the will of Zeus; for not even the son of Iapetus, kindly Prometheus, escaped his heavy anger, but of necessity strong bands confined him, although he knew many a wile.
(ll. 617-643) But when first their father was vexed in his heart with Obriareus and Cottus and Gyes, he bound them in cruel bonds, because he was jealous of their exceeding manhood and comeliness and great size: and he made them live beneath the wide-pathed earth, where they were afflicted, being set to dwell under the ground, at the end of the earth, at its great borders, in bitter anguish for a long time and with great grief at heart. But the son of Cronos and the other deathless gods whom rich-haired Rhea bare from union with Cronos, brought them up again to the light at Earth’s advising. For she herself recounted all things to the gods fully, how that with these they would gain victory and a glorious cause to vaunt themselves. For the Titan gods and as many as sprang from Cronos had long been fighting together in stubborn war with heart-grieving toil, the lordly Titans from high Othyrs, but the gods, givers of good, whom rich-haired Rhea bare in union with Cronos, from Olympus. So they, with bitter wrath, were fighting continually with one another at that time for ten full years, and the hard strife had no close or end for either side, and the issue of the war hung evenly balanced. But when he had provided those three with all things fitting, nectar and ambrosia which the gods themselves eat, and when their proud spirit revived within them all after they had fed on nectar and delicious ambrosia, then it was that the father of men and gods spoke amongst them:
(ll. 644-653) ‘Hear me, bright children of Earth and Heaven, that I may say what my heart within me bids. A long while now have we, who are sprung from Cronos and the Titan gods, fought with each other every day to get victory and to prevail. But do you show your great might and unconquerable strength, and face the Titans in bitter strife; for remember our friendly kindness, and from what sufferings you are come back to the light from your cruel bondage under misty gloom through our counsels.’
(ll. 654-663) So he said. And blameless Cottus answered him again: ‘Divine one, you speak that which we know well: nay, even of ourselves we know that your wisdom and understanding is exceeding, and that you became a defender of the deathless ones from chill doom.  And so now with fixed purpose and deliberate counsel we will aid your power in dreadful strife and will fight against the Titans in hard battle.’
(ll. 664-686) So he said: and the gods, givers of good things, applauded when they heard his word, and their spirit longed for war even more than before, and they all, both male and female, stirred up hated battle that day, the Titan gods, and all that were born of Cronos together with those dread, mighty ones of overwhelming strength whom Zeus brought up to the light from Erebus beneath the earth. An hundred arms sprang from the shoulders of all alike, and each had fifty heads growing upon his shoulders upon stout limbs. These, then, stood against the Titans in grim strife, holding huge rocks in their strong hands. And on the other part the Titans eagerly strengthened their ranks, and both sides at one time showed the work of their hands and their might. The boundless sea rang terribly around, and the earth crashed loudly: wide Heaven was shaken and groaned, and high Olympus reeled from its foundation under the charge of the undying gods, and a heavy quaking reached dim Tartarus and the deep sound of their feet in the fearful onset and of their hard missiles. So, then, they launched their grievous shafts upon one another, and the cry of both armies as they shouted reached to starry heaven; and they met together with a great battle-cry.
(ll. 687-712) Then Zeus no longer held back his might; but straight his heart was filled with fury and he showed forth all his strength. From Heaven and from Olympus he came forthwith, hurling his lightning: the bolts flew thick and fast from his strong hand together with thunder and lightning, whirling an awesome flame. The life-giving earth crashed around in burning, and the vast wood crackled loud with fire all about. All the land seethed, and Ocean’s streams and the unfruitful sea. The hot vapor lapped round the earthborn Titans: flame unspeakable rose to the bright upper air: the flashing glare of the thunder-stone and lightning blinded their eyes for all that there were strong. Astounding heat seized Chaos: and to see with eyes and to hear the sound with ears it seemed even as if Earth and wide Heaven above came together; for such a mighty crash would have arisen if Earth were being hurled to ruin, and Heaven from on high were hurling her down; so great a crash was there while the gods were meeting together in strife. Also the winds brought rumbling earthquake and duststorm, thunder and lightning and the lurid thunderbolt, which are the shafts of great Zeus, and carried the clangor and the warcry into the midst of the two hosts. An horrible uproar of terrible strife arose: mighty deeds were shown and the battle inclined. But until then, they kept at one another and fought continually in cruel war.
(ll. 713-735) And amongst the foremost Cottus and Briareos and Gyes insatiate for war raised fierce fighting: three hundred rocks, one upon another, they launched from their strong hands and overshadowed the Titans with their missiles, and buried them beneath the wide-pathed earth, and bound them in bitter chains when they had conquered them by their strength for all their great spirit, as far beneath the earth to Tartarus. For a brazen anvil falling down from heaven nine nights and days would reach the earth upon the tenth: and again, a brazen anvil falling from earth nine nights and days would reach Tartarus upon the tenth. Round it runs a fence of bronze, and night spreads in triple line all about it like a neck-circlet, while above grow the roots of the earth and unfruitful sea. There by the counsel of Zeus who drives the clouds the Titan gods are hidden under misty gloom, in a dank place where are the ends of the huge earth. And they may not go out; for Poseidon fixed gates of bronze upon it, and a wall runs all round it on every side. There Gyes and Cottus and great-souled Obriareus live, trusty warders of Zeus who holds the aegis.
(ll. 736-744) And there, all in their order, are the sources and ends of gloomy earth and misty Tartarus and the unfruitful sea and starry heaven, loathsome and dank, which even the gods abhor.
It is a great gulf, and if once a man were within the gates, he would not reach the floor until a whole year had reached its end, but cruel blast upon blast would carry him this way and that. And this marvel is awful even to the deathless gods.
(ll. 744-757) There stands the awful home of murky Night wrapped in dark clouds. In front of it the son of Iapetus stands immovably upholding the wide heaven upon his head and unwearying hands, where Night and Day draw near and greet one another as they pass the great threshold of bronze: and while the one is about to go down into the house, the other comes out at the door.
And the house never holds them both within; but always one is without the house passing over the earth, while the other stays at home and waits until the time for her journeying come; and the one holds all-seeing light for them on earth, but the other holds in her arms Sleep the brother of Death, even evil Night, wrapped in a vaporous cloud.
(ll. 758-766) And there the children of dark Night have their dwellings, Sleep and Death, awful gods. The glowing Sun never looks upon them with his beams, neither as he goes up into heaven, nor as he comes down from heaven. And the former of them roams peacefully over the earth and the sea’s broad back and is kindly to men; but the other has a heart of iron, and his spirit within him is pitiless as bronze: whomsoever of men he has once seized he holds fast: and he is hateful even to the deathless gods.
(ll. 767-774) There, in front, stand the echoing halls of the god of the lower-world, strong Hades, and of awful Persephone. A fearful hound guards the house in front, pitiless, and he has a cruel trick. On those who go in he fawns with his tail and both his ears, but suffers them not to go out back again, but keeps watch and devours whomsoever he catches going out of the gates of strong Hades and awful Persephone.
(ll. 775-806) And there dwells the goddess loathed by the deathless gods, terrible Styx, eldest daughter of back-flowing Ocean. She lives apart from the gods in her glorious house vaulted over with great rocks and propped up to heaven all round with silver pillars. Rarely does the daughter of Thaumas, swift-footed Iris, come to her with a message over the sea’s wide back.
But when strife and quarrel arise among the deathless gods, and when any of them who live in the house of Olympus lies, then Zeus sends Iris to bring in a golden jug the great oath of the gods from far away, the famous cold water which trickles down from a high and beetling rock. Far under the wide-pathed earth a branch of Oceanus flows through the dark night out of the holy stream, and a tenth part of his water is allotted to her. With nine silver-swirling streams he winds about the earth and the sea’s wide back, and then falls into the main; but the tenth flows out from a rock, a sore trouble to the gods. For whoever of the deathless gods that hold the peaks of snowy Olympus pours a libation of her water is forsworn, lies breathless until a full year is completed, and never comes near to taste ambrosia and nectar, but lies spiritless and voiceless on a strewn bed: and a heavy trance overshadows him. But when he has spent a long year in his sickness, another penance and an harder follows after the first.  But in the tenth year he comes again to join the assemblies of the deathless gods who live in the house of Olympus. Such an oath, then, did the gods appoint the eternal and primeval water of Styx to be: and it spouts through a rugged place.
(ll. 807-819) And there, all in their order, are the sources and ends of the dark earth and misty Tartarus and the unfruitful sea and starry heaven, loathsome and dank, which even the gods abhor.
And there are shining gates and an immovable threshold of bronze having unending roots and it is grown of itself. And beyond, away from all the gods, live the Titans, beyond gloomy Chaos. But the glorious allies of loud-crashing Zeus have their dwelling upon Ocean’s foundations, even Cottus and Gyes; but Briareos, being goodly, the deep-roaring Earth-Shaker made his son-in-law, giving him Cymopolea his daughter to wed.
(ll. 820-868) But when Zeus had driven the Titans from heaven, huge Earth bare her youngest child Typhoeus of the love of Tartarus, by the aid of golden Aphrodite. Strength was with his hands in all that he did and the feet of the strong god were untiring. From his shoulders grew an hundred heads of a snake, a fearful dragon, with dark, flickering tongues, and from under the brows of his eyes in his marvelous heads flashed fire, and fire burned from his heads as he glared. And there were voices in all his dreadful heads which uttered every kind of sound unspeakable; for at one time they made sounds such that the gods understood, but at another, the noise of a bull bellowing aloud in proud ungovernable fury; and at another, the sound of a lion, relentless of heart; and at another, sounds like whelps, wonderful to hear; and again, at another, he would hiss, so that the high mountains re-echoed. And truly a thing past help would have happened on that day, and he would have come to reign over mortals and immortals, had not the father of men and gods been quick to perceive it. But he thundered hard and mightily: and the earth around resounded terribly and the wide heaven above, and the sea and Ocean’s streams and the nether parts of the earth. Great Olympus reeled beneath the divine feet of the king as he arose and earth groaned thereat. And through the two of them heat took hold on the dark-blue sea, through the thunder and lightning, and through the fire from the monster, and the scorching winds and blazing thunderbolt. The whole earth seethed, and sky and sea: and the long waves raged along the beaches round and about, at the rush of the deathless gods: and there arose an endless shaking. Hades trembled where he rules over the dead below, and the Titans under Tartarus who live with Cronos, because of the unending clamor and the fearful strife. So when Zeus had raised up his might and seized his arms, thunder and lightning and lurid thunderbolt, he leaped from Olympus and struck him, and burned all the marvelous heads of the monster about him. But when Zeus had conquered him and lashed him with strokes, Typhoeus was hurled down, a maimed wreck, so that the huge earth groaned. And flame shot forth from the thunder-stricken lord in the dim rugged glens of the mount, when he was smitten. A great part of huge earth was scorched by the terrible vapor and melted as tin melts when heated by men’s art in channeled crucibles; or as iron, which is hardest of all things, is softened by glowing fire in mountain glens and melts in the divine earth through the strength of Hephaestus. Even so, then, the earth melted in the glow of the blazing fire. And in the bitterness of his anger Zeus cast him into wide Tartarus.
(ll. 869-880) And from Typhoeus come boisterous winds which blow damply, except Notus and Boreas and clear Zephyr. These are a god-sent kind, and a great blessing to men; but the others blow fitfully upon the seas. Some rush upon the misty sea and work great havoc among men with their evil, raging blasts; for varying with the season they blow, scattering ships and destroying sailors. And men who meet these upon the sea have no help against the mischief. Others again over the boundless, flowering earth spoil the fair fields of men who dwell below, filling them with dust and cruel uproar.
(ll. 881-885) But when the blessed gods had finished their toil, and settled by force their struggle for honors with the Titans, they pressed far-seeing Olympian Zeus to reign and to rule over them, by Earth’s prompting. So he divided their dignities amongst them.
(ll. 886-900) Now Zeus, king of the gods, made Metis his wife first, and she was wisest among gods and mortal men. But when she was about to bring forth the goddess bright-eyed Athene, Zeus craftily deceived her with cunning words and put her in his own belly, as Earth and starry Heaven advised. For they advised him so, to the end that no other should hold royal sway over the eternal gods in place of Zeus; for very wise children were destined to be born of her, first the maiden bright-eyed Tritogeneia, equal to her father in strength and in wise understanding; but afterwards she was to bear a son of overbearing spirit, king of gods and men. But Zeus put her into his own belly first, that the goddess might devise for him both good and evil.
(ll. 901-906) Next he married bright Themis who bare the Horae (Hours), and Eunomia (Order), Dike (Justice), and blooming Eirene (Peace), who mind the works of mortal men, and the Moerae (Fates) to whom wise Zeus gave the greatest honour, Clotho, and Lachesis, and Atropos who give mortal men evil and good to have.
(ll. 907-911) And Eurynome, the daughter of Ocean, beautiful in form, bare him three fair-cheeked Charities (Graces), Aglaea, and Euphrosyne, and lovely Thaleia, from whose eyes as they glanced flowed love that unnerves the limbs: and beautiful is their glance beneath their brows.
(ll. 912-914) Also he came to the bed of all-nourishing Demeter, and she bare white-armed Persephone whom Aidoneus carried off from her mother; but wise Zeus gave her to him.
(ll. 915-917) And again, he loved Mnemosyne with the beautiful hair: and of her the nine gold-crowned Muses were born who delight in feasts and the pleasures of song.
(ll. 918-920) And Leto was joined in love with Zeus who holds the aegis, and bare Apollo and Artemis delighting in arrows, children lovely above all the sons of Heaven.
(ll. 921-923) Lastly, he made Hera his blooming wife: and she was joined in love with the king of gods and men, and brought forth Hebe and Ares and Eileithyia.
(ll. 924-929) But Zeus himself gave birth from his own head to bright-eyed Tritogeneia, the awful, the strife-stirring, the host-leader, the unwearying, the queen, who delights in tumults and wars and battles. But Hera without union with Zeus—for she was very angry and quarreled with her mate—bare famous Hephaestus, who is skilled in crafts more than all the sons of Heaven.
(ll. 929a-929t) But Hera was very angry and quarreled with her mate. And because of this strife she bare without union with Zeus who holds the aegis a glorious son, Hephaestus, who excelled all the sons of Heaven in crafts. But Zeus lay with the fair-cheeked daughter of Ocean and Tethys apart from Hera deceiving Metis (Thought) although she was full wise. But he seized her with his hands and put her in his belly, for fear that she might bring forth something stronger than his thunderbolt: therefore did Zeus, who sits on high and dwells in the aether, swallow her down suddenly. But she straightway conceived Pallas Athene: and the father of men and gods gave her birth by way of his head on the banks of the river Trito. And she remained hidden beneath the inward parts of Zeus, even Metis, Athena’s mother, worker of righteousness, who was wiser than gods and mortal men. There the goddess (Athena) received that whereby she excelled in strength all the deathless ones who dwell in Olympus, she who made the host-scaring weapon of Athena. And with it (Zeus) gave her birth, arrayed in arms of war.
(ll. 930-933) And of Amphitrite and the loud-roaring Earth-Shaker was born great, wide-ruling Triton, and he owns the depths of the sea, living with his dear mother and the lord his father in their golden house, an awful god.
(ll. 933-937) Also Cytherea bare to Ares the shield-piercer Panic and Fear, terrible gods who drive in disorder the close ranks of men in numbing war, with the help of Ares, sacker of towns: and Harmonia whom high-spirited Cadmus made his wife.
(ll. 938-939) And Maia, the daughter of Atlas, bare to Zeus glorious Hermes, the herald of the deathless gods, for she went up into his holy bed.
(ll. 940-942) And Semele, daughter of Cadmus was joined with him in love and bare him a splendid son, joyous Dionysus,—a mortal woman an immortal son. And now they both are gods.
(ll. 943-944) And Alcmena was joined in love with Zeus who drives the clouds and bare mighty Heracles.
(ll. 945-946) And Hephaestus, the famous Lame One, made Aglaea, youngest of the Graces, his buxom wife.
(ll. 947-949) And golden-haired Dionysus made brown-haired Ariadne, the daughter of Minos, his buxom wife: and the son of Cronos made her deathless and unageing for him.
(ll. 950-955) And mighty Heracles, the valiant son of neat-ankled Alcmena, when he had finished his grievous toils, made Hebe the child of great Zeus and gold-shod Hera his shy wife in snowy Olympus. Happy he! For he has finished his great works and lives amongst the undying gods, untroubled and unageing all his days.
(ll. 956-962) And Perseis, the daughter of Ocean, bore unwearying Helios Circe and Aeetes the king. And Aeetes, the son of Helios who shows light to men, took to wife fair-cheeked Idyia, daughter of Ocean the perfect stream, by the will of the gods: and she was subject to him in love through golden Aphrodite and bare him neat-ankled Medea.
(ll. 963-968) And now farewell, you dwellers on Olympus and you islands and continents and thou briny sea within. Now sing the company of goddesses, sweet-voiced Muses of Olympus, daughter of Zeus who holds the aegis,—even those deathless ones who lay with mortal men and bare children like unto gods.
(ll. 969-974) Demeter, bright goddess, was joined in sweet love with the hero Iasion in a thrice-plowed fallow in the rich land of Crete, and bare Plutus, a kindly god who goes everywhere over land and the sea’s wide back, and him who finds him and into whose hands he comes he makes rich, bestowing great wealth upon him.
(ll. 975-978) And Harmonia, the daughter of golden Aphrodite, bare to Cadmus Ino and Semele and fair-cheeked Agave and Autonoe whom long haired Aristaeus wedded, and Polydorus also in rich-crowned Thebe.
(ll. 979-983) And the daughter of Ocean, Callirrhoe was joined in the love of rich Aphrodite with stout hearted Chrysaor and bare a son who was the strongest of all men, Geryones, whom mighty Heracles killed in sea-girt Erythea for the sake of his shambling oxen.
(ll. 984-991) And Eos bare to Tithonus brazen-crested Memnon, king of the Ethiopians, and the Lord Emathion. And to Cephalus she bare a splendid son, strong Phaethon, a man like the gods, whom, when he was a young boy in the tender flower of glorious youth with childish thoughts, laughter-loving Aphrodite seized and caught up and made a keeper of her shrine by night, a divine spirit.
(ll. 993-1002) And the son of Aeson by the will of the gods led away from Aeetes the daughter of Aeetes the heaven-nurtured king, when he had finished the many grievous labors which the great king, over-bearing Pelias, that outrageous and presumptuous doer of violence, put upon him. But when the son of Aeson had finished them, he came to Iolcus after long toil bringing the coy-eyed girl with him on his swift ship, and made her his buxom wife. And she was subject to Iason, shepherd of the people, and bare a son Medeus whom Cheiron the son of Philyra brought up in the mountains. And the will of great Zeus was fulfilled.
(ll. 1003-1007) But of the daughters of Nereus, the Old man of the Sea, Psamathe the fair goddess, was loved by Aeacus through golden Aphrodite and bare Phocus. And the silver-shod goddess Thetis was subject to Peleus and brought forth lion-hearted Achilles, the destroyer of men.
(ll. 1008-1010) And Cytherea with the beautiful crown was joined in sweet love with the hero Anchises and bare Aeneas on the peaks of Ida with its many wooded glens.
(ll. 1011-1016) And Circe the daughter of Helius, Hyperion’s son, loved steadfast Odysseus and bare Agrius and Latinus who was faultless and strong: also she brought forth Telegonus by the will of golden Aphrodite. And they ruled over the famous Tyrenians, very far off in a recess of the holy islands.
(ll. 1017-1018) And the bright goddess Calypso was joined to Odysseus in sweet love, and bare him Nausithous and Nausinous.
(ll. 1019-1020) These are the immortal goddesses who lay with mortal men and bare them children like unto gods.


2.1: NAEYC Standards
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“History is a kind of introduction to more interesting people than we can possibly meet in our restricted lives; let us not neglect the opportunity.” - Dexter Perkins
The following NAEYC Standard for Early Childhood Professional Preparation are addressed in this chapter:
The following competencies are addressed in this chapter:
The following elements of the code are touched upon in this chapter:
Section I: Ethical Responsibilities to Children
Ideals: I-1.1, I-1.2, I-1.5, I-1.8, I-1.9
Principles: P-1.1, P-1.2, P-1.7, P-1.11
Section II: Ethical Responsibilities to Families
Ideals: I-2.1, I-2.2, I-2.4, I-2.7, I-2.8, I-2.9
Principles: P-2.2, P-2.3
Section IV: Ethical Responsibilities to Community and Society
Ideals: I:4.1 (individual), I-4.6, I-4.7, I-4.8


9.3: Ferromagnets and Electromagnets
Learning Objectives
By the end of this section, you will be able to:
- Define ferromagnet.
- Describe the role of magnetic domains in magnetization.
- Explain the significance of the Curie temperature.
- Describe the relationship between electricity and magnetism.
Ferromagnets
Only certain materials, such as iron, cobalt, nickel, and gadolinium, exhibit strong magnetic effects. Such materials are called ferromagnetic , after the Latin word for iron, ferrum . A group of materials made from the alloys of the rare earth elements are also used as strong and permanent magnets; a popular one is neodymium. Other materials exhibit weak magnetic effects, which are detectable only with sensitive instruments. Not only do ferromagnetic materials respond strongly to magnets (the way iron is attracted to magnets), they can also be magnetized themselves—that is, they can be induced to be magnetic or made into permanent magnets.
When a magnet is brought near a previously unmagnetized ferromagnetic material, it causes local magnetization of the material with unlike poles closest, as in Figure 1. (This results in the attraction of the previously unmagnetized material to the magnet.) What happens on a microscopic scale is illustrated in Figure 2. The regions within the material called domains act like small bar magnets. Within domains, the poles of individual atoms are aligned.  Domains are small and randomly oriented in an unmagnetized ferromagnetic object. In response to an external magnetic field, the domains may grow to millimeter size, aligning themselves as shown in Figure 2b. This induced magnetization can be made permanent if the material is heated and then cooled, or simply tapped in the presence of other magnets.
Conversely, a permanent magnet can be demagnetized by hard blows or by heating it in the absence of another magnet. Increased thermal motion at higher temperature can disrupt and randomize the orientation and the size of the domains. There is a well-defined temperature for ferromagnetic materials, which is called the Curie temperature , above which they cannot be magnetized. The Curie temperature for iron is 1043 K \(\left(770^{\circ}C\right)\), which is well above room temperature. There are several elements and alloys that have Curie temperatures much lower than room temperature and are ferromagnetic only below those temperatures.
Electromagnets
Early in the 19th century, it was discovered that electrical currents cause magnetic effects. The first significant observation was by the Danish scientist Hans Christian Oersted (1777–1851), who found that a compass needle was deflected by a current-carrying wire. This was the first significant evidence that the movement of charges had any connection with magnets. Electromagnetism is the use of electric current to make magnets. These temporarily induced magnets are called electromagnets . Electromagnets are employed for everything from a wrecking yard crane that lifts scrapped cars to controlling the beam of a 90-km-circumference particle accelerator to the magnets in medical imaging machines (See Figure 3).
Figure 4 shows that the response of iron filings to a current-carrying coil and to a permanent bar magnet. The patterns are similar. In fact, electromagnets and ferromagnets have the same basic characteristics—for example, they have north and south poles that cannot be separated and for which like poles repel and unlike poles attract.
Combining a ferromagnet with an electromagnet can produce particularly strong magnetic effects. (See Figure 5.) Whenever strong magnetic effects are needed, such as lifting scrap metal, or in particle accelerators, electromagnets are enhanced by ferromagnetic materials. Limits to how strong the magnets can be made are imposed by coil resistance (it will overheat and melt at sufficiently high current), and so superconducting magnets may be employed. These are still limited, because superconducting properties are destroyed by too great a magnetic field.
Figure 6 shows a few uses of combinations of electromagnets and ferromagnets. Ferromagnetic materials can act as memory devices, because the orientation of the magnetic fields of small domains can be reversed or erased. Magnetic information storage on videotapes and computer hard drives are among the most common applications. This property is vital in our digital world.
Current: The Source of All Magnetism
An electromagnet creates magnetism with an electric current. In later sections we explore this more quantitatively, finding the strength and direction of magnetic fields created by various currents. But what about ferromagnets? Figure 7 shows models of how electric currents create magnetism at the submicroscopic level. (Note that we cannot directly observe the paths of individual electrons about atoms, and so a model or visual image, consistent with all direct observations, is made. We can directly observe the electron’s orbital angular momentum, its spin momentum, and subsequent magnetic moments, all of which are explained with electric-current-creating subatomic magnetism.) Currents, including those associated with other submicroscopic particles like protons, allow us to explain ferromagnetism and all other magnetic effects. Ferromagnetism, for example, results from an internal cooperative alignment of electron spins, possible in some materials but not in others.
Crucial to the statement that electric current is the source of all magnetism is the fact that it is impossible to separate north and south magnetic poles. (This is far different from the case of positive and negative charges, which are easily separated.) A current loop always produces a magnetic dipole—that is, a magnetic field that acts like a north pole and south pole pair. Since isolated north and south magnetic poles, called magnetic monopoles , are not observed, currents are used to explain all magnetic effects. If magnetic monopoles did exist, then we would have to modify this underlying connection that all magnetism is due to electrical current. There is no known reason that magnetic monopoles should not exist—they are simply never observed—and so searches at the subnuclear level continue. If they do not exist, we would like to find out why not. If they do exist, we would like to see evidence of them.
ELECTRIC CURRENTS AND MAGNETISM:
Electric current is the source of all magnetism.
PHET EXPLORATIONS: MAGNETS AND ELECTROMAGNETS
Explore the interactions between a compass and bar magnet . Discover how you can use a battery and wire to make a magnet! Can you make it a stronger magnet? Can you make the magnetic field reverse?
Summary
- Magnetic poles always occur in pairs of north and south—it is not possible to isolate north and south poles.
- All magnetism is created by electric current.
- Ferromagnetic materials, such as iron, are those that exhibit strong magnetic effects.
- The atoms in ferromagnetic materials act like small magnets (due to currents within the atoms) and can be aligned, usually in millimeter-sized regions called domains.
- Domains can grow and align on a larger scale, producing permanent magnets. Such a material is magnetized, or induced to be magnetic.
- Above a material’s Curie temperature, thermal agitation destroys the alignment of atoms, and ferromagnetism disappears.
- Electromagnets employ electric currents to make magnetic fields, often aided by induced fields in ferromagnetic materials.
Glossary
- ferromagnetic
- materials, such as iron, cobalt, nickel, and gadolinium, that exhibit strong magnetic effects
- magnetized
- to be turned into a magnet; to be induced to be magnetic
- domains
- regions within a material that behave like small bar magnets
- Curie temperature
- the temperature above which a ferromagnetic material cannot be magnetized
- electromagnetism
- the use of electrical currents to induce magnetism
- electromagnet
- an object that is temporarily magnetic when an electrical current is passed through it
- magnetic monopoles
- an isolated magnetic pole; a south pole without a north pole, or vice versa (no magnetic monopole has ever been observed)
Contributors and Attributions
-
Paul Peter Urone (Professor Emeritus at California State University, Sacramento) and Roger Hinrichs (State University of New York, College at Oswego) with Contributing Authors: Kim Dirks (University of Auckland) and Manjula Sharma (University of Sydney). This work is licensed by OpenStax University Physics under a Creative Commons Attribution License (by 4.0) .


8.2.4: Designing Simulations
Lesson
Let's simulate some real-life scenarios.
Exercise \(\PageIndex{1}\): Number Talk: Division
Find the value of each expression mentally.
\((4.2+3)\div 2\)
\((4.2+2.6+4)\div 3\)
\((4.2+2.6+4+3.6)\div 4\)
\((4.2+2.6+4+3.6+3.6)\div 5\)
Exercise \(\PageIndex{2}\): Breeding Mice
A scientist is studying the genes that determine the color of a mouse’s fur. When two mice with brown fur breed, there is a 25% chance that each baby will have white fur. For the experiment to continue, the scientist needs at least 2 out of 5 baby mice to have white fur.
To simulate this situation, you can flip two coins at the same time for each baby mouse. If you don't have coins, you can use this applet.
- If both coins land heads up, it represents a mouse with white fur.
- Any other result represents a mouse with brown fur.
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Have each person in the group simulate a litter of 5 offspring and record their results. Next, determine whether at least 2 of the offspring have white fur.
mouse 1 mouse 2 mouse 3 mouse 4 mouse 5 Do at least 2 have white fur? simulation 1 simulation 2 simulation 3 Table \(\PageIndex{1}\) - Based on the results from everyone in your group, estimate the probability that the scientist’s experiment will be able to continue.
- How could you improve your estimate?
Are you ready for more?
For a certain pair of mice, the genetics show that each offspring has a probability of \(\frac{1}{16}\) that they will be albino. Describe a simulation you could use that would estimate the probability that at least 2 of the 5 offspring are albino.
Exercise \(\PageIndex{3}\): Designing Simulations
Your teacher will give your group a paper describing a situation.
- Design a simulation that you could use to estimate a probability. Show your thinking. Organize it so it can be followed by others.
- Explain how you used the simulation to answer the questions posed in the situation.
Summary
Many real-world situations are difficult to repeat enough times to get an estimate for a probability. If we can find probabilities for parts of the situation, we may be able to simulate the situation using a process that is easier to repeat.
For example, if we know that each egg of a fish in a science experiment has a 13% chance of having a mutation, how many eggs do we need to collect to make sure we have 10 mutated eggs? If getting these eggs is difficult or expensive, it might be helpful to have an idea about how many eggs we need before trying to collect them.
We could simulate this situation by having a computer select random numbers between 1 and 100. If the number is between 1 and 13, it counts as a mutated egg. Any other number would represent a normal egg. This matches the 13% chance of each fish egg having a mutation.
We could continue asking the computer for random numbers until we get 10 numbers that are between 1 and 13. How many times we asked the computer for a random number would give us an estimate of the number of fish eggs we would need to collect.
To improve the estimate, this entire process should be repeated many times. Because computers can perform simulations quickly, we could simulate the situation 1,000 times or more.
Practice
Exercise \(\PageIndex{4}\)
A rare and delicate plant will only produce flowers from 10% of the seeds planted. To see if it is worth planting 5 seeds to see any flowers, the situation is going to be simulated. Which of these options is the best simulation? For the others, explain why it is not a good simulation.
- Another plant can be genetically modified to produce flowers 10% of the time. Plant 30 groups of 5 seeds each and wait 6 months for the plants to grow and count the fraction of groups that produce flowers.
- Roll a standard number cube 5 times. Each time a 6 appears, it represents a plant producing flowers. Repeat this process 30 times and count the fraction of times at least one number 6 appears.
- Have a computer produce 5 random digits (0 through 9). If a 9 appears in the list of digits, it represents a plant producing flowers. Repeat this process 300 times and count the fraction of times at least one number 9 appears.
- Create a spinner with 10 equal sections and mark one of them “flowers.” Spin the spinner 5 times to represent the 5 seeds. Repeat this process 30 times and count the fraction of times that at least 1 “flower” was spun.
Exercise \(\PageIndex{5}\)
Jada and Elena learned that 8% of students have asthma. They want to know the probability that in a team of 4 students, at least one of them has asthma. To simulate this, they put 25 slips of paper in a bag. Two of the slips say “asthma.” Next, they take four papers out of the bag and record whether at least one of them says “asthma.” They repeat this process 15 times.
- Jada says they could improve the accuracy of their simulation by using 100 slips of paper and marking 8 of them.
- Elena says they could improve the accuracy of their simulation by conducting 30 trials instead of 15.
- Do you agree with either of them? Explain your reasoning.
- Describe another method of simulation the same scenario.
Exercise \(\PageIndex{6}\)
The figure on the left is a trapezoidal prism. The figure on the right represents its base. Find the volume of this prism.
(From Unit 7.3.3)
Exercise \(\PageIndex{7}\)
Match each expression in the first list with an equivalent expression from the second list.
- \((8x+6y)+(2x+4y)\)
- \((8x+6y)-(2x+4y)\)
- \((8x+6y)-(2x-4y)\)
- \(8x-6y-2x+4y\)
- \(8x-6y+2x-4y\)
- \(8x-(-6y-2x+4y)\)
- \(10(x+y)\)
- \(10(x-y)\)
- \(6(x-\frac{1}{3}y)\)
- \(8x+6y+2x-4y\)
- \(8x+6y-2x+4y\)
- \(8x-2x+6y-4y\)
(From Unit 6.4.5)