12.1: Sector Reports Out
Description
Each student team presents a summary of its case study project for the class. Team presentations should offer insights into what the students have learned from this course. Depending on the number of teams in the class, it may take more than one class period for all projects to be presented.
Objectives
- Demonstrate the ability to communicate technical and business information in a presentation format.
- Demonstrate the ability to interact with peers and others.
- Demonstrate that professionalism and soft skills that employers look for in employees.
Team presentations should address the following:
- What the team discovered about cybersecurity vulnerabilities relevant to their particular sector
- What mitigation techniques can be used to alleviate these issues
- Suggestions the team has for further strengthening their network’s security
- The role of government regulation in the functioning of their organization
Grading Criteria Rubric
- Content
- Evidence of teamwork
- Professionalism
- Use of American Psychological Association (APA) style
Grade Points: 100


7.8: Courtroom Players- Judges and Court Staff
Felony Justice: An organizational analysis of criminal courts, James Eisenstein and Herbert Jacob, coined the term “courtroom workgroup.” [1] They specifically referred to the cooperative working relationship between prosecutors, defense attorneys, and judges in working together (as opposed to an adversarial relationship that the public might expect) to efficiently resolve most of the cases in the criminal courts. This chapter more generally uses the term to include all the individuals working in the criminal courts—judges, attorneys, and the variety of court staff.
accusatory phase (the pre-trial phase) and adjudicatory phase (the trial phase) of the criminal justice process include individuals who regularly work together in the trial courts. The prosecutor files the accusatory instrument called either an information or an indictment , and represents the state in plea bargaining, on pretrial motions, during the trial, and in the sentencing phase. The defense attorney represents the defendant after charges have been filed, through the pre-trial process, in a trial, and during sentencing, and maybe on the appeal as well. Judges, aided by several court personnel, conduct the pretrial, trial, and sentencing hearings. Prosecutors, defense counsel, and judges perform different roles, but all are concerned with the judicial process and the interpretation of the law. These law professionals are graduates of law schools and have passed the bar examination establishing their knowledge of the law and their ability to do legal analysis. As persons admitted by the state or federal bar associations to the practice of law, they are subject to the same legal codes of professional responsibility, disciplinary rules, and ethical rules and opinions for lawyers. Although the American criminal justice system is said to represent the adversarial model, the reality is that prosecutors, defense attorneys, judges and court staff work with cooperation and consensus rather than conflict. This is understandable when considering the common goal of efficient and expedition case processing and prescribed and agreed upon rules for achieving those goals.
Callstack:
at (Bookshelves/Corrections/Introduction_to_the_American_Criminal_Justice_System_(Burke_et_al.)/07:_Courts/7.08:_Courtroom_Players-_Judges_and_Court_Staff), /content/body/div[1]/p[2]/@if, line 1, column 3
Judicial Clerk, Law Clerk, and Judicial Assistants
swear in the witnesses, or administer the oath to the witness, take notes cataloging the recordings, etc. In some jurisdictions, the law clerks are lawyers who have just completed law school and may have already passed the bar exam. In other jurisdictions, the law clerks are not legally trained but may have specialized paralegal training or legal assistant training.
Local and State Trial Court Administrators
Indigency Verification Officers
Bailiffs
Jury Clerk
Court Clerks and Staff
Release Assistance Officers
Scheduling Clerk
taken under advisement. (Note that trial judges can either decide “from the bench”, meaning they will rule immediately on the issues before them during the hearing, or after taking the case under advisement, meaning they will rule through a written decision/opinion letter after spending time researching the law, reviewing the parties written pleadings, and considering the oral arguments).
-
Eisentstein, J., & Jacob, H. (1977). Felony Justice: An organizational analysis of criminal courts. Boston, MA: Little Brown and Co.
↵
-
Spohn, C. & Hemmens, C. (2012)
Courts: A Text/Reader
(2nd ed.). Los Angeles, CA: SAGE Publications, Inc.
↵
-
Berkson, L.C. (2005). J
udicial selection in the United States: A special report.
In E.E. Slotnick (Ed.) Judicial Politics: Readings from Judicature (3d ed., pp. 50). Washington, DC: CQ Press
↵
-
Atkins B.M. & Glick, H.R. (1974). Formal judicial recruitment and state supreme court decisions.
American Politics Quarterly
, 2, 427-449
↵
-
Dubois, P.L. (1986), Accountability, independence, and the selection of state judges: The role of popular judicial elections.
Southwestern Law Journal
, 40, 31-52
↵
-
Nagel, S. (1975).
Improving the legal process
. Lexington, MA: Lexington Books.
↵


5.5: Power Series Distributions
Power Series Distributions are discrete distributions on (a subset of) \( \N \) constructed from power series. This class of distributions is important because most of the special, discrete distributions are power series distributions.
Basic Theory
Power Series
Suppose that \(\bs{a} = (a_0, a_1, a_2, \ldots) \) is a sequence of nonnegative real numbers. We are interested in the power series with \( \bs{a} \) as the sequence of coefficients. Recall first that the partial sum of order \( n \in \N \) is \[ g_n(\theta) = \sum_{k=0}^n a_k \theta^k, \quad \theta \in \R \] The power series \( g \) is then defined by \( g(\theta) = \lim_{n \to \infty} g_n(\theta) \) for \( \theta \in \R \) for which the limit exists, and is denoted \[ g(\theta) = \sum_{n=0}^\infty a_n \theta^n \] Note that the series converges when \( \theta = 0 \), and \( g(0) = a_0 \). Beyond this trivial case, recall that there exists \( r \in [0, \infty] \) such that the series converges absolutely for \( \left|\theta\right| \lt r \) and diverges for \( \left|\theta\right| \gt r \). The number \( r \) is the radius of convergence . From now on, we assume that \( r \gt 0 \). If \( r \lt \infty \), the series may converge (absolutely) or may diverge to \( \infty \) at the endpoint \( r \). At \( -r \), the series may converge absolutely, may converge conditionally, or may diverge.
Distributions
From now on, we restrict \( \theta \) to the interval \( [0, r) \); this interval is our parameter space . Some of the results below may hold when \( r \lt \infty \) and \( \theta = r \), but dealing with this case explicitly makes the exposition unnecessarily cumbersome.
Suppose that \( N \) is a random variable with values in \( \N \). Then \( N \) has the power series distribution associated with the function \( g \) (or equivalently with the sequence \( \bs{a} \)) and with parameter \( \theta \in [0, r) \) if \( N \) has probability density function \( f_\theta \) given by \[ f_\theta(n) = \frac{a_n \theta^n}{g(\theta)}, \quad n \in \N \]
Proof
To show that \( f_\theta \) is a valid discrete probability density function, note that \( a_n \theta^n \) is nonnegative for each \( n \in \N \) and \( g(\theta) \), by definition, is the normalizing constant for the sequence \( \left(a_n \theta^n: n \in \N\right) \).
Note that when \( \theta = 0 \), the distribution is simply the point mass distribution at \( 0 \); that is, \( f_0(0) = 1 \).
The distribution function \( F_\theta \) is given by \[ F_\theta(n) = \frac{g_n(\theta)}{g(\theta)}, \quad n \in \N \]
Proof
This follows immediately from the definitions since \( F_\theta(n) = \sum_{k=0}^n f_\theta(k) \) for \( n \in \N \)
Of course, the probability density function \( f_\theta \) is most useful when the power series \( g(\theta) \) can be given in closed form, and similarly the distribution function \( F_\theta \) is most useful when the power series and the partial sums can be given in closed form
Moments
The moments of \( N \) can be expressed in terms of the underlying power series function \( g \), and the nicest expression is for the factorial moments. Recall that the permutation formula is \( t^{(k)} = t (t - 1) \cdots (t - k + 1) \) for \( t \in \R \) and \( k \in \N \), and the factorial moment of \( N \) of order \( k \in \N \) is \( \E\left(N^{(k)}\right) \).
For \( \theta \in [0, r) \), the factorial moments of \( N \) are as follows, where \( g^{(k)} \) is the \( k \)th derivative of \( g \). \[ \E\left(N^{(k)}\right) = \frac{\theta^k g^{(k)}(\theta)}{g(\theta)}, \quad k \in \N \]
Proof
Recall that a power series is infinitely differentiable in the open interval of convergence, and that the derivatives can be taken term by term. Thus \[ \E\left(N^{(k)}\right) = \sum_{n=0}^\infty n^{(k)} \frac{a_n \theta^n}{g(\theta)} = \frac{\theta^k}{g(\theta)} \sum_{n=k}^\infty a_k n^{(k)} \theta^{n-k} = \frac{\theta^k}{g(\theta)} g^{(k)}(\theta) \]
The mean and variance of \( N \) are
- \( \E(N) = \theta g^\prime(\theta) \big/ g(\theta) \)
- \( \var(N) = \theta^2 \left(g^{\prime\prime}(\theta) \big/ g(\theta) - \left[g^\prime(\theta) \big/ g(\theta)\right]^2\right) \)
Proof
- This follows from the previous result on factorial moments with \( k = 1 \).
- This also follows from the previous result since \( \var(N) = \E\left(N^{(2)}\right) + \E(N)[1 - \E(N)] \).
The probability generating function of \( N \) also has a simple expression in terms of \( g \).
For \( \theta \in (0, r) \), the probability generating function \( P \) of \( N \) is given by \[ P(t) = \E\left(t^N\right) = \frac{g(\theta t)}{g(\theta)}, \quad t \lt \frac{r}{\theta} \]
Proof
For \( t \in (0, r / \theta) \), \[ P(t) = \sum_{n=0}^\infty t^n f_\theta(n) = \frac{1}{g(\theta)} \sum_{n=0}^\infty a_n (t \theta)^n = \frac{g(t \theta)}{g(\theta)} \]
Relations
Power series distributions are closed with respect to sums of independent variables.
Suppose that \( N_1 \) and \( N_2 \) are independent, and have power series distributions relative to the functions \( g_1 \) and \( g_2 \), respectively, each with parameter value \( \theta \lt \min\{r_1, r_2\} \). Then \( N_1 + N_2 \) has the power series distribution relative to the function \( g_1 g_2 \), with parameter value \( \theta \).
Proof
A direct proof is possible, but there is an easy proof using probability generating functions. Recall that the PGF of the sum of independent variables is the product of the PGFs. Hence the PGF of \( N_1 + N_2 \) is \[ P(t) = P_1(t) P_2(t) = \frac{g_1(\theta t)}{g_1(\theta)} \frac{g_2(\theta t)}{g_2(\theta)} = \frac{g_1(\theta t) g_2(\theta t)}{g_1(\theta) g_2(\theta)}, \quad t \lt \min\left\{\frac{r_1}{\theta}, \frac{r_2}{\theta}\right\} \] The last expression is the PGF of the power series distribution relative to the function \( g_1 g_2 \), at \( \theta \).
Here is a simple corollary.
Suppose that \( (N_1, N_2, \ldots, N_k) \) is a sequence of independent variables, each with the same power series distribution, relative to the function \( g \) and with parameter value \( \theta \lt r \). Then \( N_1 + N_2 + \cdots + N_k \) has the power series distribution relative to the function \( g^k \) and with parameter \( \theta \).
In the context of this result, recall that \( (N_1, N_2, \ldots, N_k) \) is a random sample of size \( k \) from the common distribution.
Examples and Special Cases
Special Distributions
The Poisson distribution with rate parameter \( \lambda \in [0, \infty) \) is a power series distribution relative to the function \( g(\lambda) = e^\lambda \) for \( \lambda \in [0, \infty) \).
Proof
This follows directly from the definition, since the PDF of the Poisson distribution with parameter \( \lambda \) is \( f(n) = e^{-\lambda} \lambda^n / n! \) for \( n \in \N \).
The geometric distribution on \( \N \) with success parameter \( p \in (0, 1] \) is a power series distribution relative to the function \( g(\theta) = 1 \big/ (1 - \theta) \) for \( \theta \in [0, 1) \), where \( \theta = 1 - p \).
Proof
This follows directly from the definition, since the PDF of the geometric distribution on \( \N \) is \( f(n) = (1 - p)^n p = (1 - \theta) \theta^n \) for \( n \in \N \).
For fixed \( k \in (0, \infty) \), the negative binomial distribution on \( \N \) with with stopping parameter \( k \) and success parameter \( p \in (0, 1] \) is a power series distribution relative to the function \(g(\theta) = 1 \big/ (1 - \theta)^k \) for \( \theta \in [0, 1) \), where \( \theta = 1 - p \).
Proof
This follows from the result above on sums of IID variables , but can also be seen directly, since the PDF is \[ f(n) = \binom{n + k - 1}{k - 1} p^k (1 - p)^{n} = (1 - \theta)^k \binom{n + k - 1}{k - 1} \theta^n, \quad n \in \N \]
For fixed \( n \in \N_+ \), the binomial distribution with trial parameter \( n \) and success parameter \( p \in [0, 1) \) is a power series distribution relative to the function \( g(\theta) = \left(1 + \theta\right)^n \) for \( \theta \in [0, \infty) \), where \( \theta = p \big/ (1 - p) \).
Proof
Note that the PDF of the binomial distribution is \[ f(k) = \binom{n}{k} p^k (1 - p)^{n - k} = (1 - p)^n \binom{n}{k} \left(\frac{p}{1 - p}\right)^k = \frac{1}{(1 + \theta)^n} \binom{n}{k} \theta^k, \quad k \in \{0, 1, \ldots, n\} \] where \( \theta = p / (1 - p) \). This shows that the distribution is a power series distribution corresponding to the function \( g(\theta) = (1 + \theta)^n \).
The logarithmic distribution with parameter \( p \in [0, 1) \) is a power series distribution relative to the function \( g(p) = -\ln(1 - p) \) for \( p \in [0, 1) \).
Proof
This follows directly from the definition, since the PDF is \[ f(n) = \frac{1}{-\ln(1 - p)} \frac{1}{n} p^n, \quad n \in \N \]


3.14: Sentence Construction
- Explain techniques for writing effective sentences
So far we have discussed organizational practices for strong writing and the importance of keeping the audience in mind. We’ve also analyzed appropriate tone and language choices for academic discourse. Now, let’s talk about the actual writing itself.
Two key characteristics of effective academic writing are that it is precise and concise. This precision and concision must be evident at all levels, from the overall document, to paragraphing, to sentence structure to word choice, and even to punctuation. Every word or phrase should have a distinct and useful purpose.
Write Concise Sentences
As you write, always ask yourself if you are spending your readers’ time wisely. Are you writing unnecessarily complex and confusing sentences, or using 50 words when five would do? If a sentence is already plain and direct, there’s no need to fluff it up. Flowery words and phrases obscure your ideas: when writing, being concise is key. For example, why write, “Cats have a tendency toward sleeping most of the day” when you could simply write, “Cats usually sleep most of the day”? How about changing “The 12th day of the month of April” to “April 12th?” Try to pick out such sentences and substitute simpler ones.
But wait—don’t you need to inflate your text so you can meet the minimum word count? Wouldn’t it be better to use “due to the fact that” for “because” and “in addition to” for “and,” since these phrases use far more words? No! Any experienced reader will instantly see through these efforts and will likely become irritated by the resulting “flabby” prose. If you are having trouble meeting the minimum word count, a far better solution is to add more examples, details, quotations, or perspectives.
When you are succinct in your writing, you want to avoid extra, unnecessary words. For example, you don’t need to talk about the “positive benefits” of a program in your community, because the word “benefits” already implies that it is positive. Some examples of these redundant phrases are listed below.
| Redundancies | ||
| combine/join together | fill completely | unite as one |
| finish entirely | refer/return/revert bac k to | emphasize/stress strongly |
| examine (closely) | suddenly interrupt | better/further enhance |
| eventually evolve over time | strictly forbid | rely/depend heavily |
| plan ahead | harshly condemn | protest against |
| completely surround on all sides | estimate/approximate roughly | gather/assemble together |
| clearly articulate | carefully consider | successfully prove |
| future plan | mutual agreement | years of age |
| in actual fact | positive benefits | end result/product |
Write Clear Sentences
Students sometimes worry that their sentences don’t sound smart enough and they feel like they need to use the thesaurus to find fancy words instead of using their natural vocabulary. Fancy words and complicated sentences are not always better. Clear sentences are strong sentences.
Compare these two sentences (the first is taken from President John F. Kennedy’s inaugural address):
- Do not ask what your country can do for you; ask what you can do for your country.

Although the second sentence is longer and harder to grasp, that doesn’t make it more intelligent. In fact, it’s far more impressive to write a complex thought in simple prose than vice versa. Beware, however, that you do not lose meaning when you make a sentence simpler; cut out only the most unnecessary “fluffy” adjectives, but don’t sacrifice being descriptive.
Clear writing involves knowing what you want to say before you say it. So a lack of clarity often comes from unclear thinking or poor planning. This, unfortunately, leads to confused or annoyed readers. For many of us, our ideas become more clear as we draft our essays. That’s why the revision process is so important. As you clarify your ideas, you need to ensure that each sentence conveys one idea, and that each paragraph thoroughly develops one unified concept.
Avoid vague and unnecessary words
Are you very hungry?  Is your English class really great?  Words like very and really don’t say much. Instead of using stock or clichéd phrases, try to be more specific about what you mean. Below are some examples of overused intensifiers and clichés you should be wary of.
| Overused Intensifiers | |||||
| absolutely | actually | assuredly | certainly | clearly | completely |
| considerably | definitely | effectively | extremely | fundamentally | drastically |
| highly | in fact | incredibly | inevitably | indeed | interestingly |
| markedly | naturally | of course | particularly | significantly | surely |
| totally | utterly | very | really | remarkably | tremendously |
| Clichés | Alternatives |
| as plain as day | plainly, obvious, clear |
| ballpark figure | about, approximately |
| few and far between | rare, infrequent |
| needless to say | of course, obviously |
| last but not least | finally, lastly |
| as far as ___ is concerned | according to |
Vary the Length of your Sentences
Your sentences should vary in length (short sentence). Avoid having too many long sentences because they take longer to read and are often more complex (longer sentence). Reserve the short sentences for main points and use longer sentences for supporting points that clarify or explain cause and effect relationships (longer sentence). If you feel the sentence is too long, break it into two sentences (medium sentence). You do not want your reader to have to read a sentence twice to understand it (short sentence). (Note: you’ll learn more in a later module about using colons and semi-colons to structure your complicated and longer sentences so that don’t get out of control, grammatically.)
Name the People
Directly state who or what group is acting in your sentences. Note the contrast in power and clarity among the sentences below
- Without people: A citywide ban on indoor smoking in Duluth originally caused a marked drop in bar patronage.
- With people: When the Duluth City Council passed a citywide ban on indoor smoking, many people stopped going to bars.
Use Active Verbs
Consider replacing “be-verbs” (is, am, are, was, were, be, has/have been) with active verbs that allow you to compose powerful sentences shaped around action. Below the italics are the same sentences that have been transformed with active verbs.
- To be : The sharp rise in fuel prices is a serious challenge to trucking firms. It makes it hard for them to provide timely service to customers and to meet payroll expenses.
- Active : Sharply rising fuel prices challenge trucking firms by causing delays in customer service and payroll.
- To be : Primary causes of the rise in fuel prices are an issue of confusion for many citizens. They don’t know how to fight the rise because they don’t know its cause.
- Active : Primary causes of rising fuel prices elude many citizens, making them unaware of how to fight the increase.
Watch this video for tips and more examples of how to avoid wordy or redundant writing.
You can view the transcript for “Avoiding Wordiness and Redundancy” here (opens in new window) .
Use Parallel Structure Effectively
Simply put, parallellism is the practice of using the same patterns in words and structures in order to provide balance to sentences and paragraphs.
Parallel structure can be applied to a single sentence, a paragraph, or even multiple paragraphs. Compare the two following sentences:
- Yara loves running, to swim, and biking.
- Yara loves running, swimming, and biking.
Was the second sentence a smoother read than the first? The second sentence uses parallelism—all three verbs are gerunds (running, swimming, biking) —whereas in the first sentence two are gerunds (running and biking) and one is an infinitive (to swim). When reading the first sentence, it’s easy to trip up over the mismatching items. Using strong parallel structure improves writing style and readability and makes sentences easier to process.
Compare the following examples:
-
Lacking parallelism: “She likes cooking, jogging, and to read.”
- Parallel: “She likes cooking, jogging, and reading.”
- Parallel: “She likes to cook, jog, and read.”
-
Lacking parallelism: “The dog ran across the yard and jumped over the fence, and
down the alley he sprinted
.”
- Parallel: “The dog ran across the yard, jumped over the fence, and sprinted down the alley .”
The parallel examples sound much better to your ears.
You can also apply parallelism across a passage:
Manuel painted eight paintings in the last week. Jennifer sculpted five statues in the last month. Zama wrote fifteen songs in the last two months.
Each of the sentences in the preceding paragraph has the same structure: Name + -ed verb + number of things + in the past time period. When using parallelism across multiple sentences, be sure that you’re using it well. If you aren’t careful, you can stray into being repetitive.
Look at the following items. Identify and address any issues with parallelism.
- Low self-esteem can manifest itself in various behaviors. Some individuals may become paralyzed at the prospect of making a decision. Other individuals may bend their wills to others’ in order to keep the peace. Yet another symptom is the retreat from society as a whole—to become isolated.
- The influence of genetics on human behavior has been shown through studies of twins who were separated at birth. Not only do these sets of individuals share many physical characteristics, but they also tend to have the same sort of interests and biases and utilize similar mental processes.
- Nocturne in Black and Gold (The Falling Rocket) by James Abbott McNeil Whistler is very emblematic of the impressionist movement: its dark colors, contrast, and lack of definite form reflect the attitudes of the day.
[practice-area rows=”4″][/practice-area]
[reveal-answer q=”486627″]Show Answer[/reveal-answer]
[hidden-answer a=”486627″]
-
The first two sentences that identify behaviors of low self-esteem both start with the construction adjective +
individuals
+
may
verb. Changing the third sentence to match this construction will create a stronger introduction to the paper:
- Low self-esteem can manifest itself in various behaviors. Some individuals may become paralyzed at the prospect of making a decision. Other individuals may bend their wills to others’ in order to keep the peace. Yet other individuals may retreat from society as a whole and become isolated.
-
If you wanted to make the whole sentence more parallel, you may want to adjust the sentence to match the structure of the phrase “Not only do these sets of individuals share many physical characteristics”:
- Not only do these sets of individuals share many physical characteristics, but they also share similar interests, biases, and mental processes.
-
The items in “its dark colors, contrast, and lack of definite form” don’t quite match up. While they are all nouns, each item has a different structure (adjective noun, noun, noun +
of
+ adjective noun). Here are a couple suggestions for more parallel items:
- Its depth of color, intensity of contrast, and lack of form reflect the attitudes of the day.
- Its dark colors, intense contrast, and lax forms reflect the attitudes of the day.
[/hidden-answer]
Effective Use of Parallelism and Repetition
Parallelism can also involve repeated words or repeated phrases. These uses are part of “rhetoric” (a field that focuses on persuading readers). Here are a few examples of repetition:
- “ The inherent vice of capitalism is the unequal sharing of blessings; the inherent virtue of socialism is the equal sharing of miseries.” —Winston Churchill
- “Let every nation know, whether it wishes us well or ill, that we shall pay any price, bear any burden, meet any hardship, support any friend, oppose any foe to assure the survival and the success of liberty.” —John F. Kennedy
- “And that government of the people, by the people, for the people , shall not perish from the earth.” —Abraham Lincoln, Gettysburg Address
When used this way, parallelism makes your writing or speaking much stronger. These repeated phrases seem to bind the work together and make it more powerful—and more inspiring.
Contributors and Attributions
- Modification, adaptation, and original content. Authored by : Audrey Fisch for Lumen Learning. Provided by : Lumen Learning. License : CC BY: Attribution
- Sentence Structure. Authored by : Chris Manning, Sally Pierce, and Melissa Lucken . Located at : https://pb.openlcc.net/expressionandinquiry/chapter/7-2-sentence-structure/ . Project : Expression and Inquiry. License : CC BY: Attribution
- Analyze Each Part of Your Paper. Authored by : Marianne Botos, Lynn McClelland, Stephanie Polliard, Pamela Osback . Located at : https://pvccenglish.files.wordpress.com/2010/09/eng-101-inside-pages-proof2-no-pro.pdf . Project : Horse of a Different Color: English Composition and Rhetoric . License : CC BY: Attribution
- Communicating with Precision. Authored by : Suzan Last. Located at : https://pressbooks.bccampus.ca/technicalwriting/chapter/communicatingprecision/#fig2.2.1 . Project : Technical Writing. License : CC BY: Attribution
- Avoiding Wordiness and Redundancy. Provided by : WUWriting Center. Located at : https://www.youtube.com/watch?time_continue=49&v=sxxjNtM9ZpA&feature=emb_logo . License : Other . License Terms : Standard YouTube License


8.6: Examining False Confessions
As noted at the beginning of this chapter, the goal of ethical interviewing, questioning, and interrogation is to elicit the truth, and the truth can include statements that are either inculpatory confessions of guilt or exculpatory denial of involvement in a crime. Whenever an investigator has interrogated a suspect, and a confession of guilt has been obtained, that investigator needs to take some additional steps to ensure that the confession can be verified as truthful before it goes to court. These additional steps are required because, although the investigator has not used any illegal or unethical techniques, the court will still consider whether the accused, for some reason, has confessed to a crime they did not commit. A skilled defense lawyer will often present arguments alleging that psychological stresses of guilt or hopelessness from exposure to overwhelming evidence have been used to persuade a suspect to confess to a crime they did not commit. In such cases, it is helpful for the court to hear any additional statements made by the accused, such as those that reveal that the suspect had direct knowledge of the criminal event that could only be known to the criminal responsible.
In police investigations, there are many details of the criminal event that will be known to the police through their examination of the crime scene or through the interview with witnesses or victims. These details can include the actual way the crime was committed, such as the sequence of events, the tools used in the crime; or the means of entry, the path of entry/exit, along with other obscure facts that could only be known by the actual perpetrator. There are opportunities in a crime scene examination for the investigator to observe one or more unique facts that can be withheld as “hold back evidence.” This hold-back evidence is not made part of reports or media release and is kept exclusively to test for false confessions. Confessing to the crime is one thing, but confessing to the crime and revealing intimate details is much more compelling to the court. Regardless of the effort and care that investigators take to not end up with a false confession, they still occur, and there are some more common scenarios where false confessions happen. It is important for an investigator to consider these possibilities when a confession is obtained. These situations are:
- The confessor was enlisted to take the blame — On occasions where persons are part of organized crime, a person of lower status within the group is assigned or sacrificed to take the blame for a crime in place of a person of higher status. These organizational pawns are usually persons with a more minor criminal history or are young offenders, as they are likely to receive a lesser sentence for the offense.
- The Sacrificial Confessor — Like the confessor enlisted in an organized criminal organization, there is another type of sacrificial confessor; the type who steps forward to take the blame to protect a friend or loved one. These are voluntary confessors, but their false confession can be exposed by questioning the confessor about the hold back details of the event.
- The Mentally Ill False Confessor — This type of false confessor is encountered when there is significant media attention surrounding a crime. As Pickersgill (2015) noted, an innocent person may voluntarily provide a false confession because of a pathological need for notoriety or the need to self-punish due to guilt over an unrelated past offense. Additionally, those suffering from psychosis, endogenous depression, and Munchausen Syndrome may falsely confess to a crime they did not commit (Abed, 2105) . As with other false confessors, these people can be discovered using hold-back detail questioning.


8.5: Tumor Suppressor Genes
More than 30 genes are classified as tumor suppressors . The normal functions of these genes include repair of DNA, induction of programmed cell death ( apoptosis ) and prevention of abnormal cell division. In contrast to proto-oncogenes, in tumor suppressors it is loss-of-function mutations that contribute to the progression of cancer. This means that tumor suppressor mutations tend to be recessive, and thus both alleles must be mutated in order to allow abnormal growth to proceed. It is perhaps not surprising that mutations in tumor suppressor genes, are more likely than oncogenes to be inherited. An example is the tumor suppressor gene, BRCA1 , which is involved in DNA-repair. Inherited mutations in BRCA1 increase a woman’s lifetime risk of breast cancer by up to seven times, although these heritable mutations account for only about 10% of breast cancer. Thus, sporadic rather than inherited mutations are the most common sources of both oncogenes and disabled tumor suppressor genes.
An important tumor suppressor gene is a transcription factor named p53 . Other proteins in the cell sense DNA damage, or abnormalities in the cell cycle and activate p53 through several mechanisms including phosphorylation (attachment of phosphate to specific site on the protein) and transport into the nucleus. In its active form, p53 induces the transcription of genes with several different types of tumor suppressing functions, including DNA repair, cell cycle arrest, and apoptosis. Over 50% of human tumors contain mutations in p53. People who inherit only one function copy of p53 have a greatly increased incidence of early onset cancer. However, as with the other cancer related genes we have discussed, most mutations in p53 are sporadic, rather than inherited. Mutation of p53, through formation of pyrimidine dimers in the genes following exposure to UV light, has been causally linked to squamous cell and basal cell carcinomas (but not melanomas, highlighting the variety and complexities of mechanisms that can cause cancer).
Inherited Cancer Predisposition
While cancer itself is not inherited, mutations that can drive cancer can be passed from parent to offspring. Many of the commonly inherited cancer-associated mutations are in tumor suppressor genes. In most cases, individuals inherit only one mutant allele of the tumor suppressor; they are heterozygous for the recessive mutation. However, if the second copy (due to random chance) becomes mutated or deleted in a somatic cell, that cell (and all its descendants) now lack the tumor suppressor entirely. This process is known as loss-of-heterozygosity.
Contributors and Attributions
-
Dr. Todd Nickle and Isabelle Barrette-Ng (Mount Royal University) The content on this page is licensed under CC SA 3.0 licensing guidelines.


9.1.13: Suggested Resources
9.1.2 Entrepreneurial Marketing and the Marketing Mix
American Marketing Association: https://www.ama.org
Small Business Administration: https://www.sba.gov/
9.1.4 Marketing Techniques and Tools for Entrepreneurs
AMA Digital Marketing Certification: https://www.ama.org/events-training/...ification.aspx
AMA on Demand course: Digital Marketing: Delivering a Custom Experience: www.ama.org/events-training/...ce-051717.aspx
Google Ads: https://ads.google.com/home/
Google Analytics: https://analytics.google.com/analyti...on/#/provision
Hubspot Google Ads guide: https://blog.hubspot.com/marketing/google-adwords-ppc
9.1.5 Entrepreneurial Branding
Hubspot’s Beginner’s guide to branding: https://blog.hubspot.com/agency/deve...SHcJI2E.mailto
9.1.6 Marketing Strategy and the Marketing Plan
Business Model Canvas: https://strategyzer.com/canvas/business-model-canvas
Hubspot Marketing Plan templates: https://blog.hubspot.com/marketing/m...late-generator
Small Business Administration: https://www.sba.gov/business-guide/m...arketing-sales
9.1.7 Sales and Customer Service
Cialdini online tools: https://www.influenceatwork.com/
Hoffman Sales Training: https://sellhoffman.com/
Neil Rackman: http://neilrackham.com/
Spin Selling: https://blog.hubspot.com/sales/spin-...ultimate-guide
Zig Ziglar: https://www.ziglar.com/
The State of Customer Service: https://offers.hubspot.com/state-of-...8-5de8fcbb40c1
Cialdini, R. B. (2001). Influence: Science and Practice (4th ed.). Boston: Allyn & Bacon: Explains some aspects of the sales process in a fun and fact-based manner.


14.E: DNA Structure and Function (Exercises)
14.1: Historical Basis of Modern Understanding
Modern understandings of DNA have evolved from the discovery of nucleic acid to the development of the double-helix model. In the 1860s, Friedrich Miescher, a physician by profession, was the first person to isolate phosphate-rich chemicals from white blood cells or leukocytes. He named these chemicals (which would eventually be known as RNA and DNA) nuclein because they were isolated from the nuclei of the cells.
Review Questions
If DNA of a particular species was analyzed and it was found that it contains 27 percent A, what would be the percentage of C?
- 27 percent
- 30 percent
- 23 percent
- 54 percent
- Answer
-
C
The experiments by Hershey and Chase helped confirm that DNA was the hereditary material on the basis of the finding that:
- radioactive phage were found in the pellet
- radioactive cells were found in the supernatant
- radioactive sulfur was found inside the cell
- radioactive phosphorus was found in the cell
- Answer
-
D
Free Response
Explain Griffith's transformation experiments. What did he conclude from them?
- Answer
-
Live R cells acquired genetic information from the heat-killed S cells that “transformed” the R cells into S cells.
Why were radioactive sulfur and phosphorous used to label bacteriophage in Hershey and Chase's experiments?
- Answer
-
Sulfur is an element found in proteins and phosphorus is a component of nucleic acids.
14.2: DNA Structure and Sequencing
The building blocks of DNA are nucleotides. The important components of the nucleotide are a nitrogenous base, deoxyribose (5-carbon sugar), and a phosphate group. The nucleotide is named depending on the nitrogenous base. The nitrogenous base can be a purine such as adenine (A) and guanine (G), or a pyrimidine such as cytosine (C) and thymine (T).
Review Questions
DNA double helix does not have which of the following?
- antiparallel configuration
- complementary base pairing
- major and minor grooves
- uracil
- Answer
-
D
In eukaryotes, what is the DNA wrapped around?
- single-stranded binding proteins
- sliding clamp
- polymerase
- histones
- Answer
-
D
Free Response
Provide a brief summary of the Sanger sequencing method.
- Answer
-
The template DNA strand is mixed with a DNA polymerase, a primer, the 4 deoxynucleotides, and a limiting concentration of 4 dideoxynucleotides. DNA polymerase synthesizes a strand complementary to the template. Incorporation of ddNTPs at different locations results in DNA fragments that have terminated at every possible base in the template. These fragments are separated by gel electrophoresis and visualized by a laser detector to determine the sequence of bases.
Describe the structure and complementary base pairing of DNA.
- Answer
-
DNA has two strands in anti-parallel orientation. The sugar-phosphate linkages form a backbone on the outside, and the bases are paired on the inside: A with T, and G with C, like rungs on a spiral ladder.
14.3: Basics of DNA Replication
The elucidation of the structure of the double helix provided a hint as to how DNA divides and makes copies of itself. This model suggests that the two strands of the double helix separate during replication, and each strand serves as a template from which the new complementary strand is copied. What was not clear was how the replication took place. There were three models suggested: conservative, semi-conservative, and dispersive.
Review Questions
Meselson and Stahl's experiments proved that DNA replicates by which mode?
- conservative
- semi-conservative
- dispersive
- none of the above
- Answer
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B
If the sequence of the 5'-3' strand is AATGCTAC, then the complementary sequence has the following sequence:
- 3'-AATGCTAC-5'
- 3'-CATCGTAA-5'
- 3'-TTACGATG-5'
- 3'-GTAGCATT-5'
- Answer
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C
Free Response
How did the scientific community learn that DNA replication takes place in a semi-conservative fashion?
- Answer
-
Meselson’s experiments with E. coli grown in 15 N deduced this finding.
14.4: DNA Replication in Prokaryotes
DNA replication has been extremely well studied in prokaryotes primarily because of the small size of the genome and the mutants that are available. E. coli has 4.6 million base pairs in a single circular chromosome and all of it gets replicated in approximately 42 minutes, starting from a single origin of replication and proceeding around the circle in both directions. This means that approximately 1000 nucleotides are added per second. The process is quite rapid and occurs without many mistake
Review Questions
Which of the following components is not involved during the formation of the replication fork?
- single-strand binding proteins
- helicase
- origin of replication
- ligase
- Answer
-
D
Which of the following does the enzyme primase synthesize?
- DNA primer
- RNA primer
- Okazaki fragments
- phosphodiester linkage
- Answer
-
B
In which direction does DNA replication take place?
- 5'-3'
- 3'-5'
- 5'
- 3'
- Answer
-
A
Free Response
DNA replication is bidirectional and discontinuous; explain your understanding of those concepts.
- Answer
-
At an origin of replication, two replication forks are formed that are extended in two directions. On the lagging strand, Okazaki fragments are formed in a discontinuous manner.
What are Okazaki fragments and how they are formed?
- Answer
-
Short DNA fragments are formed on the lagging strand synthesized in a direction away from the replication fork. These are synthesized by DNA pol.
If the rate of replication in a particular prokaryote is 900 nucleotides per second, how long would it take 1.2 million base pair genomes to make two copies?
- Answer
-
1333 seconds or 22.2 minutes.
Explain the events taking place at the replication fork. If the gene for helicase is mutated, what part of replication will be affected?
- Answer
-
At the replication fork, the events taking place are helicase action, binding of single-strand binding proteins, primer synthesis, and synthesis of new strands. If there is a mutated helicase gene, the replication fork will not be extended.
What is the role of a primer in DNA replication? What would happen if you forgot to add a primer in a tube containing the reaction mix for a DNA sequencing reaction?
- Answer
-
Primer provides a 3'-OH group for DNA pol to start adding nucleotides. There would be no reaction in the tube without a primer, and no bands would be visible on the electrophoresis.
14.5: DNA Replication in Eukaryotes
Eukaryotic genomes are much more complex and larger in size than prokaryotic genomes. The human genome has three billion base pairs per haploid set of chromosomes, and 6 billion base pairs are replicated during the S phase of the cell cycle. There are multiple origins of replication on the eukaryotic chromosome; humans can have up to 100,000 origins of replication
Review Questions
The ends of the linear chromosomes are maintained by
- helicase
- primase
- DNA pol
- telomerase
- Answer
-
D
Free Response
How do the linear chromosomes in eukaryotes ensure that its ends are replicated completely?
- Answer
-
Telomerase has an inbuilt RNA template that extends the 3' end, so primer is synthesized and extended. Thus, the ends are protected.
14.6: DNA Repair
DNA replication is a highly accurate process, but mistakes can occasionally occur, such as a DNA polymerase inserting a wrong base. Uncorrected mistakes may sometimes lead to serious consequences, such as cancer. Repair mechanisms correct the mistakes. In rare cases, mistakes are not corrected, leading to mutations; in other cases, repair enzymes are themselves mutated or defective.
Review Questions
During proofreading, which of the following enzymes reads the DNA?
- primase
- topoisomerase
- DNA pol
- helicase
- Answer
-
C
The initial mechanism for repairing nucleotide errors in DNA is ________.
- mismatch repair
- DNA polymerase proofreading
- nucleotide excision repair
- thymine dimers
- Answer
-
B
Free Response
What is the consequence of mutation of a mismatch repair enzyme? How will this affect the function of a gene?
- Answer
-
Mutations are not repaired, as in the case of xeroderma pigmentosa. Gene function may be affected or it may not be expressed.


11.1: Key Positions
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The debate about human protection hinges on the issue of whether a state’s right to be secure and free from external interference should be conditional on its fulfilment of certain responsibilities to its citizens, most obviously protection from mass violence. We might plot various responses to this question along two axes – the first relating to our conception of whether moral progress is possible in world politics (more optimistic or more pessimistic) and the other relating to which actors should be privileged (states or individuals). The first axis refers to the way we understand the potentiality and limits of world politics. Some approaches are prefaced on an optimistic vision that dialogue between communities makes moral consensus and shared purposes possible (Linklater 1998). The alternative is a fatalistic or ‘tragic’ conception of world politics based on the view that the world is composed of culturally distinct units with different values that pursue their own, distinct goals with limited possibility for cooperation (Lebow 2003). This account is sceptical of progress, doubts that morality does (or should) play a role in world affairs, and predicts that efforts to spread moral values will prove costly and counterproductive. The second axis relates to what sort of actor should be privileged – states or individuals. It is common for theories of International Relations to privilege the state on the grounds that it is the principal actor in world affairs, the main source of order, and the bearer of international rights and responsibilities. An alternative perspective privileges individuals as the only irreducible actor. Individuals cannot be means to an end; they must be seen as ends in themselves. From these two axes, we derive four ethical positions.
1. Optimistic and state-centred: a rule-governed international society
This accepts that progress in international affairs is possible, but that in a world characterised by radical difference the basis for progress should be voluntary cooperation between states in a rule-governed international society of states. Perspectives housed in this quadrant hold that the common good is best served by privileging the rules of co-existence found in the UN charter. This focuses especially on the legal ban on the use force and ensuring that the two exceptions to that ban are not abused (Articles 42 and 51). According to this view, allowing states a free hand to promote human protection in other states would create disorder by allowing wars to protect and impose one state’s values on others. Disorder would weaken the international system, undermine human development, and make cooperation between states more difficult. This view dovetails with the commonly held legal view that there is a general prohibition on interference except when authorised by the UN Security Council. This account is unnecessarily pessimistic about the capacity of states to reach consensus about shared moral principles. There is relatively little evidence to suggest that the incremental expansion of collective action into new areas of peace and security, such as human protection, has given rise to greater disorder. This account also overlooks the flexibility built into the Security Council to redefine its role in international peace and security to take account of changing conditions, should it decide to do so.
2. Tragic and state-centred: the realities of life in an international state of nature
This perspective espouses a communitarian view about the diversity of communities and the relativity of values, but rejects even basic claims about the capacity of states to agree meaningful rules of co-existence, let alone substantive rules. This account suggests that norms and rules are irrelevant as causes of behaviour when set against material factors such as economic gain, territory and the national interest. To paraphrase a prominent realist, Edward Hallett Carr, international interference for ‘protection’ would in fact be nothing other than the interests and preferences of the powerful masquerading as universal morality. This account counsels against humanitarian activism. It doubts the capacity of states to be altruistic and thus sees all state action as exercises in the self-interested use of power that undermines world order. Few, if any, states openly subscribe to this approach. Accepting that states tend to do only what they perceive to be in their interests does not get us very far analytically. To understand why states act in certain ways we need to understand variation in the way that states (even similar states) construct their interests and this requires a deeper understanding of the factors that guide national decision-making.
3. Optimistic and individual-centred: defending humanity and our common values
The third perspective is the one most positively disposed to advancing human protection. It is usually associated with liberalism and a broader cosmopolitan view that all humans belong to a single world community. It holds that states have positive duties to protect foreigners from tyranny as well as a right to do so since human rights are universal rights that ought to be defended everywhere. According to theorists in this tradition, states have agreed certain minimum standards of behaviour. As such, action across borders to support human protection is not about imposing the will of a few powerful states but about protecting and enforcing basic values and/or the collective will of international society. While this view is on strong ground when it comes to the theoretical right of the UN Security Council to mandate enforcement action, when it comes to a more generalised right to intervention the theory is contradicted by strong bodies of legal thought and state practice that counsel against it. Not surprisingly, therefore, liberal cosmopolitans tend to be divided on whether there is such a general right of intervention outside the boundaries of existing international law.
4. Tragic and people-centred: the distinctiveness of humanitarian action
These accounts tend to privilege traditional forms of humanitarian assistance and exhibit deep scepticism about military intervention on the grounds that it tends to make situations worse and reinforces the militarist ideals that are among the chief underlying causes of humanitarian crises in the first place. Precisely because of this scepticism, however, these accounts help to widen our understanding of the tools that might be used to protect populations. In exposing some of the intrinsic limitations of forcible action to promote human protection, these approaches emphasise that interventions are selective, partial and never solely humanitarian. That said, critics question how suffering can be alleviated let alone prevented without taking a political stance and so there are real limits to the physical protection that can be afforded by humanitarian action alone. This ‘individual-centred’ approach is vulnerable to many of the criticisms levelled against the ‘tragic’ conception. Notably, its prescriptions often fall well short of what is needed to protect vulnerable populations.


5.6: Power Rule For Exponents
This rule helps to simplify an exponential expression raised to a power. This rule is often confused with the product rule, so understanding this rule is important to successfully simplify exponential expressions.
For any real number \(a\) and any numbers \(m\) and \(n\), the power rule for exponents is the following:
\((a^m)^n = a^{m\cdot n}\)
Idea:
Given the expression
\(\begin{aligned} &(2^2 )^3 && \text{Use the exponent definition to expand the expression inside the parentheses.} \\ &(2 \cdot 2)^3 && \text{Now use the exponent definition to expand according to the exponent outside the parentheses.}\\ &(2 \cdot 2) \cdot (2 \cdot 2) \cdot (2 \cdot 2) = 2^6 && = 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 = 2^{1+1+1+1+1+1 }= 2^{6} \text{ (Product Rule of Exponents) }\end{aligned}\)
Hence, \((2^2 ) ^3 = 2^{2\cdot 3 }= 2^6\)
Simplify the following expression using the power rule for exponents.
\((−3^4 )^3\)
Solution
\((−3)^{4\cdot 3 }= (−3)^{12}\)
Simplify the following expression using the power rule for exponents.
\((−3^4 )^3\)
Solution
\((5y)^{3\cdot 7 }= (5y)^{21}\)
Simplify the following expression using the power rule for exponents.
\(((−y)^5 )^2\)
Solution
\((−y)^{5\cdot 2 }= (−y)^{10 }= y^{10}\)
Simplify the following expression using the power rule for exponents.
\((x^{−2 })^3\)
Solution
\(x^{−2\cdot 3 }= x^{−6 }= \dfrac{1 }{x^6}\)
Hint: Parentheses in the problem is a strong indicator of simplifying using the power rule for exponents.
Simplify the expression using the power rule for exponents.
- \((x^3 )^5\)
- \(((−y)^3 )^7\)
- \(((−6y)^8 ) ^{−3}\)
- \((x^{−2 }) ^{−3}\)
- \((r^4 )^5\)
- \((−p^7 )^7\)
- \(((3k)^{−3 })^5\)


<IP_ADDRESS>: Quotation Marks
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Quotation Marks
Don’t Forget the Quotation Marks
Quotation marks are how we tell our readers we are including words that aren't our own. Whether we're using dialog or quote material from our research, quotation marks are important punctuation. The reality is that punctuation marks can really make a difference in whether or not you are breaking the law. After all, if you use someone’s words and don't let your readers know you are using someone else’s words, that constitutes plagiarism, which is most certainly illegal.
So, if you have doubts about this whole quotation thing, the following pages will be extremely helpful. This super-cool video can help as well.
Dialog
Quotation Marks with Dialog
You may not find yourself needing to use dialog very often in academic writing, but you may be asked to write narrative essays in some classes, which often contain dialog.
When you use dialog, it’s important to use quotation marks to set apart the speech from the rest of your text. Otherwise, separating the dialog from the rest of the writing can be very confusing for readers.
- This time, my basketball coach said, “I know you can do it.” It turned out he did not really know what he was talking about.
Quoting Sources
Quotation Marks with Quoted Material
You should use quotation marks any time you use words directly from another source. Sometimes, students think putting a citation or reference at the end “covers it,” but you must use quotation marks to indicate borrowed words.
- “Quotation marks serve primarily to tell the reader the exact words someone used” (Hope, 2010, p. 21).
 You should still cite with an in-text citation, but you shouldn’t use quotation marks.
The key to borrowing information from sources is to remember that any words appearing inside quotation marks belong to someone else. Words that do not appear inside quotation marks are assumed to be yours.
Single Quotes
What are those single quotes for?
Now that you know what quotation marks are used for, you may wonder about the single quotation marks—the one that look like ‘this.’
Single quotation marks are used for quotes within quotes, as illustrated in the following example:
The article read, “When the quarterback for the Green Bay Packers was interviewed, he said he was ‘upset’ about the call that affected the game.”
You may even encounter situations where you’ll close single quotation marks and double quotation marks at the same time, leaving you with “something like ‘this.’” Don’t worry if this happens. It is correct. It just means the quote within the quote ended at the same time the main quote ended.


9.4: Which Analysis Should You Conduct?
One of the most important concept that you need to understand is deciding which analysis you should conduct for a particular situation. To help you to figure out the analysis to conduct, there are a series of questions you should ask yourself.
-
Does the problem deal with mean or proportion?
Sometimes the problem states explicitly the words mean or proportion, but other times you have to figure it out based on the information you are given. If you counted number of individuals that responded in the affirmative to a question, then you are dealing with proportion. If you measured something, then you are dealing with mean. -
Does the problem have one or two samples?
So look to see if one group was measured or if two groups were measured. If you have the data sets, then it is usually easy to figure out if there is one or two samples, then there is either one data set or two data sets. If you don’t have the data, then you need to decide if the problem describes collecting data from one group or from two groups. -
If you have two samples, then you need to determine if the samples are independent or dependent.
If the individuals are different for both samples, then most likely the samples are independent. If you can’t tell, then determine if a data value from the first sample influences the data value in the second sample. In other words, can you pair data values together so you can find the difference, and that difference has meaning. If the answer is yes, then the samples are paired. Otherwise, the samples are independent. -
Does the situation involve a hypothesis test or a confidence interval?
If the problem talks about "do the data show", "is there evidence of", "test to see", then you are doing a hypothesis test. If the problem talks about "find the value", "estimate the" or "find the interval", then you are doing a confidence interval.
So if you have a situation that has two samples, independent samples, involving the mean, and is a hypothesis test, then you have a two-sample independent t-test. Now you look up the assumptions and the formula or technology process for doing this test. Every hypothesis test involves the same six steps, and you just have to use the correct assumptions and calculations. Every confidence interval has the same five steps, and again you just need to use the correct assumptions and calculations. So this is why it is so important to figure out what analysis you should conduct.
Data Sources :
AP exam scores . (2013, November 20). Retrieved from wiki.stat.ucla.edu/socr/index...08_APExamScore s
Buy sushi grade fish online . (2013, November 20). Retrieved from http://www.catalinaop.com/
Center for Disease Control and Prevention, Prevalence of Autism Spectrum Disorders - Autism and Developmental Disabilities Monitoring Network. (2008). Autism and developmental disabilities monitoring network-2012. Retrieved from website: www.cdc.gov/ncbddd/autism/doc...nityReport.pdf
Cholesterol levels after heart attack. (2013, September 25). Retrieved from http://www.statsci.org/data/general/cholest.html
Flanagan, R., Rooney, C., & Griffiths, C. (2005). Fatal poisoning in childhood, england & wales 1968-2000. Forensic Science International , 148:121-129, Retrieved from http://www.cdc.gov/nchs/data/ice/fat...ning_child.pdf
Friday the 13th datafile. (2013, November 25). Retrieved from lib.stat.cmu.edu/DASL/Datafil...aythe13th.html
Gettler, L. T., McDade, T. W., Feranil, A. B., & Kuzawa, C. W. (2011). Longitudinal evidence that fatherhood decreases testosterone in human males. The Proceedings of the National Academy of Sciences, PNAS 2011 , doi: 10.1073/pnas.1105403108 Length of NZ rivers. (2013, September 25). Retrieved from http://www.statsci.org/data/oz/nzrivers.html
Lim, L. L. United Nations, International Labour Office. (2002). Female labour-force participation . Retrieved from website: www.un.org/esa/population/pub...ty/RevisedLIMp aper.PDF
Median income of males . (2013, October 9). Retrieved from http://www.prb.org/DataFinder/Topic/...s.aspx?ind=137
Olson, K., & Hanson, J. (1997). Using reiki to manage pain: a preliminary report. Cancer Prev Control , 1(2), 108-13. Retrieved from http://www.ncbi.nlm.nih.gov/pubmed/9765732
Population reference bureau. (2013, October 8). Retrieved from http://www.prb.org/DataFinder/Topic/...gs.aspx?ind=25
Seafood online . (2013, November 20). Retrieved from http://www.allfreshseafood.com/
SOCR 012708 id data hotdogs. (2013, November 13). Retrieved from http://wiki.stat.ucla.edu/socr/index...D_Data_HotDogs
SOCR data nips infantvitK shotdata. (2013, November 16). Retrieved from http://wiki.stat.ucla.edu/socr/index...tVitK_ShotData
SOCR data Oct2009 id ni. (2013, November 16). Retrieved from http://wiki.stat.ucla.edu/socr/index..._Oct2009_ID_NI
Statistics brain. (2013, November 30). Retrieved from http://www.statisticbrain.com/infidelity-statistics/
Student t-distribution. (2013, November 25). Retrieved from lib.stat.cmu.edu/DASL/Stories/student.html


5.2: Derivatives of Extended-Real Functions
For a while (in §§2 and 3), we limit ourselves to extended-real functions. Below, \(f\) and \(g\) are real or extended real (f, \(g : E^{1} \rightarrow E^{*}).\) We assume, however, that they are not constantly infinite on any interval \((a, b), a<b\).
If \(f^{\prime}(p)>0\) at some \(p \in E^{1},\) then
\[x<p<y\]
implies
\[f(x)<f(p)<f(y)\]
for all \(x, y\) in a sufficiently small globe \(G_{p}(\delta)=(p-\delta, p+\delta).\)
Similarly, if \(f^{\prime}(p)<0,\) then \(x<p<y\) implies \(f(x)>f(p)>f(y)\) for \(x, y\) in some \(G_{p}(\delta).\)
- Proof
-
If \(f^{\prime}(p)>0,\) the "0" case in Definition 1 of §1, is excluded, so
\[f^{\prime}(p)=\lim _{x \rightarrow p} \frac{\Delta f}{\Delta x}>0.\]
Hence we must also have \(\Delta f / \Delta x>0\) for \(x\) in some \(G_{p}(\delta)\).
It follows that \(\Delta f\) and \(\Delta x\) have the same sign in \(G_{p}(\delta);\) i.e.,
\[f(x)-f(p)>0 \text { if } x>p \text { and } f(x)-f(p)<0 \text { if } x<p.\]
(This implies \(f(p) \neq \pm \infty.\) Why? Hence
\[x<p<y \Longrightarrow f(x)<f(p)<f(y),\]
as claimed; similarly in case \(f^{\prime}(p)<0. \quad \square\)
If \(f(p)\) is the maximum or minimum value of \(f(x)\) for \(x\) in some \(G_{p}(\delta),\) then \(f^{\prime}(p)=0;\) i.e., \(f\) has a zero derivative, or none at all, at \(p.\)
For, by Lemma 1, \(f^{\prime}(p) \neq 0\) excludes a maximum or minimum at \(p.\) (Why?)
Note 1. Thus \(f^{\prime}(p)=0\) is a necessary condition for a local maximum or minimum at \(p.\) It is insufficient, however. For example, if \(f(x)=x^{3}, f\) has no maxima or minima at all, yet \(f^{\prime}(0)=0 .\) For sufficient conditions, see §6.
Figure 22 illustrates these facts at the points \(p_{2}, p_{3}, \ldots, p_{11}.\) Note that in Figure 22, the isolated points \(P, Q, R\) belong to the graph.
Geometrically, \(f^{\prime}(p)=0\) means that the tangent at \(p\) is horizontal, or that a two-sided tangent does not exist at \(p.\)
Let \(f : E^{1} \rightarrow E^{*}\) be relatively continuous on an interval \([a, b]\), with \(f^{\prime} \neq 0\) on \((a, b).\) Then \(f\) is strictly monotone on \([a, b],\) and \(f^{\prime}\) is signconstant there (possibly 0 at a and b), with \(f^{\prime} \geq 0\) if \(f \uparrow,\) and \(f^{\prime} \leq 0\) if \(f \downarrow\).
- Proof
-
By Theorem 2 of Chapter 4, §8, \(f\) attains a least value \(m,\) and a largest value \(M,\) at some points of \([a, b].\) However, neither can occur at an interior point \(p \in(a, b),\) for, by Corollary 1, this would imply \(f^{\prime}(p)=0,\) contrary to our assumption.
Thus \(M=f(a)\) or \(M=f(b);\) for the moment we assume \(M=f(b)\) and \(m=f(a).\) We must have \(m<M,\) for \(m=M\) would make \(f\) constant on \([a, b]\), implying \(f^{\prime}=0.\) Thus \(m=f(a)<f(b)=M.\)
Now let \(a \leq x<y \leq b\). Applying the previous argument to each of the intervals \([a, x],[a, y],[x, y],\) and \([x, b]\) (now using that \(m=f(a)<f(b)=M )\), we find that
\[f(a) \leq f(x)<f(y) \leq f(b). \quad \text { (Why?) }\]
Thus \(a \leq x<y \leq b\) implies \(f(x)<f(y);\) i.e., \(f\) increases on \([a, b].\) Hence \(f^{\prime}\) cannot be negative at any \(p \in[a, b],\) for, otherwise, by Lemma 1, \(f\) would decrease at \(p.\) Thus \(f^{\prime} \geq 0\) on \([a, b].\)
In the case \(M=f(a)>f(b)=m,\) we would obtain \(f^{\prime} \leq 0\). \(\quad \square\)
Caution:
The function \(f\) may increase or decrease at \(p\) even if \(f^{\prime}(p)=0.\)
See Note 1.
If : \(E^{1} \rightarrow E^{*}\) is relatively continuous on \([a, b]\) and if \(f(a)=f(b),\) then \(f^{\prime}(p)=0\) for at least one interior point \(p \in(a, b)\).
For, if \(f^{\prime} \neq 0\) on all of \((a, b),\) then by Theorem 1, \(f\) would be strictly monotone on \([a, b],\) so the equality \(f(a)=f(b)\) would be impossible.
Figure 22 illustrates this on the intervals \(\left[p_{2}, p_{4}\right]\) and \(\left[p_{4}, p_{6}\right],\) with \(f^{\prime}\left(p_{3}\right)=\) \(f^{\prime}\left(p_{5}\right)=0.\) A discontinuity at 0 causes an apparent failure on \([0, p_{2}].\)
Note 2. Theorem 1 and Corollary 2 hold even if \(f(a)\) and \(f(b)\) are infinite, if continuity is interpreted in the sense of the metric \(\rho^{\prime}\) of Problem 5 in Chapter 3, §11. (Weierstrass' Theorem 2 of Chapter 4, §8 applies to \(\left(E^{*}, \rho^{\prime}\right),\) with the same proof.)
Let the functions \(f, g : E^{1} \rightarrow E^{*}\) be relatively continuous and finite on \([a, b]\) and have derivatives on \((a, b),\) with \(f^{\prime}\) and \(g^{\prime}\) never both infinite at the same point \(p \in(a, b).\) Then
\[g^{\prime}(q)[f(b)-f(a)]=f^{\prime}(q)[g(b)-g(a)] \text { for at least one } q \in(a, b).\]
- Proof
-
Let \(A=f(b)-f(a)\) and \(B=g(b)-g(a).\) We must show that \(A g^{\prime}(q)=B f^{\prime}(q)\) for some \(q \in(a, b)\). For this purpose, consider the function \(h=A g-B f\). It is relatively continuous and finite on \([a, b],\) as are \(g\) and \(f.\) Also,
\[h(a)=f(b) g(a)-g(b) f(a)=h(b) . \quad \text { (Verify!) }\]
Thus by Corollary 2, \(h^{\prime}(q)=0\) for some \(q \in(a, b).\) Here, by Theorem 4 of §1, \(h^{\prime}=(A g-B f)^{\prime}=A g^{\prime}-B f^{\prime}.\) (This is legitimate, for, by assumption, \(f^{\prime}\) and \(g^{\prime}\) never both become infinite, so no indeterminate limits occur.) Thus \(h^{\prime}(q)=A g^{\prime}(q)-B f^{\prime}(q)=0,\) and (1) follows. \(\quad \square\)
If \(f : E^{1} \rightarrow E^{1}\) is relatively continuous on \([a, b]\) with a derivative on \((a, b),\) then
\[f(b)-f(a)=f^{\prime}(q)(b-a) \text { for at least one } q \in(a, b).\]
- Proof
-
Take \(g(x)=x\) in Theorem 2, so \(g^{\prime}=1\) on \(E^{1}. \square\)
Note 3. Geometrically,
\[\frac{f(b)-f(a)}{b-a}\]
is the slope of the secant through \((a, f(a))\) and \((b, f(b)),\) and \(f^{\prime}(q)\) is the slope of the tangent line at \(q.\) Thus Corollary 3 states that the secant is parallel to the tangent at some intermediate point \(q;\) see Figure 23. Theorem 2 states the same for curves given parametrically: \(x=f(t), y=g(t)\).
Let \(f\) be as in Corollary 3. Then
(i) \(f\) is constant on \([a, b]\) iff \(f^{\prime}=0\) on \((a, b)\);
(ii) \(f \uparrow\) on \([a, b]\) iff \(f^{\prime} \geq 0\) on \((a, b);\) and
(iii) \(f \downarrow\) on \([a, b]\) iff \(f^{\prime} \leq 0\) on \((a, b)\).
- Proof
-
Let \(f^{\prime}=0\) on \((a, b).\) If \(a \leq x \leq y \leq b,\) apply Corollary 3 to the interval \([x, y]\) to obtain
\[f(y)-f(x)=f^{\prime}(q)(y-x) \text { for some } q \in(a, b) \text { and } f^{\prime}(q)=0.\]
Thus \(f(y)-f(x)=0\) for \(x, y \in[a, b],\) so \(f\) is constant.
The rest is left to the reader. \(\quad \square\)
Let \(f : E^{1} \rightarrow E^{1}\) be relatively continuous and strictly monotone on an interval \(I \subseteq E^{1}\). Let \(f^{\prime}(p) \neq 0\) at some interior point \(p \in I.\) Then the inverse function \(g=f^{-1}\) (with \(f\) restricted to \(I)\) has a derivative at \(q=f(p),\) and
\[g^{\prime}(q)=\frac{1}{f^{\prime}(p)}.\]
(If \(f^{\prime}(p)=\pm \infty,\) then \(g^{\prime}(q)=0.)\)
- Proof
-
By Theorem 3 of Chapter 4, §9, \(g=f^{-1}\) is strictly monotone and relatively continuous on \(f[I],\) itself an interval. If \(p\) is interior to \(I,\) then \(q=f(p)\) is interior to \(f[I].\) (Why?)
Now if \(y \in f[I],\) we set
\[\Delta g=g(y)-g(q), \Delta y=y-q, x=f^{-1}(y)=g(y), \text { and } f(x)=y\]
and obtain
\[\frac{\Delta g}{\Delta y}=\frac{g(y)-g(q)}{y-q}=\frac{x-p}{f(x)-f(p)}=\frac{\Delta x}{\Delta f} \text { for } x \neq p.\]
Now if \(y \rightarrow q,\) the continuity of \(g\) at \(q\) yields \(g(y) \rightarrow g(q);\) i.e., \(x \rightarrow p.\) Also, \(x \neq p\) iff \(y \neq q\), for \(f\) and \(g\) are one-to-one functions. Thus we may substitute \(y=f(x)\) or \(x=g(y)\) to get
\[g^{\prime}(q)=\lim _{y \rightarrow q} \frac{\Delta g}{\Delta y}=\lim _{x \rightarrow p} \frac{\Delta x}{\Delta f}=\frac{1}{\lim _{x \rightarrow p}(\Delta f / \Delta x)}=\frac{1}{f^{\prime}(p)},\]
where we use the convention \(\frac{1}{\infty}=0\) if \(f^{\prime}(p)=\infty. \quad \square\)
(A) Let
\[f(x)=\log _{a}|x| \text { with } f(0)=0.\]
Let \(p>0.\) Then \((\forall x>0)\)
\[\begin{aligned} \Delta f &=f(x)-f(p)=\log _{a} x-\log _{a} p=\log _{a}(x / p) \\ &=\log _{a} \frac{p+(x-p)}{p}=\log _{a}\left(1+\frac{\Delta x}{p}\right). \end{aligned}\]
Thus
\[\frac{\Delta f}{\Delta x}=\log _{a}\left(1+\frac{\Delta x}{p}\right)^{1 / \Delta x}.\]
Now let \(z=\Delta x / p.\) (Why is this substitution admissible?) Then using the formula
\[\lim _{z \rightarrow 0}(1+z)^{1 / z}=e \quad \text { (see Chapter 4, §2, Example (C)) }\]
and the continuity of the log and power functions, we obtain
\[f^{\prime}(p)=\lim _{x \rightarrow p} \frac{\Delta f}{\Delta x}=\lim _{z \rightarrow 0} \log _{a}\left[(1+z)^{1 / z}\right]^{1 / p}=\log _{a} e^{1 / p}=\frac{1}{p} \log _{a} e.\]
The same formula results also if \(p<0,\) i.e., \(|p|=-p.\) At \(p=0, f\) has one-sided derivatives \(( \pm \infty)\) only (verify!), so \(f^{\prime}(0)=0\) by Definition 1 in §1.
(B) The inverse of the log \(_{a}\) function is the exponential \(g : E^{1} \rightarrow E^{1},\) with
\[g(y)=a^{y} \quad(a>0, a \neq 1).\]
By Theorem 3, we have
\[\left(\forall q \in E^{1}\right) \quad g^{\prime}(q)=\frac{1}{f^{\prime}(p)}, p=g(q)=a^{q}.\]
Thus
\[g^{\prime}(q)=\frac{1}{\frac{1}{p} \log _{a} e}=\frac{p}{\log _{a} e}=\frac{a^{q}}{\log _{a} e}.\]
Symbolically,
\[\left(\log _{a}|x|\right)^{\prime}=\frac{1}{x} \log _{a} e(x \neq 0) ; \quad\left(a^{x}\right)^{\prime}=\frac{a^{x}}{\log _{a} e}=a^{x} \ln a.\]
In particular, if \(a=e,\) we have \(\log _{e} a=1\) and \(\log _{a} x=\ln x ;\) hence
\[(\ln |x|)^{\prime}=\frac{1}{x}(x \neq 0) \quad \text { and } \quad\left(e^{x}\right)^{\prime}=e^{x} \quad\left(x \in E^{1}\right).\]
(C) The power function \(g :(0,+\infty) \rightarrow E^{1}\) is given by
\[g(x)=x^{a}=\exp (a \cdot \ln x) \text { for } x>0 \text { and fixed } a \in E^{1}.\]
By the chain rule (§1, Theorem 3), we obtain
\[g^{\prime}(x)=\exp (a \cdot \ln x) \cdot \frac{a}{x}=x^{a} \cdot \frac{a}{x}=a \cdot x^{a-1}.\]
Thus we have the symbolic formula
\[\left(x^{a}\right)^{\prime}=a \cdot x^{a-1} \text { for } x>0 \text { and fixed } a \in E^{1}.\]
If \(f : E^{1} \rightarrow E^{*}\) is relatively continuous and has a derivative on an interval I, then \(f^{\prime}\) has the Darboux property (Chapter 4, §9 ) on \(I.\)
- Proof
-
Let \(p, q \in I\) and \(f^{\prime}(p)<c<f^{\prime}(q).\) Put \(g(x)=f(x)-c x.\) Assume \(g^{\prime} \neq 0\) on \((p, q)\) and find a contradiction to Theorem 1. Details are left to the reader. \(\quad \square\)


1.12: Book XII
THE SIRENS, SCYLLA AND CHARYBDIS, THE CATTLE OF THE SUN.
“After we were clear of the river Oceanus, and had got out into the open sea, we went on till we reached the Aeaean island where there is dawn and sun-rise as in other places. We then drew our ship on to the sands and got out of her on to the shore, where we went to sleep and waited till day should break.
“Then, when the child of morning, rosy-fingered Dawn, appeared, I sent some men to Circe’s house to fetch the body of Elpenor. We cut firewood from a wood where the headland jutted out into the sea, and after we had wept over him and lamented him we performed his funeral rites. When his body and armour had been burned to ashes, we raised a cairn, set a stone over it, and at the top of the cairn we fixed the oar that he had been used to row with.
“While we were doing all this, Circe, who knew that we had got back from the house of Hades, dressed herself and came to us as fast as she could; and her maid servants came with her bringing us bread, meat, and wine.  In the meantime I will tell Ulysses about your course, and will explain everything to him so as to prevent your suffering from misadventure either by land or sea.’
“We agreed to do as she had said, and feasted through the livelong day to the going down of the sun, but when the sun had set and it came on dark, the men laid themselves down to sleep by the stern cables of the ship. Then Circe took me by the hand and bade me be seated away from the others, while she reclined by my side and asked me all about our adventures.
“‘So far so good,’ said she, when I had ended my story, ‘and now pay attention to what I am about to tell you—heaven itself, indeed, will recall it to your recollection. First you will come to the Sirens who enchant all who come near them. If any one unwarily draws in too close and hears the singing of the Sirens, his wife and children will never welcome him home again, for they sit in a green field and warble him to death with the sweetness of their song.  Therefore pass these Sirens by, and stop your men’s ears with wax that none of them may hear; but if you like you can listen yourself, for you may get the men to bind you as you stand upright on a cross piece half way up the mast, 99 and they must lash the rope’s ends to the mast itself, that you may have the pleasure of listening. If you beg and pray the men to unloose you, then they must bind you faster.
“‘When your crew have taken you past these Sirens, I cannot give you coherent directions 100 as to which of two courses you are to take; I will lay the two alternatives before you, and you must consider them for yourself. On the one hand there are some overhanging rocks against which the deep blue waves of Amphitrite beat with terrific fury; the blessed gods call these rocks the Wanderers. Here not even a bird may pass, no, not even the timid doves that bring ambrosia to Father Jove, but the sheer rock always carries off one of them, and Father Jove has to send another to make up their number; no ship that ever yet came to these rocks has got away again, but the waves and whirlwinds of fire are freighted with wreckage and with the bodies of dead men. The only vessel that ever sailed and got through, was the famous Argo on her way from the house of Aetes, and she too would have gone against these great rocks, only that Juno piloted her past them for the love she bore to Jason.
“‘Of these two rocks the one reaches heaven and its peak is lost in a dark cloud. This never leaves it, so that the top is never clear not even in summer and early autumn. No man though he had twenty hands and twenty feet could get a foothold on it and climb it, for it runs sheer up, as smooth as though it had been polished. In the middle of it there is a large cavern, looking West and turned towards Erebus; you must take your ship this way, but the cave is so high up that not even the stoutest archer could send an arrow into it. Inside it Scylla sits and yelps with a voice that you might take to be that of a young hound, but in truth she is a dreadful monster and no one—not even a god—could face her without being terror-struck. She has twelve mis-shapen feet, and six necks of the most prodigious length; and at the end of each neck she has a frightful head with three rows of teeth in each, all set very close together, so that they would crunch any one to death in a moment, and she sits deep within her shady cell thrusting out her heads and peering all round the rock, fishing for dolphins or dogfish or any larger monster that she can catch, of the thousands with which Amphitrite teems. No ship ever yet got past her without losing some men, for she shoots out all her heads at once, and carries off a man in each mouth.
“‘You will find the other rock lie lower, but they are so close together that there is not more than a bow-shot between them.  Three times in the day does she vomit forth her waters, and three times she sucks them down again; see that you be not there when she is sucking, for if you are, Neptune himself could not save you; you must hug the Scylla side and drive ship by as fast as you can, for you had better lose six men than your whole crew.’
“‘Is there no way,’ said I, ‘of escaping Charybdis, and at the same time keeping Scylla off when she is trying to harm my men?’
“‘You dare devil,’ replied the goddess, ‘you are always wanting to fight somebody or something; you will not let yourself be beaten even by the immortals. For Scylla is not mortal; moreover she is savage, extreme, rude, cruel and invincible. There is no help for it; your best chance will be to get by her as fast as ever you can, for if you dawdle about her rock while you are putting on your armour, she may catch you with a second cast of her six heads, and snap up another half dozen of your men; so drive your ship past her at full speed, and roar out lustily to Crataiis who is Scylla’s dam, bad luck to her; she will then stop her from making a second raid upon you.’
“‘You will now come to the Thrinacian island, and here you will see many herds of cattle and flocks of sheep belonging to the sun-god—seven herds of cattle and seven flocks of sheep, with fifty head in each flock. They do not breed, nor do they become fewer in number, and they are tended by the goddesses Phaethusa and Lampetie, who are children of the sun-god Hyperion by Neaera. Their mother when she had borne them and had done suckling them sent them to the Thrinacian island, which was a long way off, to live there and look after their father’s flocks and herds. If you leave these flocks unharmed, and think of nothing but getting home, you may yet after much hardship reach Ithaca; but if you harm them, then I forewarn you of the destruction both of your ship and of your comrades; and even though you may yourself escape, you will return late, in bad plight, after losing all your men.’
“Here she ended, and dawn enthroned in gold began to show in heaven, whereon she returned inland. I then went on board and told my men to loose the ship from her moorings; so they at once got into her, took their places, and began to smite the grey sea with their oars. Presently the great and cunning goddess Circe befriended us with a fair wind that blew dead aft, and staid steadily with us, keeping our sails well filled, so we did whatever wanted doing to the ship’s gear, and let her go as wind and helmsman headed her.
“Then, being much troubled in mind, I said to my men, ‘My friends, it is not right that one or two of us alone should know the prophecies that Circe has made me, I will therefore tell you about them, so that whether we live or die we may do so with our eyes open. First she said we were to keep clear of the Sirens, who sit and sing most beautifully in a field of flowers; but she said I might hear them myself so long as no one else did. Therefore, take me and bind me to the crosspiece half way up the mast; bind me as I stand upright, with a bond so fast that I cannot possibly break away, and lash the rope’s ends to the mast itself. If I beg and pray you to set me free, then bind me more tightly still.’
“I had hardly finished telling everything to the men before we reached the island of the two Sirens, 102 for the wind had been very favourable. Then all of a sudden it fell dead calm; there was not a breath of wind nor a ripple upon the water, so the men furled the sails and stowed them; then taking to their oars they whitened the water with the foam they raised in rowing.  Then I kneaded the wax in my strong hands till it became soft, which it soon did between the kneading and the rays of the sun-god son of Hyperion. Then I stopped the ears of all my men, and they bound me hands and feet to the mast as I stood upright on the cross piece; but they went on rowing themselves. When we had got within earshot of the land, and the ship was going at a good rate, the Sirens saw that we were getting in shore and began with their singing.
“‘Come here,’ they sang, ‘renowned Ulysses, honour to the Achaean name, and listen to our two voices. No one ever sailed past us without staying to hear the enchanting sweetness of our song—and he who listens will go on his way not only charmed, but wiser, for we know all the ills that the gods laid upon the Argives and Trojans before Troy, and can tell you everything that is going to happen over the whole world.’
“They sang these words most musically, and as I longed to hear them further I made signs by frowning to my men that they should set me free; but they quickened their stroke, and Eurylochus and Perimedes bound me with still stronger bonds till we had got out of hearing of the Sirens’ voices. Then my men took the wax from their ears and unbound me.
“Immediately after we had got past the island I saw a great wave from which spray was rising, and I heard a loud roaring sound. The men were so frightened that they loosed hold of their oars, for the whole sea resounded with the rushing of the waters, 103 but the ship stayed where it was, for the men had left off rowing. I went round, therefore, and exhorted them man by man not to lose heart.
“‘My friends,’ said I, ‘this is not the first time that we have been in danger, and we are in nothing like so bad a case as when the Cyclops shut us up in his cave; nevertheless, my courage and wise counsel saved us then, and we shall live to look back on all this as well. Now, therefore, let us all do as I say, trust in Jove and row on with might and main. As for you, coxswain, these are your orders; attend to them, for the ship is in your hands; turn her head away from these steaming rapids and hug the rock, or she will give you the slip and be over yonder before you know where you are, and you will be the death of us.’
“So they did as I told them; but I said nothing about the awful monster Scylla, for I knew the men would not go on rowing if I did, but would huddle together in the hold. In one thing only did I disobey Circe’s strict instructions—I put on my armour. Then seizing two strong spears I took my stand on the ship’s bows, for it was there that I expected first to see the monster of the rock, who was to do my men so much harm; but I could not make her out anywhere, though I strained my eyes with looking the gloomy rock all over and over.
“Then we entered the Straits in great fear of mind, for on the one hand was Scylla, and on the other dread Charybdis kept sucking up the salt water. As she vomited it up, it was like the water in a cauldron when it is boiling over upon a great fire, and the spray reached the top of the rocks on either side. When she began to suck again, we could see the water all inside whirling round and round, and it made a deafening sound as it broke against the rocks. We could see the bottom of the whirlpool all black with sand and mud, and the men were at their wits ends for fear. While we were taken up with this, and were expecting each moment to be our last, Scylla pounced down suddenly upon us and snatched up my six best men. I was looking at once after both ship and men, and in a moment I saw their hands and feet ever so high above me, struggling in the air as Scylla was carrying them off, and I heard them call out my name in one last despairing cry. As a fisherman, seated, spear in hand, upon some jutting rock 104 throws bait into the water to deceive the poor little fishes, and spears them with the ox’s horn with which his spear is shod, throwing them gasping on to the land as he catches them one by one—even so did Scylla land these panting creatures on her rock and munch them up at the mouth of her den, while they screamed and stretched out their hands to me in their mortal agony. This was the most sickening sight that I saw throughout all my voyages.
“When we had passed the [Wandering] rocks, with Scylla and terrible Charybdis, we reached the noble island of the sun-god, where were the goodly cattle and sheep belonging to the sun Hyperion. While still at sea in my ship I could bear the cattle lowing as they came home to the yards, and the sheep bleating. Then I remembered what the blind Theban prophet Teiresias had told me, and how carefully Aeaean Circe had warned me to shun the island of the blessed sun-god. So being much troubled I said to the men, ‘My men, I know you are hard pressed, but listen while I tell you the prophecy that Teiresias made me, and how carefully Aeaean Circe warned me to shun the island of the blessed sun-god, for it was here, she said, that our worst danger would lie. Head the ship, therefore, away from the island.’
“The men were in despair at this, and Eurylochus at once gave me an insolent answer. ‘Ulysses,’ said he, ‘you are cruel; you are very strong yourself and never get worn out; you seem to be made of iron, and now, though your men are exhausted with toil and want of sleep, you will not let them land and cook themselves a good supper upon this island, but bid them put out to sea and go faring fruitlessly on through the watches of the flying night. It is by night that the winds blow hardest and do so much damage; how can we escape should one of those sudden squalls spring up from South West or West, which so often wreck a vessel when our lords the gods are unpropitious? Now, therefore, let us obey the behests of night and prepare our supper here hard by the ship; to-morrow morning we will go on board again and put out to sea.’
“Thus spoke Eurylochus, and the men approved his words. I saw that heaven meant us a mischief and said, ‘You force me to yield, for you are many against one, but at any rate each one of you must take his solemn oath that if he meet with a herd of cattle or a large flock of sheep, he will not be so mad as to kill a single head of either, but will be satisfied with the food that Circe has given us.’
“They all swore as I bade them, and when they had completed their oath we made the ship fast in a harbour that was near a stream of fresh water, and the men went ashore and cooked their suppers.
“In the third watch of the night when the stars had shifted their places, Jove raised a great gale of wind that flew a hurricane so that land and sea were covered with thick clouds, and night sprang forth out of the heavens. When the child of morning, rosy-fingered Dawn, appeared, we brought the ship to land and drew her into a cave wherein the sea-nymphs hold their courts and dances, and I called the men together in council.
“‘My friends,’ said I, ‘we have meat and drink in the ship, let us mind, therefore, and not touch the cattle, or we shall suffer for it; for these cattle and sheep belong to the mighty sun, who sees and gives ear to everything.’ And again they promised that they would obey.
“For a whole month the wind blew steadily from the South, and there was no other wind, but only South and East. 105 As long as corn and wine held out the men did not touch the cattle when they were hungry; when, however, they had eaten all there was in the ship, they were forced to go further afield, with hook and line, catching birds, and taking whatever they could lay their hands on; for they were starving. One day, therefore, I went up inland that I might pray heaven to show me some means of getting away. When I had gone far enough to be clear of all my men, and had found a place that was well sheltered from the wind, I washed my hands and prayed to all the gods in Olympus till by and by they sent me off into a sweet sleep.
“Meanwhile Eurylochus had been giving evil counsel to the men, ‘Listen to me,’ said he, ‘my poor comrades. All deaths are bad enough but there is none so bad as famine. Why should not we drive in the best of these cows and offer them in sacrifice to the immortal gods? If we ever get back to Ithaca, we can build a fine temple to the sun-god and enrich it with every kind of ornament; if, however, he is determined to sink our ship out of revenge for these homed cattle, and the other gods are of the same mind, I for one would rather drink salt water once for all and have done with it, than be starved to death by inches in such a desert island as this is.’
“Thus spoke Eurylochus, and the men approved his words. Now the cattle, so fair and goodly, were feeding not far from the ship; the men, therefore, drove in the best of them, and they all stood round them saying their prayers, and using young oak-shoots instead of barley-meal, for there was no barley left. When they had done praying they killed the cows and dressed their carcasses; they cut out the thigh bones, wrapped them round in two layers of fat, and set some pieces of raw meat on top of them. They had no wine with which to make drink-offerings over the sacrifice while it was cooking, so they kept pouring on a little water from time to time while the inward meats were being grilled; then, when the thigh bones were burned and they had tasted the inward meats, they cut the rest up small and put the pieces upon the spits.
 As I drew near I began to smell hot roast meat, so I groaned out a prayer to the immortal gods. ‘Father Jove,’ I exclaimed, ‘and all you other gods who live in everlasting bliss, you have done me a cruel mischief by the sleep into which you have sent me; see what fine work these men of mine have been making in my absence.’
“Meanwhile Lampetie went straight off to the sun and told him we had been killing his cows, whereon he flew into a great rage, and said to the immortals, ‘Father Jove, and all you other gods who live in everlasting bliss, I must have vengeance on the crew of Ulysses’ ship: they have had the insolence to kill my cows, which were the one thing I loved to look upon, whether I was going up heaven or down again. If they do not square accounts with me about my cows, I will go down to Hades and shine there among the dead.’
“‘Sun,’ said Jove, ‘go on shining upon us gods and upon mankind over the fruitful earth.
“As soon as I got down to my ship and to the sea shore I rebuked each one of the men separately, but we could see no way out of it, for the cows were dead already. And indeed the gods began at once to show signs and wonders among us, for the hides of the cattle crawled about, and the joints upon the spits began to low like cows, and the meat, whether cooked or raw, kept on making a noise just as cows do.
“For six days my men kept driving in the best cows and feasting upon them, but when Jove the son of Saturn had added a seventh day, the fury of the gale abated; we therefore went on board, raised our masts, spread sail, and put out to sea. As soon as we were well away from the island, and could see nothing but sky and sea, the son of Saturn raised a black cloud over our ship, and the sea grew dark beneath it. We did not get on much further, for in another moment we were caught by a terrific squall from the West that snapped the forestays of the mast so that it fell aft, while all the ship’s gear tumbled about at the bottom of the vessel. The mast fell upon the head of the helmsman in the ship’s stern, so that the bones of his head were crushed to pieces, and he fell overboard as though he were diving, with no more life left in him.
“Then Jove let fly with his thunderbolts, and the ship went round and round, and was filled with fire and brimstone as the lightning struck it. The men all fell into the sea; they were carried about in the water round the ship, looking like so many sea-gulls, but the god presently deprived them of all chance of getting home again.
“I stuck to the ship till the sea knocked her sides from her keel (which drifted about by itself) and struck the mast out of her in the direction of the keel; but there was a backstay of stout ox-thong still hanging about it, and with this I lashed the mast and keel together, and getting astride of them was carried wherever the winds chose to take me.
“[The gale from the West had now spent its force, and the wind got into the South again, which frightened me lest I should be taken back to the terrible whirlpool of Charybdis. This indeed was what actually happened, for I was borne along by the waves all night, and by sunrise had reached the rock of Scylla, and the whirlpool. She was then sucking down the salt sea water, 106 but I was carried aloft toward the fig tree, which I caught hold of and clung on to like a bat. I could not plant my feet anywhere so as to stand securely, for the roots were a long way off and the boughs that overshadowed the whole pool were too high, too vast, and too far apart for me to reach them; so I hung patiently on, waiting till the pool should discharge my mast and raft again—and a very long while it seemed. A jury-man is not more glad to get home to supper, after having been long detained in court by troublesome cases, than I was to see my raft beginning to work its way out of the whirlpool again. At last I let go with my hands and feet, and fell heavily into the sea, hard by my raft on to which I then got, and began to row with my hands. As for Scylla, the father of gods and men would not let her get further sight of me—otherwise I should have certainly been lost. 107
“Hence I was carried along for nine days till on the tenth night the gods stranded me on the Ogygian island, where dwells the great and powerful goddess Calypso. She took me in and was kind to me, but I need say no more about this, for I told you and your noble wife all about it yesterday, and I hate saying the same thing over and over again.”