1.1.1: Early Experiments of Atomic Theory
Development of Atomic Theory
Since the ancient times, humans thought of explaining the material world in all of its complexity. The basic idea behind all element theories is that the matter that surrounds us is composed of more simple matter. This matter may be composed of even simpler matter. The most simple matter would be called an element.
The first element theories were one element theories: The greek philosopher Thales thought water was the only element, and everything was a form of water. Anaximenes thought air was the only element, and Heraclitus believed fire was the only element (Figure 1.1.1).
However, with only one element assumed it was difficult to explain the material world in all its complexity satisfactorily. This could be done more satisfactorily by a multi-element theory. The first philosopher who introduced a multi-element theory was Empedocles. He suggested a four-element theory with fire, air, water, and soil as the elements (Figure 1.1.2).
First atomistic ideas
The element theories of Thales, Anaximenes, Heraklitus, and Empedocles were all non-atomistic. This means that they did not include the idea that elements were made of small particles that were indivisible. The first greek philosophers that introduced atomistic element theory were Leukippes, and Democrites (Figure 1.1.3). They assumed that particles cannot be divided into smaller particles infinitely often. Ultimately, after many divisions, one would arrive at particles that could not be further divided, and these particles would be called atoms. Atomistic element theory allows for many different elements which helps to explain the complexity of the material world satisfactorily. However, Leukippes and Democrites did not know how many different elements there were, and how different atoms of different elements were actually distinguished. This question would not be answered until about 2000 years later.
Modern Atomic Theories
Although the atomistic idea was already known in the antique, it became forgotten for a long time and was only reintroduced about 2000 years later with Dalton’s atom hypothesis. What lead to Dalton’s atom hypothesis? The first discovery that was important to the development of modern atomic theory was the law of the conservation of mass by Antoine Lavoisier (Fig. 1.1.4). Historically, the conservation of mass and weight was kept obscure for millennia by the buoyant effect of the Earth's atmosphere on the weight of gases, an effect not understood until the vacuum pump first allowed the effective weighing of gases using scales. Until then, in many instances mass seemed to appear or disappear. For example, the mass of wood seems to disappear when it is burned. However, the mass of the wood actually does not disappear it is just converted into the mass of gases, mainly carbon dioxide. When scientists realized that mass never disappeared they could for the first time embark on quantitative studies of the transformations of substances. This in turn led to the idea of chemical elements, as well as the idea that all chemical processes and transformations are simple reactions between these elements. The law of conservation of mass states that the mass of a closed system of substances will remain constant, regardless of the processes acting inside the system. An equivalent statement is that matter cannot be created or destroyed, although it may change form. This implies that for any chemical process in a closed system, the mass of the reactants must equal the mass of the products.
Law of Constant Composition
The discovery of the law of the conservation of mass led to the discovery of the law of the constant composition (also called law of definitive proportions) by Joseph Proust (Fig. 1.1.5). This law was the result of chemical analysis that determined the mass ratio of elements in pure substances. It was found that a pure substance always contains exactly the same proportion of elements by mass. For example the element analysis of pure substances containing the elements carbon and oxygen would be either 42.9% carbon and 57.1% oxygen or 27.3% carbon and 72.7% oxygen.
The law was questioned by Proust's fellow Frenchman Claude Louis Berthollet, who argued that the elements could combine in any proportion. The very existence of this debate was because at the time the distinction between pure chemical compounds and mixtures had not yet been fully developed. When two pure compounds of two different elements are mixed, then the mixture can have a continuous mass ratio between the two elements because compounds can be mixed at any ratio. So, for the example in the two compounds between carbon and oxygen, in mixtures of the two there could be carbon to oxygen ratios varying continuously between 27.7 % to 42.9% carbon, and 42.9% to 72.7% oxygen. It was an accomplishment of Proust that he was able to correctly distinguish between pure compounds and mixtures.
The Law of Multiple Proportions
John Dalton (Fig. 1.1.6) discovered the law of multiple proportions by close analysis of Proust’s law of constant composition. He noticed that if two elements form more than one compound between them, then the ratios of the masses of the second element which combines with a fixed mass of the first element will be the ratios of small whole numbers, also called integer numbers. Let us see what is the meaning of the law of the multiple proportions by an example:
The first compound contains 42.9% by mass carbon and 57.1% by mass oxygen.
The second compound contains 27.3% by mass carbon and 72.7% by mass oxygen.
Show that the data are consistent with the Law of Multiple Proportions!
Solution
In 100 g of the first compound (100 is chosen to make calculations easier) there are 57.1 g O and 42.9 g C.
The mass of O per gram C is:
57.1 g O / 42.9 g C = 1.33 g O per g C
In 100 g of the second compound, there are 72.7 g O and 27.3 g C.
The mass of oxygen per gram of carbon is:
72.7 g O / 27.3 g C = 2.66 g O per g C
Dividing the mass O per g C of the second (larger value) compound by the mass O per g C of the first compound gives:
2.66 : 1.33 = 2 : 1
2 and 1 are both integer numbers.
Dalton's Atom Hypothesis
Dalton argued that atoms could explain the law of the multiple proportions. If one assumed that elements were made of the same type of indivisible particles, that are identical in mass and all properties then, because these particles can only come in integer numbers, different atoms can be combined to form compounds also only in integer numbers. Thus, in a pure compound atoms of unlike elements would be combined in small whole number ratios. Consequently a given compound always has the same relative number and types of atoms. Chemical reactions would involve reorganization of atoms, but the atoms would retain their identity. Atoms could be rearranged in a chemical reaction but not created or destroyed.
Figure 1.1.7 is a simple illustration how atoms can explain the law of multiple proportions. The blue and red balls symbolize different atoms of different elements. It is possible to combine a red atom with one, two, three, or four blue atoms to make four different compounds. It is for example also possible to combine two red atoms with one, two or three blue atoms. In all of these compounds as well as in all other thinkable ones, the blue and red atoms can only be combined in integer numbers.
Dalton's Atom Symbols
Dalton also thought of symbols for the atoms of the different elements. The symbols are different from the element symbols that are used today, but the concept is the same. You can see some of them in Figure 1.1.8. For example oxygen is represented by a white ball, while carbon is symbolized by a black ball. You can also see that Dalton already combined atom symbols of different elements to illustrate compounds.  In this case he correctly identified the ratios of atoms in the two compounds. However, you can see that this is not always the case. For example, he combined one hydrogen atom (white ball with a dot in the middle) with one oxygen atom to indicate the composition of water. However, as we know today, a water molecule has two hydrogen atoms and one oxygen atom. Why has he been right with the carbon-oxygen compounds, but wrong about the water? The answer is that at the time he could determine the atom ratios only from the law of the multiple proportions. At the time there was only one compound known that was made of hydrogen and oxygen, water, so he assumed the simplest atom ratio of 1:1. If he had known hydrogen peroxide, which has the composition H 2 O 2 , and thus half as much hydrogen per oxygen, he would have probably correctly assigned the correct hydrogen to oxygen ratio to water. In the case of the carbon oxides, he assigned the compositions correctly because both carbon monoxide and carbon dioxide were known at the time.
https://commons.wikimedia.org/wiki/F...an_symbols.png )


3.12.1: Review Questions
Review Questions
State Kepler’s three laws in your own words.
2.
Why did Kepler need Tycho Brahe’s data to formulate his laws?
3.
Which has more mass: an armful of feathers or an armful of lead? Which has more volume: a kilogram of feathers or a kilogram of lead? Which has higher density: a kilogram of feathers or a kilogram of lead?
4.
Explain how Kepler was able to find a relationship (his third law) between the orbital periods and distances of the planets that did not depend on the masses of the planets or the Sun.
5.
Write out Newton’s three laws of motion in terms of what happens with the momentum of objects.
6.
Which major planet has the largest . . .
- semimajor axis?
- average orbital speed around the Sun?
- orbital period around the Sun?
- eccentricity?
7.
Why do we say that Neptune was the first planet to be discovered through the use of mathematics?
8.
Why was Brahe reluctant to provide Kepler with all his data at one time?
9.
According to Kepler’s second law, where in a planet’s orbit would it be moving fastest? Where would it be moving slowest?
10.
The gas pedal, the brakes, and the steering wheel all have the ability to accelerate a car—how?
11.
Explain how a rocket can propel itself using Newton’s third law.
12.
A certain material has a mass of 565 g while occupying
13.
To calculate the momentum of an object, which properties of an object do you need to know?
14.
To calculate the angular momentum of an object, which properties of an object do you need to know?
15.
What was the great insight Newton had regarding Earth’s gravity that allowed him to develop the universal law of gravitation?
16.
Which of these properties of an object best quantifies its inertia: velocity, acceleration, volume, mass, or temperature?
17.
Pluto’s orbit is more eccentric than any of the major planets. What does that mean?
18.
Why is Tycho Brahe often called “the greatest naked-eye astronomer” of all time?


1.1: Nerve Fibers and the Strang Quartet
We wish to confirm, by example, the prefatory claim that matrix algebra is a useful means of organizing (stating and solving) multivariable problems. In our first such example we investigate the response of a nerve fiber to a constant current stimulus. Ideally, a nerve fiber is simply a cylinder of radius aa and length \(l\) that conducts electricity both along its length and across its lateral membrane. Though we shall, in subsequent chapters, delve more deeply into the biophysics, here, in our first outing, we shall stick to its purely resistive properties. The latter are expressed via two quantities:
- \(\rho_{i}\) the resistivity in \(\Omega cm\) of the cytoplasm that fills the cell, and
- \(\rho_{m}\) the resistivity in \(\Omega cm^{2}\) of the cell's lateral membrane.
Although current surely varies from point to point along the fiber it is hoped that these variations are regular enough to be captured by a multicompartment model. By that we mean that we choose a number \(N\) and divide the fiber into \(N\) segments each of length \(\frac{l}{N}\) Denoting a segment's axial resistance
\[R_{i} = \frac{\rho_{i} \frac{l}{N}}{\pi a^2} \nonumber\]
and membrane resistance
\[R_{m} = \frac{\rho_{m}}{2\pi a \frac{l}{N}} \nonumber\]
we arrive at the lumped circuit model of Figure 1. For a fiber in culture we may assume a constant extracellular potential, e.g., zero. We accomplish this by connecting and grounding the extracellular nodes, see Figure 2.
Figure 2 also incorporates the exogenous disturbance , a current stimulus between ground and the left end of the fiber. Our immediate goal is to compute the resulting currents through each resistor and the potential at each of the nodes. Our long--range goal is to provide a modeling methodology that can be used across the engineering and science disciplines. As an aid to computing the desired quantities we give them names. With respect to figure 3, we label the vector of potentials
\[x = \begin{pmatrix} {x_{1}}&{x_{2}}&{x_{3}}&{x_{4}} \end{pmatrix} \nonumber\]
\[y = \begin{pmatrix} {y_{1}}&{y_{2}}&{y_{3}}&{y_{4}}&{y_{5}}&{y_{6}} \end{pmatrix} \nonumber\]
We have also (arbitrarily) assigned directions to the currents as a graphical aid in the consistent application of the basic circuit laws.
We incorporate the circuit laws in a modeling methodology that takes the form of a Strang Quartet:
- (S1) Express the voltage drops via \(\textbf{e} = -(A \textbf{x})\)
- (S2) Express Ohm's Law via \(\textbf{y} = G \textbf{e}\)
- (S3) Express Kirchhoff's Current Law via \(A^{T} \textbf{y} = -\textbf{f}\)
- (S4) Combine the above into \(A^{T}GA \textbf{x} = \textbf{f}\)
The \(A\) in (S1) is the node-edge adjacency matrix -- it encodes the network's connectivity. The \(G\) in (S2) is the diagonal matrix of edge conductances -- it encodes the physics of the network. The \(\textbf{f}\) in (S3) is the vector of current sources -- it encodes the network's stimuli. The culminating \(A^{T}GA\) in (S4) is the symmetric matrix whose inverse, when applied to \(\textbf{f}\), reveals the vector of potentials, \(\textbf{x}\). In order to make these ideas our own we must work many, many examples.
Strang Quartet, Step 1
With respect to the circuit of Figure 3, in accordance with step 1, we express the six potential differences (always tail minus head)
\[e_{1} = x_{1}-x_{2} \nonumber\]
\[e_{2} = x_{2} \nonumber\]
\[e_{3} = x_{2}-x_{3} \nonumber\]
\[e_{4} = x_{3} \nonumber\]
\[e_{5} = x_{3}-x_{4} \nonumber\]
\[e_{6} = x_{4} \nonumber\]
Such long, tedious lists cry out for matrix representation, to wit \( \textbf{e} = -(A \textbf{x})\) where
\[A = \begin{pmatrix} {-1}&{1}&{0}&{0}\\ {0}&{-1}&{0}&{0}\\ {0}&{-1}&{1}&{0}\\ {0}&{0}&{-1}&{0}\\ {0}&{0}&{-1}&{1}\\ {0}&{0}&{0}&{-1}\\ \end{pmatrix} \nonumber\]
Strang Quartet, Step 2
Step 2, Ohm's Law, states:
The current along an edge is equal to the potential drop across the edge divided by the resistance of the edge.
In our case,
\[\begin{array}{ccccc} {y_{j} = \frac{e_{j}}{R_{i}},}&{j = 1, 3, 5}&{and}&{y_{j} = \frac{e_{j}}{R_{m}},}&{j = 2, 4, 6} \nonumber \end{array}\]
or, in matrix notation, \(\textbf{y} = G \textbf{e}\) where
\[A = \begin{pmatrix} {\frac{1}{R_{i}}}&{0}&{0}&{0}&{0}&{0}\\ {0}&{\frac{1}{R_{m}}}&{0}&{0}&{0}&{0}\\ {0}&{0}&{\frac{1}{R_{i}}}&{0}&{0}&{0}\\ {0}&{0}&{0}&{\frac{1}{R_{m}}}&{0}&{0}\\ {0}&{0}&{0}&{0}&{\frac{1}{R_{i}}}&{0}\\ {0}&{0}&{0}&{0}&{0}&{\frac{1}{R_{m}}}\\ \end{pmatrix} \nonumber\]
Strang Quartet, Step 3
Step 3, Kirchhoff's Current Law, states:
The sum of the currents into each node must be zero.
In our case
\[i_{0}-y_{1}=0 \nonumber\]
\[y_{1}-y_{2}-y_{3} = 0 \nonumber\]
\[y_{3}-y_{4}-y_{5} = 0 \nonumber\]
\[y_{5}-y_{6} = 0 \nonumber\]
or, in matrix terms
\[B \textbf{y} = -\textbf{f} \nonumber\]
where
\[\begin{array}{ccc} {B = \begin{pmatrix} {-1}&{0}&{0}&{0}&{0}&{0}\\ {1}&{-1}&{-1}&{0}&{0}&{0}\\ {0}&{0}&{1}&{-1}&{-1}&{0}\\ {0}&{0}&{0}&{0}&{1}&{-1}\\ \end{pmatrix}}&{and}&{f = \begin{pmatrix} {i_{0}}\\ {0}\\ {0}\\ {0} \end{pmatrix}} \nonumber \end{array}\]
Strang Quartet, Step 4
Looking back at A
\[A = \begin{pmatrix} {-1}&{1}&{0}&{0}\\ {0}&{-1}&{0}&{0}\\ {0}&{-1}&{1}&{0}\\ {0}&{0}&{-1}&{0}\\ {0}&{0}&{-1}&{1}\\ {0}&{0}&{0}&{-1}\\ \end{pmatrix} \nonumber\]
we recognize in B the transpose of A
- (S1) \(\textbf{e} = -(A \textbf{x})\)
- (S2) \(\textbf{y} = G \textbf{e}\)
- (S3) \(A^{T} \textbf{y} = -\textbf{f}\)
On substitution of the first two into the third we arrive, in accordance with (S4), at
\(A^{T}GA \textbf{x} = \textbf{f}\)
This is a system of four equations for the 4 unknown potentials, \(x_{1}\) through \(x_{4}\) As you know, the system Equation may have either 1, 0, or infinitely many solutions, depending on \(\textbf{f}\) and \(A^{T}GA\) We shall devote (FIX ME CNXN TO CHAPTER 3 AND 4) to an unraveling of the previous sentence. For now, we cross our fingers and 'solve' by invoking the Matlab program
Figure 5.
This program is a bit more ambitious than the above in that it allows us to specify the number of compartments and that rather than just spewing the x and y values it plots them as a function of distance along the fiber. We note that, as expected, everything tapers off with distance from the source and that the axial current is significantly greater than the membrane, or leakage, current.
We have seen in the previous example how a current source may produce a potential difference across a cell's membrane. We note that, even in the absence of electrical stimuli, there is always a difference in potential between the inside and outside of a living cell. In fact, this difference is the biologist's definition of 'living.' Life is maintained by the fact that the cell's interior is rich in potassium ions, \(K^{+}\) and poor in sodium ions, \(Na^{+}\) while in the exterior medium it is just the opposite. These concentration differences beget potential differences under the guise of the Nernst potentials:
- Nernst potentials
\[\begin{array}{ccc} {E_{Na} = \frac{RT}{F} \log \frac{[Na]_{o}}{[Na]_{i}}}&{and}&{E_{K} = \frac{RT}{F} \log \frac{[K]_{o}}{[K]_{i}}} \nonumber \end{array}\]
where R is the gas constant, T is temperature, and F is the Faraday constant.Associated with these potentials are membrane resistances
\[\begin{array}{ccc} {\rho_{m, Na}}&{and}&{\rho_{m,K}} \nonumber \end{array}\]
that together produce the \(\rho_{m}\) above via
\[\frac{1}{\rho_{m}} = \frac{1}{\rho_{m, Na}}+\frac{1}{\rho_{m,K}} \nonumber\]
and produce the aforementioned rest potential
\[E_{m} = \rho_{m}(\frac{E_{Na}}{\rho_{m, Na}}+\frac{E_{K}}{\rho_{m,K}} \nonumber\]
With respect to our old circuit model, each compartment now sports a battery in series with its membrane resistance, as shown in Figure 6.
Revisiting step (S1-4) we note that in (S1) the even numbered voltage drops are now
\[e_{2} = x_{2}-E_{m} \nonumber\]
\[e_{4} = x_{3}-E_{m} \nonumber\]
\[e_{6} = x_{4}-E_{m} \nonumber\]
We accommodate such things by generalizing (S1) to:
- (S1') Express the voltage drops as \(e = \textbf{b}-A \textbf{x}\) where \(\textbf{b}\) is the vector of batteries.
No changes are necessary for (S2) and (S3). The final step now reads,
- (S4') Combine (S1'), (S2), and (S3) to produce \(A^{T}GA \textbf{x} = A^{T}G \textbf{b} \textbf{f}\)
Returning to Figure 6, we note that
\[\begin{array}{ccc} {\textbf{b} = -\begin{pmatrix} E_{m} \begin{pmatrix} {0}\\ {1}\\ {0}\\ {1}\\ {0}\\ {1} \end{pmatrix} \end{pmatrix}}&{and}&{A^{T}G \textbf{b} = \frac{E_{m}}{R_{m}} \begin{pmatrix} {0}\\ {1}\\ {1}\\ {1} \end{pmatrix}} \nonumber \end{array}\]
This requires only minor changes to our old code. The results of its use are indicated in the next two figures.


34.19: Harriet Jacobs and William Peter Blatty- Interpretations of Slavery, Maternity, and Weaponized Religion
Most people have heard of The Exorcist ; growing up, the only aspect of the movie I knew about was that the story involved demonic possession. Sounds scary, right? Would it scare you more to know that the film is eerily similar to early American slave narratives?
In 1971, the psychological horror novel The Exorcist was published. A mere two years later, William Friedkin directed a film adaptation of the book, with the original author, William Peter Blatty, returning to compose the screenplay. The book and film received polarizing reception, mostly for its crude depictions of religious figures and controversial plot. Those facts aside, the book and film are terrific pieces of fiction; if anything, the story is a character study on the essence of the human condition. The narrative explores themes such as loss, the search for meaning, and religious faith. Beyond those, the story’s most glaring depiction of terror is disempowerment. In other words, The Exorcist is about a kind of slavery. Harriet Jacobs, a former enslaved person in the nineteenth century, wrote about her experiences in what would become Incidents in the Life of a Slave Girl . Jacobs’ novel shares similar themes to The Exorcist . Taking place in different historical and social contexts, Blatty’s and Jacobs’ stories present characters that struggle with maternity, religious stability, and mental and physical freedom.
Let’s begin with the theme of maternity. In The Exorcist , the main character is Chris MacNeil, an actress that lives with her daughter Reagan in Georgetown, D.C; the location is notable, as it is the American capitol. Chris is an atheist; the loss of her young son made untrustworthy of higher authority. She is also a divorced parent. She initially believes her broken family structure is what causes Reagan to exhibit her sudden physical and mental outbreaks. Throughout the book and film, Chris unconditionally vows to help her daughter, the only meaningful part of life she has to hold on to, despite the despair and pain it brings her. The family structure is important in The Exorcist .
Beyond a slave narrative, Inciden ts in the Life of a Slave Girl is primarily a story about maternity and the mother’s role to selflessly protect her children. Such as The Exorcist , Linda suffers child loss and parent separation. The plot focuses on parental responsibility in the first half of the book. In one instance, Linda observes a woman who has her children taken from her on the slave trade: “I met that mother in the street, and her wild, haggard face lives to-day in my mind. She wrung her hands in anguish, and exclaimed, ‘Gone! All gone!  I had no words wherewith to comfort her. Instances of this kind are of daily, yea, of hourly occurrence” (17).  Later in the book, after her escape from Dr. Flint, Linda hides in a small cellar elsewhere in town. She confines herself to her hiding place with little physical activity and nourishment. Despite her self-proclaimed exile, she is more free than ever before. In this shack, she is willing to suffer physical debilitation so that she can see her children emancipated: “My friends feared I should become a cripple for life; and I was so weary of my long imprisonment that, had it not been for the hope of serving my children, I should have been thankful to die; but for their sakes, I was willing to bear on” (105).
The Exorcis t’s second primary protagonist is Damien Karras, a Jesuit priest. Karras suffers an existential crisis after his mother’s sickness and inevitable death. Most of the novel and film follow his struggle through depression, loss of empowerment, and eventual redemption. He is left with little answers, and this is the source of his religious instability. Early in the story, he announces his dwindling faith: “Some of there [patients’] problems come down to faith, there vocation, the meaning of there lives, and I can’t cut it anymore. I need out. I’m unfit. I think I’ve lost my faith, Tom.” In Incidents , Linda similarly questions whether God is real or not: “Sometimes I thought God was a compassionate Father… At other times, it seemed to me there was no justice or mercy in the divine government” (102). In both The Exorcist and Incidents in the Life of a Slave Girl , the protagonists suffer tragedies that make them question their divine protection.
The last notable theme is literal slavery. In Harriet Jacobs’ story, Linda is an enslaved woman. Duh. However, she suffers from more than physical slavery.  Flint continuously deceives Linda, yet she is forthright in her conviction for a better life. Flint claims that he is a good master, and that he treats Linda well. As Linda describes, “He hoped I had become convinced of the injury I was doing myself by incurring his displeasure” (37). Furthermore, Linda states that slaveholders ceaselessly pressure enslaved women to physically (sexually) and mentally (religiously) subjugate: “The slave girl is reared in an atmosphere of licentiousness and fear… If these fail to accomplish their purpose, she is whipped or starved into submission to their will” (45). In Inciden ts in the Life of a Slave Girl , slaveholders utilize fear as a tool for control. Additionally, slaveholders use their physical prowess to supplement their mental tyranny. This tactic is used to an extreme in The Exorcist ; Reagan MacNeil suffers from bodily trauma, deterioration, and overall fear. However, she isn’t the only victim; her mother is equally disturbed by her daughter’s actions. Chris despairs as she watches her daughter slowly rot and descend into madness. Reagan is merely a tool to plunge her mother into a position of maternal vulnerability, and therefore, mental and spiritual slavery.
The Exorcist is an expressionist film about the loss of faith and meaning. For instance, this clip from the film shows the interaction between Damien and Reagan; the overall exchange appears to Damien’s physical manifestation of anxieties and weak mental fortitude. Later in the climactic exorcist scene, Reagan encourages Karras to embrace his feeling of regret. The demon says that he is responsible for his mother’s death, and that he did nothing to save her. The physical torture in The Exorcist represents the deteriorating state of a slave’s psyche.
Neither The Exorcist nor Incidents explains meaning of life’s sufferings. If anything, Incidents in the Life of a Slave Girl explores humanity’s power to create opportunity from seemingly nothing. In The Exorcist , Reagan’s possession is largely ambiguous; Pazuzu’s (the demon) motive is never clear to the characters. At the end of the film (and book) Damien questions the meaning of the MacNeils’ suffering. Father Merrin offers him an answer: “I think the point is to make us despair; to see ourselves as animal and ugly; to reject the possibility that God could love us.” In The Exorcist and Incidents in the Life of a Slave Girl , the power to make others reject life is the ultimate source of subjugation.
To me, The Exorcist transcends most contemporary fiction because of its ability to exist in two mediums (novel and film). Yet, the story remains presentation and humane message is consistent in both versions. As I read the book, I felt a connection with the story that I don’t see in the film. On the other hand, when I watched the film, I read the actors’ emotional language that I couldn’t see in the book. For that reason, the film and book complement each other (the movie uses Blatty’s original dialogue from the book verbatim, too).
 The narrative is multi-layered; it’s a scary story that can be enjoyed for its surface spectacle, but is also a humane story that challenges important existential questions. The Exorcist , similar to Incidents in the Life of a Slave Girl , can be examined through many different analytical lenses. Both of these stories are timeless, but The Exorcist is a product of the mid-wentieth century, while Incidents in the Life of a Slave Girl is from the nineteenth entury. On the surface, The Exorcist is decrepit and vulgar. But that’s exactly the point; it’s about the human will to search for higher meaning, despite encountering arbitrary cruelty.
Bibliography
Jacobs, Harriet. Incidents in the Life of a Slave Girl , edited by Paul Negri, Dover Publications, 2001.
Blatty, William Peter. The Exorcist . Harper & Row, 1971.
The Exorcist . Dir. William Friedkin. Warner Bros., 1973. Film.


21.16: Punctuation
This section covers the major marks of punctuation: commas, apostrophes, semicolons, colons, periods, question marks, exclamation points, dashes, and parentheses. (For using brackets and ellipses, see Quotations .)
Commas
Commas alert readers to brief pauses within sentences.
Commas with Main Clauses
Use a comma before a coordinating conjunction ( for, and, nor, but, or, yet , or so ) joining main clauses:
Businesses in the metropolitan area are growing, and unemployment is down.
Many job seekers use online sites like Indeed.com, but a few still send traditional cover letters and résumés through the mail.
A solution must be determined soon, or the problem will continue.
Commas with Introductory Information
Use a comma after an introductory element at the start of a sentence:
After class is over , we should get lunch and review our notes.
Shuffling his feet nervously , he waited for the train.
However , the circumstances have not changed.
Commas with Nonessential and Essential Information
(See Editing Focus: Commas with Nonessential and Essential Information for a related discussion of commas.)
Nonessential information refers to information that is usually not necessary to the basic meaning of a sentence. Nonessential information is set off by commas. In the following sentence, the word original tells readers which labs no longer meet the needs of the teachers and students. The underlined information adds information but does not change the meaning of the sentence and thus is nonessential to the basic meaning:
The original technical education labs , which were installed 50 years ago, no longer meet the needs of the teachers and students.
Essential information , on the other hand, is necessary to the meaning of the sentence. In following example, the word original is no longer part of the sentence; the underlined words convey necessary information about the labs:
The technical education labs that were installed 50 years ago no longer meet the needs of the teachers and students.
You can test whether information is nonessential by removing the information. If the meaning of the sentence is unchanged, the information is nonessential. If the meaning becomes too general or changes, the information is essential. In the sentence above, only the labs installed 50 years ago, as opposed to other labs, no longer meet the needs of teachers and students. Note, also, the use of which with nonessential information and that with essential information.
Commas Around Nonessential Information
Place commas around information that is not essential to the meaning of a sentence:
The entire technology department , which consists of nine teachers and five staff members, has contributed to a report on the needed updates to the technical education labs.
The technology department chair , who teaches welding, wrote the final report.
Updates to the labs will begin in June , when school is not in session .
No Commas Around Essential Information
Do not place commas around essential information:
According to the technical education teachers, the labs need equipment that students are likely to encounter in the workplace .
Faculty who teach auto mechanics have requested updates to their lab.
The teachers are concerned about the labs because students are not learning the skills they need .
The amount of lab space that needs to be updated is substantial.
The department has consulted the industry expert Stacy James .
Serial (Oxford or Harvard) Commas
For clarity, use a comma between items in a series:
He studied all the notes, emails, memos, and reports related to the data breach.
Be aware, however, that certain style manuals, such as the AP Stylebook , do not use the serial comma, also called the Oxford or Harvard comma.
Commas with Numbers, Dates, Titles with Names, and Addresses
The sign gave the city’s population as 122,887.
Nobel Prize winner Toni Morrison died on August 5, 2019.
Diana Wong, M.D., is a practicing obstetrician.
The mailing address for the Smithsonian Institution is 600 Maryland Avenue SW, Washington, D.C., 20002.
Common Comma Errors
Misplaced commas can make sentences choppy and obscure the intended meaning.
No Comma after a Subject or a Verb
Anyone who was still at the party, left when the band stopped playing.
The party ended, after the band stopped playing.
No Comma after a Conjunction Connecting Parts of a Compound Subject, Verb, or Object
Some musicians in the band, and many of the guests danced until midnight. (compound subject)
The band stopped after two hours, and took a well-deserved break. (compound verb)
Guests enjoyed the music, and the dancing. (compound object)
No Comma after a Series
The band played 80s rock, punk, and new wave, all night long.
No Comma before an Indirect Quotation
Online reviews say, that the band is the best in the area.
Apostrophes
An apostrophe has two functions. It indicates possession, and it forms contractions.
Apostrophes to Show Possession
Use an apostrophe and -s to indicate possession with a singular noun or an indefinite pronoun:
Jack ’ s brother is my sister ’ s coworker.
In their family, everyone ’ s favorite dessert is ice cream.
If the ’s in a singular noun is pronounced, add apostrophe -s :
The business ’ s inconsistent hours caused customers to go elsewhere.
Los Angeles ’ s airport, LAX, is one of the busiest in the United States.
If the ’s is not pronounced in a singular noun, some writers choose to add an apostrophe alone; however, MLA, APA, and Chicago use the apostrophe and s in these cases:
David Myers ’ book, The Pursuit of Happiness , was published in 1992.
David Myers ’ s book, The Pursuit of Happiness , was published in 1992.
When the noun is plural and ends in -s , place the apostrophe after the final -s :
American households ’ incomes have grown since the 1970s because more women have entered the workforce.
These families ’ expenses have risen too.
When the noun is plural and does not end in -s , add an apostrophe and -s :
Social media ’ s effect on contemporary life cannot be underestimated.
During the pandemic, parents’ stress grew as they helped with their children ’ s schooling.
Apostrophes to Form Contractions
Contractions are common in speech and in informal writing. Use an apostrophe in contractions:
When I say I can ’ t , I mean I won ’ t .
It ’ s the best option under the circumstances.
“ You ’ re the best friend anyone can have,” Mikayla said.
They ’ re driving to their favorite hangout spot.
Common Apostrophe Errors
Apostrophes are not used to form plural nouns, singular verbs, or personal or relative pronouns.
Not in Plural Nouns
How many hotel rooms [not room’s ] should be reserved for the wedding?
The Lewises and the Riveras [not Lewis’s and Rivera’s or Lewis’ and Riveras’ ] have confirmed their reservations.
Not with Verbs Ending in -s
Nikki runs [not run’s ] every day.
Jamal walks [not walk’s ] to work.
Not with Possessive Personal Pronouns or Relative Pronouns
The book is yours [not your’s ].
The dog was barking and wagging its [not it’s ] tail.
Whose [not who’s ] apartment is this?
Other Punctuation
Semicolons
The semicolon joins main clauses (a clause that contains a subject and a predicate and can stand alone as a sentence). A semicolon is also used to separate items in a series that contain commas.
-
Use a semicolon to join main clauses that are closely related in meaning and that are not joined by a coordinating conjunction (
for
,
and
,
nor
,
but
,
or
,
yet
, or
so
).
Originally built in 1928, the school had been remodeled multiple times ; the result was an architectural mashup. -
Use a semicolon to join main clauses that are connected by a transitional word or phrase such as
for example
,
however
,
therefore
,
indeed
,
or after all
:
The governor has proposed increased funding to K-12 public schools ; however , the legislature must approve the budget. -
Use a semicolon between items in a series that contain internal commas:
The candidates for the award are Michael, who won the essay competition ; Sasha, the top debater; and Giselle, who directed several student productions.
Colons
A colon introduces lists, summaries, and quotations. A colon also separates titles from subtitles.
- A colon can introduce a list: Successful athletes have the following qualities : physical ability, mental toughness, commitment, and optimism .
-
A colon can also introduce a summary or an explanation, which may or may not be a main clause (a clause that contains a subject and a predicate and can stand alone as a sentence):
The team had one goal left before the end of the season: to win the state championship. -
Book titles often include a subtitle. A colon separates the subtitle from the title:
Forcing the Spring: Inside the Fight for Marriage Equality
End Punctuation
A sentence ends with a period, a question mark, or an exclamation point.
-
A
period
ends declarative (statement) and imperative (command) sentences:
The administration canceled classes .
Do not attempt to drive to school this morning . -
A
question mark
ends a direct question and indicates uncertainty in dates:
Where is Times Square ?
She asked, “What time is it ? ” -
An
exclamation point
ends an emphatic or emotional sentence:
“What a mess ! ” she blurted out.
“Stop ! That hurts ! ” he shouted.
Dashes and Parentheses
Dashes and parentheses enclose nonessential information in a sentence.
-
Use a
dash
or dashes to set off nonessential information, to indicate a contrast or a pause, or to mark a change of direction.
We did not notice the rain at first — it began so softly — but soon we were soaked.
Nothing is as exciting as seeing a snowy owl in a winter farm field — except maybe seeing two snowy owls. -
Use
parentheses
to enclose nonessential information such as explanations, asides, examples, and dates.
He graduated with high honors ( magna cum laude ) and found a job immediately.
The city of Madison ( home of the University of Wisconsin ) is the state capital of Wisconsin.


22.5: Checklist for Tracheostomy Suctioning and Sample Documentation
Tracheostomy suctioning may be performed with open or closed technique. Open suctioning requires disconnection of the patient from the oxygen source, whereas closed suctioning uses an inline suctioning catheter that does not require disconnection. This checklist will explain the open suctioning technique.
Indications for tracheostomy suctioning include the following:
- The need to maintain the patency and integrity of the artificial airway
- Deterioration of oxygen saturation and/or arterial blood gas values
- Visible secretions in the airway
- The patient’s inability to generate an effective spontaneous cough
- Acute respiratory distress
- Suspected aspiration of gastric or upper-airway secretions
- The need to obtain a sputum specimen [1]
Similar assessments and monitoring apply when performing tracheostomy suctioning compared with other types of suctioning with the addition of assessing the stoma. The stoma should be free from redness and drainage. Hyperoxygenation using a bag mask valve attached to an oxygen source may be required before and during the open suctioning procedure based on the patient’s oxygenation status. See Figure \(\PageIndex{1}\) [2] for an image of an example of sterile tracheostomy suctioning kit.
- To ensure patient safety, a replacement tracheostomy tube, an obturator, a bag valve mask (Ambu bag), and suction catheter kit must always be available in the room.
- Communication should be facilitated with the patient using writing when possible.
- Follow agency policy regarding hyperoxygenation and hyperventilation prior to and during suctioning.
- Do not suction for more than 15 seconds per pass. [3]
- During the procedure, it is important to continually monitor the patient’s pulse oximetry to determine if the oxygen saturation is maintaining at an adequate level.
- Perform oral care after suctioning according to agency policy.
Checklist for Tracheostomy Suctioning [4]
Use the checklist below to review the steps for “Tracheostomy Suctioning.”
Steps
Disclaimer: Always review and follow agency policy regarding this specific skill.
 It is helpful to request assistance from a second nurse if preoxygenating the patient before suction passes.
-
Perform safety steps.
- Perform hand hygiene.
- Check the room for transmission-based precautions.
- Introduce yourself, your role, the purpose of your visit, and an estimate of the time it will take.
- Confirm patient ID using two patient identifiers (e.g., name and date of birth).
- Explain the process to the patient and ask if they have any questions.
- Be organized and systematic.
- Use appropriate listening and questioning skills.
- Listen and attend to patient cues.
- Ensure the patient’s privacy and dignity.
- Assess ABCs.
- Verify that there are a backup tracheostomy and bag valve device available at the bedside.
- Assess lung sounds, heart rate and rhythm, and pulse oximetry.
- Raise the head of the bed to waist level. Place the patient in a semi-Fowler’s position and apply the pulse oximeter for monitoring during the procedure.
- Turn on the suction. Set the suction gauge to appropriate setting based on age of the patient.
- Perform hand hygiene. Don appropriate PPE (gown and mask).
- Open the suction catheter package faced away from you to maintain sterility.
- Don the sterile gloves from the kit.
- Remove the sterile fluid and check the expiration date.
- Open the sterile container used for flushing the catheter and place it back into the kit. Pour the sterile fluid into the sterile container using sterile technique.
- Remove the suction catheter from the packaging. Ensure the catheter size is not greater than half of the inner diameter of the tracheostomy tube.
- Keep the catheter sterile by holding it with your dominant hand and attaching it to the suction tubing with your nondominant hand. Note that your nondominant hand is no longer sterile.
- Test the suction and lubricate the sterile catheter by using your sterile hand to dip the end into the sterile saline while occluding the thumb control.
- Ask an assistant to preoxygenate the patient with 100% oxygen for 30 to 60 seconds using a handheld bag valve mask (Ambu bag) per agency protocol. Alternatively, ask the patient to take two or three deep breaths if able.
-
Insert the catheter into the patient’s tracheostomy tube using your sterile hand without applying suctioning:
- For shallow suctioning, insert the catheter the length of the tracheostomy tube before beginning any suctioning.
- For deep suctioning, insert the catheter until resistance is met (at the carina) and withdraw 1 centimeter before beginning suctioning.
- Do not force the catheter.
- Keep the dominant (sterile) hand at least one inch from the end of the trach tube.
- To apply suction, place your nondominant thumb over the control valve
- Withdraw the catheter while continually rotating it between your fingers to suction all sides of the tracheostomy tube. Do not suction longer than 15 seconds to prevent hypoxia. Follow agency policy regarding the use of intermittent or continuous suctioning. Do not contaminate the catheter as you remove it from the trach tube.
- Suction sterile saline each time the suction catheter is removed to flush the catheter and suction tubing of secretions.
- Assess the patient response to suctioning; hyperoxygenation may be required. If dysrhythmia or bradycardia occur, stop the procedure.
- Allow the patient to rest. After the patient’s pulse oximetry returns to baseline, a second suctioning pass can be initiated if clinically indicated. Encourage the patient to cough and deep breath to remove secretions between suctioning passes.
- Do not insert the suction catheter more than two times. If the patient’s respiratory status does not improve or it worsens, call for emergency assistance.
- Reattach the preexisting oxygen delivery device to the patient with your noncontaminated hand.
- Evaluate the effectiveness of the procedure and the patient’s respiratory status. Assess patency of the airway and pulse oximetry.
- Remove the catheter from the tubing and then remove gloves while holding the catheter inside the glove. Perform hand hygiene.
- Turn off the suction.
- Perform proper hand hygiene and don clean gloves.
- Reassess lung sounds, heart rate and rhythm, and pulse oximetry for improvement .
- Perform patient oral care.
- Remove gloves and perform proper hand hygiene.
- Assist the patient to a comfortable position, ask if they have any questions, and thank them for their time.
-
Ensure safety measures when leaving the room:
- CALL LIGHT: Within reach
- BED: Low and locked (in lowest position and brakes on)
- SIDERAILS: Secured
- TABLE: Within reach
- ROOM: Risk-free for falls (scan room and clear any obstacles)
- Perform hand hygiene.
- Document the procedure and related assessment findings. Report any concerns according to agency policy.
Sample Documentation
Sample Documentation of Expected Findings
Mucus present at entrance to tracheostomy tube. Hyperoxygenation provided for 30 seconds before and after suctioning using a bag valve mask with FiO2 100%. Patient’s pulse oximetry remained 92-96% during suctioning. Moderate amount of thick, white mucus without odor was suctioned. Post procedure: HR 78, RR 18, O2 sat 96%, and lung sounds clear throughout all lobes. Patient tolerated the procedure without discomfort.
Sample Documentation of Unexpected Findings
Mucus present at entrance to tracheostomy tube. Hyperoxygenation provided for 30 seconds before and after suctioning using a bag valve mask with FiO2 100%. During the first suctioning pass, the ECG demonstrated bradycardia with HR dropping into the 50s. Suctioning was stopped. Trach tube was reattached to the mechanical ventilator and emergency assistance was requested from the respiratory therapist. Moderate amount of thick, white mucus without odor was suctioned. Post procedure, HR 78, RR 18, O2 sat 96% and lung sounds clear throughout all lobes.
- American Association for Respiratory Care. (2010). AARC clinical practice guideline: Endotracheal suctioning of mechanically ventilated patients with artificial airways 2010. Respiratory Care, 55 (6), 758-764. www.rcjournal.com/cpgs/pdf/06.10.0758.pdf↵
- “Example of a Sterile Tracheostomy Kit” by Julie Teeter at Gateway Technical College is licensed under CC BY 4.0 ↵
- American Association for Respiratory Care. (2010). AARC clinical practice guideline: Endotracheal suctioning of mechanically ventilated patients with artificial airways 2010. Respiratory Care, 55 (6), 758-764. www.rcjournal.com/cpgs/pdf/06.10.0758.pdf↵
- Tracheostomy suctioning. (2020). Lippincott procedures. http://procedures.lww.com ↵


2.4.15: Summary
Proof systems provide purely syntactic methods for characterizing consequence and compatibility between sentences. The sequent calculus is one such proof system. A derivation in it consists of a tree of sequents (a sequent \(\Gamma \Sequent \Delta\) consists of two sequences of formulas separated by \(\Sequent\) ). The topmost sequents in a derivation are initial sequents of the form \(A \Sequent A\) . All other sequents, for the derivation to be correct, must be correctly justified by one of a number of inference rules . These come in pairs; a rule for operating on the left and on the right side of a sequent for each connective and quantifier. For instance, if a sequent \(\Gamma \Sequent \Delta, A \lif B\) is justified by the \(\RightR{\lif}\) rule, the preceding sequent (the premise ) must be \(A, \Gamma \Sequent \Delta, B\) . Some rules also allow the order or number of sentences in a sequent to be manipulated, e.g., the \(\RightR{\Exchange}\) rule allows two formulas on the right side of a sequent to be switched.
If there is a derivation of the sequent \(\quad \Sequent A\) , we say \(A\) is a theorem and write \(\Proves A\) . If there is a derivation of \(\Gamma_0 \Sequent A\) where every \(B\) in \(\Gamma_0\) is in \(\Gamma\) , we say \(A\) is derivable from \(\Gamma\) and write \(\Gamma \Proves A\) . If there is a derivation of \(\Gamma_0 \Sequent \quad\) where every \(B\) in \(\Gamma_0\) is in \(\Gamma\) , we say \(\Gamma\) is inconsistent , otherwise consistent . These notions are interrelated, e.g., \(\Gamma \Proves A\) iff \(\Gamma \cup \{\lnot A\}\) is inconsistent. They are also related to the corresponding semantic notions, e.g., if \(\Gamma \Proves A\) then \(\Gamma \Entails A\) . This property of proof systems—what can be derived from \(\Gamma\) is guaranteed to be entailed by \(\Gamma\) —is called soundness . The soundness theorem is proved by induction on the length of derivations, showing that each individual inference preserves validity of the conclusion sequent provided the premise sequents are valid.


3.4: Gustav Holst - The Planets
While John Williams’s approach to creating the Star Wars soundtrack can be traced through Wagner, his music is more heavily influenced by other composers and works. The most frequently noted of these is the orchestral suite The Planets (1914-1916) by British composer Gustav Holst (1874- 1934). The reasons for which Williams chose to borrow from Holst are simple enough to understand. Holst was one of the first composers to write music about outer space, and he did so with a dramatic flair that has kept this work in the repertoire ever since its 1920 premiere.
Holst and The Planets
Holst studied composition at the Royal College of Music in London, where he met with moderate success. He was not attracted to the life of a professional musician (Holst played the trombone), but he struggled to make a living as a composer. In 1903, therefore, Holst began teaching music in schools. Although he would write some of his most successful music for the orchestras he directed, he had little time in which to pursue his craft. Nevertheless, Holst continued to produce serious concert pieces and his reputation steadily grew.
Holst finally earned national attention in 1920, first with a work for choir and orchestra entitled The Hymn of Jesus and then with The Planets . The Hymn of Jesus paved the way for The Planets ’ success by establishing for Holst a reputation as a mystic and spiritual composer. As we will see, these qualities are prominent in the orchestral suite. Although the entire suite was not premiered until 1920, Holst had been at work on it since 1913. He first wrote the music for two pianos, and produced the orchestral score only after the composition was complete.
Much of Holst’s work as a composer can be traced to his personal interests. This is certainly true of The Planets . In 1913, Holst travelled to Majorca with a group of fellow artists, who introduced him to the study of astrology. Holst became fascinated and immersed himself in the work of British astrologist Alan Leo, reading his book What Is a Horoscope and How Is It Cast ?. The idea of composing an orchestral suite came to him almost immediately, and he began sketching the first movement, “Mars,” that same year.
Holst’s intent was to capture the astrological significance of each of the planets, as described by Leo. He was interested in the specific characteristics bestowed on those who were born under the influence of each individual planet. At the same time, Holst was a composer first and an astrologer second. His primary concern was musical cohesion and expression. As a result, he frequently deviated from Leo’s prescription, and in the end used Leo’s writings merely as an inspiration for his own creative work.
It seems that Holst was worried that audiences would not take his music seriously. An orchestral work inspired by celestial bodies, after all, might easily be dismissed as a mere novelty, especially when compared to the traditional symphonies that formed the core of the concert hall repertoire (see Chapter 7). For this reason, Holst first titled his suite Seven Pieces for Orchestra , only later changing it to The Planets . He added the individual movement names, indicating which planet the music is about, only just before the work was published. The descriptive titles qualify The Planets as program music , a term used to identify an instrumental composition that tells a story or paints a picture. Holst chose not to order the movements in order of their distance from the sun, instead swapping Mars and Mercury. The reason for this decision is clear enough: The music that Holst composed to depict Mars makes a great opener for the work.
The Planets was a massive success. It was immediately programmed by orchestras all over England and has since become one of the most familiar and most frequently performed pieces in the orchestral repertoire. All the same, Holst came to regret his biggest hit. He continued to develop and grow as a composer, and within just a few years he considered The Planets to be outdated. Critics, on the other hand, were disappointed when Holst’s new compositions did not sound like his original blockbuster. Although Holst went on to write many beloved works, he never matched the success of The Planets.
We will examine the first and last movements of Holst’s suite: “Mars, the Bringer of War” and “Neptune, the Mystic.” “Mars” served as a model for John Williams’s “Imperial March” in the Star Wars soundtrack, while “Neptune” seems to have had a general influence on Williams’s musical portrayals of space.
Mars12
In astrological terms, the planet Mars is associated with confidence, self assertion, aggression, energy, strength, ambition, and impulsiveness. Leo described those born under the influence of Mars as “fond of liberty, freedom, and independence,” noting that they “may be relied upon for courage” and are “fond of adventure and progress” but are also “headstrong and at times too forceful.” In mythological terms, Mars is the ancient Roman god of war.
|
“Mars” from The Planets 12. Composer: Gustav Holst Performance: Chicago Symphony Orchestra, conducted by James Levine (1990) |
Holst seems to have combined these influences in his music, which is overtly militaristic. The staccato rhythms heard at the beginning are the rhythms of a military march. At first they are played by the entire string section using a special technique, known as col legno , for which players turn their bows upside down and bounce the wooden stick on the string. Later, the snare drum—an actual military instrument—plays the same rhythm, which is heard almost throughout the movement. There is something very strange about Holst’s march, however: It is in quintuple meter, with five beats per measure. It would be very difficult to actually march to this music.
Holst uses other strategies as well to communicate the character of Mars. The first melody we hear is low and ominous, consisting only of a rising gesture followed by a small descent. As the texture thickens, the volume increases and the melodic gestures seems more threatening. The introduction of trumpets and other brass instruments reinforces the militaristic flavor of the movement. In the middle section, the trumpets seem to be sounding battle calls. Finally, the whole movement comes to a crashing close with the strings and brass playing as loudly and violently as possible.
Neptune13
Holst’s representation of Neptune, the final planet in his suite, is entirely different. This is natural enough, given Holst’s astrological mindset, for the influence of Neptune is associated with idealism, dreams, dissolution, artistry, empathy, illusion, and vagueness. Holst creates music, therefore, that captures these same qualities.
|
“Neptune” from The Planets 13. Composer: Gustav Holst Performance: Chicago Symphony Orchestra, conducted by James Levine (1990) |
We might begin with a discussion of timbre. “Neptune” includes a sound that is completely absent from the other movements: women’s voices. Holst includes two choirs of sopranos and altos , making for six separate vocal parts. The women don’t sing words, however, but are instead instructed to sustain long, open “ah” vowels. The singers therefore function in the same way as instruments, bringing an ethereal, transparent quality to the upper register of the orchestra.
Apart from the voices, “Neptune” calls for the same instruments as “Mars.” However, Holst deploys these instruments quite differently. He hardly uses the brass section at all, relegating them to low, sustained pitches in the background of the texture. Holst assigns the melody to wind instruments, with a preference for the airy sound of the flutes and the reedy timbre of the oboe and English horn. He also foregrounds the two harps and a percussion instrument called the celeste, which has a keyboard similar to that of a piano but produces the sound of bells.
The articulation in “Neptune” is completely unlike that heard in “Mars.” While “Mars” is characterized by abrupt, accented rhythms, the pitches in “Neptune” are sustained and connected. Interestingly, this is the only movement that Holst originally composed for organ instead of piano. He felt that the organ, which can sustain pitches indefinitely, was better able to capture his musical vision. While both “Mars” and “Neptune” are in quintuple meter, the differences in articulation and tempo (“Neptune” is much slower) means that the two movements have completely different effects on the listener.
Finally, we might say something about the melody and harmony. There are no catchy tunes in “Neptune.” Instead, the wind instruments and voices repeat floaty, circular melodies that don’t seem to go anywhere. “Neptune” is also not in any particular key. Instead, the music rocks back and forth between seemingly unrelated harmonies. All of this creates the sensation of being unmoored. It is hard to predict where the music is going, but easy to enjoy the beautiful sounds.


2.2: Use the Language of Algebra (Part 2)
Simplify Expressions Using the Order of Operations
We’ve introduced most of the symbols and notation used in algebra, but now we need to clarify the order of operations. Otherwise, expressions may have different meanings, and they may result in different values. For example, consider the expression: \[4 + 3 \cdot 7 \nonumber\]
| Some students say it simplifies to | 49 | Some students say it simplifies to | 25 |
| Since 4 + 3 gives 7. | 4 + 3 • 7 = 7 • 7 | Since 3 • 7 is 21. | 4 + 3 • 7 = 4 + 21 |
| And 7 • 7 is 49. | 7 • 7 = 49 | And 21 + 4 makes 25. | 4 + 21 = 25 |
Imagine the confusion that could result if every problem had several different correct answers. The same expression should give the same result. So mathematicians established some guidelines called the order of operations, which outlines the order in which parts of an expression must be simplified.
When simplifying mathematical expressions perform the operations in the following order:
- P arentheses and other Grouping Symbols
- Simplify all expressions inside the parentheses or other grouping symbols, working on the innermost parentheses first.
- E xponents
- Simplify all expressions with exponents.
- M ultiplication and D ivision
- Perform all multiplication and division in order from left to right. These operations have equal priority.
- A ddition and S ubtraction
- Perform all addition and subtraction in order from left to right. These operations have equal priority.
Students often ask, “How will I remember the order?” Here is a way to help you remember: Take the first letter of each key word and substitute the silly phrase. P lease E xcuse M y D ear A unt S ally.
| Order of Operations | |
|---|---|
| P lease | P arentheses |
| E xcuse | E xponents |
| M y D ear | M ultiplication and D ivision |
| A unt S ally | A ddition and S ubtraction |
It’s good that ‘ M y D ear’ goes together, as this reminds us that m ultiplication and d ivision have equal priority. We do not always do multiplication before division or always do division before multiplication. We do them in order from left to right.
Similarly, ‘ A unt S ally’ goes together and so reminds us that a ddition and s ubtraction also have equal priority and we do them in order from left to right.
Simplify the expressions:
- \(4 + 3 • 7\)
- \((4 + 3) • 7\)
Solution
| Are there any parentheses? No. Are there any exponents? No. Is there any multiplication or division? Yes. | \(4 + 3 \cdot 7\) |
| Multiply first. | \(4 + \textcolor{red}{3 \cdot 7}\) |
| Add. | \(4 + 21\) |
| \(25\) |
| Are there any parentheses? Yes. | \((4 + 3) \cdot 7\) |
| Simplify inside the parentheses. | \(\textcolor{red}{(4 + 3)} \cdot 7\) |
| Are there any exponents? No. Is there any multiplication or division? Yes. | \((7)7\) |
| Multiply. | \(49\) |
Simplify the expressions:
- \(12 − 5 • 2\)
- \((12 − 5) • 2\)
- Answer a
-
\(2\)
- Answer b
-
\(14\)
Simplify the expressions:
- \(8 + 3 • 9\)
- \((8 + 3) • 9\)
- Answer a
-
\(35\)
- Answer b
-
\(99\)
Simplify:
- \(18 ÷ 9 • 2\)
- \(18 • 9 ÷ 2\)
Solution
| Are there any parentheses? No. Are there any exponents? No. Is there any multiplication or division? Yes. | \(18 \div 9 \cdot 2\) |
| Multiply and divide from left to right. Divide. | \(\textcolor{red}{2} \cdot 2\) |
| Multiply. | \(4\) |
| Are there any parentheses? No. Are there any exponents? No. Is there any multiplication or division? Yes. | \(18 \cdot 9 \div 2\) |
| Multiply and divide from left to right. Multiply. | \(\textcolor{red}{162} \div 2\) |
| Divide. | \(81\) |
Simplify: \(42 ÷ 7 • 3\)
- Answer
-
\(18\)
Simplify: \(12 • 3 ÷ 4\)
- Answer
-
\(9\)
Simplify: \(18 ÷ 6 + 4(5 − 2)\).
Solution
| Parentheses? Yes, subtract first. | \(18 \div 6 + 4(5-2)\) |
| Exponents? No. Multiplication or division? Yes. | \(18 \div 6 + 4(\textcolor{red}{3})\) |
| Divide first because we multiply and divide left to right. | \(\textcolor{red}{3} + 4(3)\) |
| Any other multiplication or division? Yes. Multiply. | \(3 + \textcolor{red}{12}\) |
| Any other multiplication or division? No. Any addition or subtraction? Yes | \(15\) |
Simplify: \(30 ÷ 5 + 10(3 − 2)\)
- Answer
-
\(16\)
Simplify: \(70 ÷ 10 + 4(6 − 2)\)
- Answer
-
\(23\)
When there are multiple grouping symbols, we simplify the innermost parentheses first and work outward.
Simplify: \(5 + 2^3 + 3[6 − 3(4 − 2)]\).
Solution
| Are there any parentheses (or other grouping symbol)? Yes. | \(5 + 2^{3} + 3[6-3(4-2)]\) |
| Focus on the parentheses that are inside the brackets. | \(5 + 2^{3} + 3[6-3 \textcolor{red}{(4-2)}]\) |
| Subtract. | \(5 + 2^{3} + 3[6- \textcolor{red}{3(2)}]\) |
| Continue inside the brackets and multiply. | \(5 + 2^{3} + 3[6- \textcolor{red}{6}]\) |
| Continue inside the brackets and subtract. | \(5 + 2^{3} + 3[\textcolor{red}{0}]\) |
| The expression inside the brackets requires no further simplification. | |
| Are there any exponents? Yes. | \(5 + \textcolor{red}{2^{3}} + 3[0]\) |
| Simplify exponents. | \(5 + \textcolor{red}{8} + 3[0]\) |
| Is there any multiplication or division? Yes. | \(5 + 8 + \textcolor{red}{3[0]}\) |
| Multiply. | \(5 + 8 + \textcolor{red}{0}\) |
| Is there any addition or subtraction? Yes. | \(textcolor{red}{5+8+0}\) |
| Add. | \(\textcolor{red}{13} + 0\) |
| Add. | \(13\) |
Simplify: \(9 + 5^3 − [4(9 + 3)]\)
- Answer
-
\(86\)
Simplify: \(7^2 − 2[4(5 + 1)]\)
- Answer
-
\(1\)
Simplify: \(2^3 + 34 ÷ 3 − 5^2\).
Solution
| If an expression has several exponents, they may be simplified in the same step. | \(2^{3} + 3^{4} \div 3 - 5{2}\) |
| Simplify exponents. | \(\textcolor{red}{2^{3}} + \textcolor{red}{3^{4}} \div 3 - \textcolor{red}{5^{2}}\) |
| Divide. | \(8 + \textcolor{red}{81 \div 3} - 25\) |
| Add. | \(\textcolor{red}{8+27} - 25\) |
| Subtract. | \(\textcolor{red}{35-25}\) |
| \(10\) |
Simplify: \(3^2 + 2^4 ÷ 2 + 4^3\)
- Answer
-
\(81\)
Simplify: \(6^2 − 5^3 ÷ 5 + 8^2\)
- Answer
-
\(75\)
Access Additional Online Resources
Key Concepts
| Operation | Notation | Say: | The result is… |
|---|---|---|---|
| Addition | the sum of | ||
| Multiplication | The product of | ||
| Subtraction | the difference of | ||
| Division | \(a\div b, a/b, \dfrac{a}{b}, a \overline{\smash{)}b}\) | The quotient of |
-
Equality Symbol
- The symbol \(=\) is called the equal sign.
-
Inequality
- \(a>b\) is read \(a\) is greater than \(b\)
| Algebraic Notation | Say |
|---|---|
| is less than or equal to | |
| is greater than or equal to |
-
Exponential Notation
- For any expression \(a^n\) is a factor multiplied by itself
- The expression of
Order of Operations When simplifying mathematical expressions perform the operations in the following order:
- Parentheses and other Grouping Symbols: Simplify all expressions inside the parentheses or other grouping symbols, working on the innermost parentheses first.
- Exponents: Simplify all expressions with exponents.
- Multiplication and Division: Perform all multiplication and division in order from left to right. These operations have equal priority.
- Addition and Subtraction: Perform all addition and subtraction in order from left to right. These operations have equal priority.
Glossary
- expressions
-
An expression is a number, a variable, or a combination of numbers and variables and operation symbols.
- equation
-
An equation is made up of two expressions connected by an equal sign.
Practice Makes Perfect
Use Variables and Algebraic Symbols
In the following exercises, translate from algebraic notation to words.
- 16 − 9
- 25 − 7
- 5 • 6
- 3 • 9
- 28 ÷ 4
- 45 ÷ 5
- x + 8
- x + 11
- (2)(7)
- (4)(8)
- 14 < 21
- 17 < 35
- 36 ≥ 19
- 42 ≥ 27
- 3n = 24
- 6n = 36
- y − 1 > 6
- y − 4 > 8
- 2 ≤ 18 ÷ 6
- 3 ≤ 20 ÷ 4
- a ≠ 7 • 4
- a ≠ 1 • 12
Identify Expressions and Equations
In the following exercises, determine if each is an expression or an equation.
- 9 • 6 = 54
- 7 • 9 = 63
- 5 • 4 + 3
- 6 • 3 + 5
- x + 7
- x + 9
- y − 5 = 25
- y − 8 = 32
Simplify Expressions with Exponents
In the following exercises, write in exponential form.
- 3 • 3 • 3 • 3 • 3 • 3 • 3
- 4 • 4 • 4 • 4 • 4 • 4
- x • x • x • x • x
- y • y • y • y • y • y
In the following exercises, write in expanded form.
- 5 3
- 8 3
- 2 8
- 10 5
Simplify Expressions Using the Order of Operations
In the following exercises, simplify.
- (a) 3 + 8 • 5 (b) (3+8) • 5
- (a) 2 + 6 • 3 (b) (2+6) • 3
- 2 3 − 12 ÷ (9 − 5)
- 3 2 − 18 ÷ (11 − 5)
- 3 • 8 + 5 • 2
- 4 • 7 + 3 • 5
- 2 + 8(6 + 1)
- 4 + 6(3 + 6)
- 4 • 12 / 8
- 2 • 36 / 6
- 6 + 10 / 2 + 2
- 9 + 12 / 3 + 4
- (6 + 10) ÷ (2 + 2)
- (9 + 12) ÷ (3 + 4)
- 20 ÷ 4 + 6 • 5
- 33 ÷ 3 + 8 • 2
- 20 ÷ (4 + 6) • 5
- 33 ÷ (3 + 8) • 2
- 4 2 + 5 2
- 3 2 + 7 2
- (4 + 5) 2
- (3 + 7) 2
- 3(1 + 9 • 6) − 4 2
- 5(2 + 8 • 4) − 7 2
- 2[1 + 3(10 − 2)]
- 5[2 + 4(3 − 2)]
Everyday Math
- Basketball In the 2014 NBA playoffs, the San Antonio Spurs beat the Miami Heat. The table below shows the heights of the starters on each team. Use this table to fill in the appropriate symbol (=, <, >).
| Spurs | Height | Heat | Height |
|---|---|---|---|
| Tim Duncan | 83″ | Rashard Lewis | 82" |
| Boris Diaw | 80" | LeBron James | 80" |
| Kawhi Leonard | 79" | Chris Bosh | 83" |
| Tony Parker | 74" | Dwyane Wade | 76" |
| Danny Green | 78" | Ray Allen | 77" |
- Height of Tim Duncan____Height of Rashard Lewis
- Height of Boris Diaw____Height of LeBron James
- Height of Kawhi Leonard____Height of Chris Bosh
- Height of Tony Parker____Height of Dwyane Wade
- Height of Danny Green____Height of Ray Allen
- Elevation In Colorado there are more than 50 mountains with an elevation of over 14,000 feet. The table shows the ten tallest. Use this table to fill in the appropriate inequality symbol.
| Mountain | Elevation |
|---|---|
| Mt. Elbert | 14,433′ |
| Mt. Massive | 14,421′ |
| Mt. Harvard | 14,420′ |
| Blanca Peak | 14,345′ |
| La Plata Peak | 14,336′ |
| Uncompahgre Peak | 14,309′ |
| Crestone Peak | 14,294′ |
| Mt. Lincoln | 14,286′ |
| Grays Peak | 14,270′ |
| Mt. Antero | 14,269′ |
- Elevation of La Plata Peak____Elevation of Mt. Antero
- Elevation of Blanca Peak____Elevation of Mt. Elbert
- Elevation of Gray’s Peak____Elevation of Mt. Lincoln
- Elevation of Mt. Massive____Elevation of Crestone Peak
- Elevation of Mt. Harvard____Elevation of Uncompahgre Peak
Writing Exercises
- Explain the difference between an expression and an equation.
- Why is it important to use the order of operations to simplify an expression?
Self Check
(a) After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.
(b) If most of your checks were:
…confidently. Congratulations! You have achieved the objectives in this section. Reflect on the study skills you used so that you can continue to use them. What did you do to become confident of your ability to do these things? Be specific.
…with some help. This must be addressed quickly because topics you do not master become potholes in your road to success. In math, every topic builds upon previous work. It is important to make sure you have a strong foundation before you move on. Who can you ask for help? Your fellow classmates and instructor are good resources. Is there a place on campus where math tutors are available? Can your study skills be improved?
…no—I don’t get it! This is a warning sign and you must not ignore it. You should get help right away or you will quickly be overwhelmed. See your instructor as soon as you can to discuss your situation. Together you can come up with a plan to get you the help you need.
Contributors and Attributions
- Lynn Marecek (Santa Ana College) and MaryAnne Anthony-Smith (formerly of Santa Ana College). This content produced by OpenStax and is licensed under a Creative Commons Attribution License 4.0 license.


5.3: Mudrocks
By definition, mudrocks contain more than 50% mud-sized particles (silt and clay). They are the most abundant sedimentary rocks because the sediment typically is deposited in calm environments relatively far from tectonically-active areas. Although they commonly contain abundant organic material and are important source rocks in petroleum systems, they are understudied because they weather quickly and are generally not well exposed at the surface and because specialized techniques and equipment are needed to fully understand the fine-grained particles that make up these rocks.
Mudrock Classification
Unfortunately, there is no one universally accepted classification scheme for mudrocks. We use the term mudrock to refer to all rocks containing >50% clay and silt. If further subdivision is required, we use the terms siltstone (<33% clay), mudstone (33-67% clay), and claystone (>67% clay).
We use the term shale to describe a mudrock that has pronounced fissility (breaks into sheets); this takes the place of terms like mudrock, siltstone, mudstone, and claystone. Modifiers like sandy, pebbly, etc. are useful in some situations.
Important Properties
Stratification and Weathering
The outcrop appearance of a mudrock reflects some combination of resistance to weathering and nature of primary stratification. Adjectives like shale, platy (flattened), blocky (equant), hackly (equant with sharp edges), etc. are very useful when describing mudrocks in outcrop.
Color
If its primary and reflects the characteristics of the sediment at the time of deposition, the color of a mudrock can tell your something about the organic content and amount of oxygen in the environment where the sediment was deposited. Red mudrocks reflect very little organic material and abundant oxygen in the system at the time of deposition; many are deposited in terrestrial environments. Green/gray color reflects reducing conditions with a modest amount of organic material; these conditions exist in a variety of environments. Black mudrocks have abundant organic material and record anoxic conditions at the time of deposition; these sorts of conditions can occur in a variety of environments from oxbow lakes on a floodplain to deep marine sediments.
Mudrocks can form anywhere there are calm waters. Understanding how and where they formed is facilitated by comparing the physical characteristics described above with characteristics like context, fossil content, color, and detailed analysis of mineralogy and geochemistry (especially of organic components).
Figure \(\PageIndex{2}\): Mudrock colors and textures. A) Bright yellow, red, and/or purple colors are commonly associated with paleosols (James St. John via Wikimedia Commons ; CC BY 2.0 ). B) The blocky texture and red/green colors of this mudrock suggest that it is a poorly developed paleosol that formed in mostly oxidizing conditions. C) Internally massive greenish gray mudrock with siderite nodules and associated coal; together these features suggest deposition in a reducing swampy environment. D) Platy dark gray to black shales with minor siltstone and sandstones. These rocks likely formed in an organic-rich standing body of water. B-D from Michael C. Rygel via Wikimedia Commons ; CC BY-SA 4.0 .
Components
Mudrocks are composted of silt-sized particles that are typically composed of quartz, feldspar, or other common minerals … some might even be large enough to classify using the petrographic microscope.
Although the terminology is confusing, many of the clay-sized particles (<1/256 mm) in a mudrock happen to be “ clay minerals ” which is a name applied to a specific group of aluminosilicate and phyllosilicates minerals. These clay minerals are derived from weathering (hydrolysis) of feldspar and mica.
Mineralogy
Clay minerals are made of alternating layers of silicon-oxygen tetrahedra ( tetrahedral sheets ) and alumina-oxygen octahedra ( octahedral sheets ). These sheets can be layered in a variety of ways and may even alternate with interlayer cations or water. Clay minerals can be grouped into two main families: 1:1 clay minerals and 2:1 clay minerals.
1:1 clay minerals are the product of more intense/prolonged weathering that progressively strips interlayer cations from 2:1 clay minerals which concentrates Si, Fe, and Al in a simpler structure. Their fundamental building block is a single octahedral layer bonded to a single tetrahedral layer. Kaolinite is probably the best known and most important 1:1 clay mineral because of its close association with alumina- and/or iron-rich soils ( bauxites and laterites , respectively)
The fundamental building block of 2:1 clay minerals is an octahedral sheet sandwiched between two tetrahedral sheets. Between these T-O-T packages, variable amounts of Al, Mg, Fe, water, or other interlayer cations determine the mineralogy of the specimen. These relatively complex clay minerals tend to form in temperate areas. Noteworthy 2:1 clay minerals include:
- “ Swelling clays ” like montmorillonite and vermiculite are 2:1 clays that can retain significant amounts of water
- Glauconite is a green, iron-rich clay mineral that forms as a replacement of fecal pellets in reducing marine conditions
-
Bentonite
is a 2:1 clay formed from weathered volcanic ash beds by alkaline & acidic water, respectively. Given their volcanic origin, dateable minerals like zircon are commonly found with bentonites.
« Previous page
Figure \(\PageIndex{4}\): Noteworthy clay minerals. A) Granule-sized Silurian glauconite pellets from Ohio (
James Cheshire
via
Wikimedia Commons
;
public domain
) B) Black shales and bentonites from the Cretaceous Benton Shale (James St. John via
Wikimedia Commons
;
CC BY 2.0
). C) White pellets of vermiculite are commonly added to potting soil to help retain water (
M Tullottes
via
Wikimedia Commons
;
public domain
). D) Bag of bentonite - a swelling clay that is commonly used to seal well casings (
Corey872
via
Wikimedia Commons
;
public domain
). E) Kaolinite and, to a lesser degree, montmorillonite and bentonite, are commonly used in pottery clay (Knecht03 via
Wikimedia Commons
,
CC BY SA 3.0
). Laterites are soils that are enriched in kaolinite and iron via intense tropical weathering; they are commonly used as brick and road bed material (
Vinayaraj
via
Wikimedia Commons
;
CC BY-SA 4.0
).
Readings and Resources
- Kumari and Mohan, 2021, Basics of Clay Minerals and Their Characteristic Properties
- Potter et al., 1980, Sedimentology of Shale, Springer-Verlag, New York, 306 p., ISBN 0-387-90430-1


<IP_ADDRESS>: Exposing Yourself Whilst Trying To Expose Others
-
- Last updated
- Save as PDF
- Robin DeRosa, Abby Goode et al.
- Plymouth State University/
Interestingly enough, it seems as though, while Mary Rowlandson tries to depict her encounter in an awful light (and arguably many parts of the experience are), she also seems to undermine herself much like De Las Casas does when trying to explain his own experience. While they both place themselves as the direct victim, they end up also revealing many enlightening and kind aspects of the Native Americans and, ironically, shed themselves in a more negative light whenever they then immediately go on to remind the reader what “terrible creatures” the Native Americans are in the very same breath. Rowlandson seems to depict the Native Americans as complete monsters, as she often uses animalistic and demonic traits in descriptions, such as when she writes, “Oh the roaring, the singing and dancing, and yelling of those black creatures in the night, which made the place a lively resemblance of hell” (The First Remove).  Also, “those black creatures”…. Yikes. Aside from the blatant racism in those words, she pairs it with “in the night”, which subtly creates this general context and correlation of dark being evil and sinister. In case that point isn’t clear enough to the audience, she becomes more blunt in her meaning by literally describing it all as “a lively resemblance of hell”. This type of description essentially sets the tone for the rest of her writings, as she constantly refers back to this type of description of the Native Americans often. However, though her initial intention with these words is to portray her captors in a negative light, it begins to backfire. By “The Second Remove” onward, we begin to see moments of kindness and mercy amongst the Native Americans. When Rowlandson’s child is ill, one of the men carries her on a horse. They also give Rowlandson a Bible and tell her she is allowed to practice her faith, along with offering her hospitality and more food and even money for her work towards “The Eighth Remove”. Now of course other actions of the Native Americans were wrong (taking Rowlandson against her will for instance), but it exposes the Native Americans to also hold much more kindness than I presume the Colonists did to their victims. Yet, right after mentioning these acts of kindness, our author then spouts another scathing line about how these people are “heathens”. One last but notably important thing is that like in Disney’s
Pocahontas”
the Native Americans speak English to Rowlandson,
for
her–something I don’t necessarily know how to break down now. But we already see traces of erasure within the homes of the Native Americans, and this merits further discussion on how deep the roots of this erasure really are and how they began.


2.4: Discussion- Bede (Caedmon) and the Dream of the Rood
Source readings : Cædmon’s “Hymn”; “The Dream of the Rood”
Discussion Prompt
Answer all parts of all questions.
- In the selection from Bede, Bede discusses the circumstances of the development of Caedmon’s “Hymn.” What is your interpretation of the fact that Caedmon, who was not a learned man, was suddenly able to write such inspired poetry? Is it significant that the hymn came to Caedmon in a dream? Explain.
- In “The Dream of the Rood” there is more than one first person speaker: the narrator and the Rood (also known as the “tree,” referring to an actual tree or its subsequent form as Jesus’s cross). Demonstrate an understanding of the poem’s structure by identifying who is speaking and where. (You can use brief quotations and/or line numbers to identify this in your answer.) What are the tree’s (rood’s) feelings about being used for the purpose of Jesus’s cross? What are the narrator’s feelings about dreaming about the Rood?
Discussion Board Instructions
Answer each question, unless otherwise specified. Number your answers (do not copy the prompt into your answers.) Answers need not be of equal length, but all answers must be well developed. The word count total (250+) refers to all answers added together.
In the first sentence or two of your first answer identify the name of the work and full name of the author (if applicable).
Include at least one quotation from the work in your overall response. Use line number(s) to identify the location of your citation. No works cited page is needed.
Grading Rubric
| Levels of Achievement | |||||
|---|---|---|---|---|---|
| Criteria | Excellent | Good | Adequate | Inadequate | Unacceptable |
| Response: Content Length and Development | 22 Points | 19 Points | 16 Points | 11 Points | 0 Points |
| Meets or exceeds the minimum length requirement. Demonstrates insight and understanding of the text(s) in an excellent, thorough, detailed, clear, and well developed response to the entire prompt. Response is comprised primarily of the student’s own answer(s), but is supported by at least one well chosen quotation. | Meets the minimum length requirement. Demonstrates understanding of the text(s) in a good, clear, well developed response to the entire prompt. Response is comprised primarily of the student’s own answer(s), but is supported by at least one well chosen quotation. | Meets or nearly meets the minimum length requirement. Demonstrates a basic understanding of the text(s) in a developed response to the prompt. Includes an adequate amount of the student’s own answer(s), but may incorporate too much summary, paraphrase, or quotations or lack a quotation for support. | Meets or falls 15%+ short of the minimum length requirement. Inadequately responds to the prompt with answer(s) that are substantively incorrect, superficial, underdeveloped, and/or reliant mostly on summary, paraphrase, or quotations. | Unacceptable development: Fails to meet at least 50% of the length requirement. | |
| Response: Source Identification and Citation | 4 points | 3.5 points | 3 Points | 2 Points | 0 Points |
| Clearly identifies by title and full name of author the name(s) of work(s) to be discussed. Cites material from source(s) as instructed in the assignment. | Identifies the work(s) and author(s). Cites material from source(s) as instructed in the assignment. | Identifies the work(s) or author(s). Cites adequately. | Inadequately identifies source(s) and author(s) and/or inadequately cites source(s). | Lacks identification and citation of source(s). | |
| Response: Grammar and Mechanics | 4 Points | 3.5 Points | 3 Points | 2 Points | 0 Points |
| Response is free or nearly free of errors in grammar (including but not limited to use of full sentences and appropriate word choice) and mechanics (including but not limited to spelling and punctuation). | Response demonstrates occasional errors in grammar or mechanics that do not affect overall clarity. | Demonstrates errors in grammar or mechanics that occasionally affect meaning. | Inadequately meets standards for grammar and mechanics. Clarity is frequently affected. | Unacceptable level of errors in grammar or mechanics. Clarity is greatly affected. | |
| Comment 1: Engagement and Content | 7 Points | 6 Points | 5 Points | 3.5 Points | 0 Points |
| Demonstrates thorough engagement in a comment that is detailed, well crafted, and reflective. | Demonstrates effective engagement in a comment that is effectively crafted and reflective. | Demonstrates an adequate engagement in a comment that addresses at least one point of an answer to the other student’s response. | Demonstrates inadequate engagement in a comment that only superficially or tangentially addresses the content of the other student’s response. | Unacceptable development: Fails to meet at least 50% of the minimum length requirement. | |
| Comment 1: Grammar and Mechanics and Length Requirement | 3 Points | 2.5 Points | 2 Points | 1.5 Points | 0 Points |
| Contains few if any grammar or mechanics issues. Meets or exceeds the minimum length requirement. | Contains few if any grammar or mechanics issues. Meets the length requirement. | Contains grammar and/or mechanics issues that occasionally affect clarity. Meets or falls within 10% of the minimum length requirement. | Inadequately meets standards for grammar and mechanics. Clarity is frequently affected. Meets or falls 15%+ short of the minimum length requirement. | Unacceptable level of errors in grammar or mechanics that greatly affect clarity. (No credit for this element if fails to meet at least 50% of the minimum length requirement.) | |
| Comment 2: Engagement and Content | 7 Points | 6 Points | 5 Points | 3.5 Points | 0 Points |
| Demonstrates thorough engagement with the content of the other student’s response in a comment that is detailed, well crafted, and reflective. | Demonstrates effective engagement in a comment that is effectively crafted and reflective. | Demonstrates an adequate engagement in a comment that engages with at least one point of content in the other student’s response. | Demonstrates inadequate engagement in a comment that only superficially or tangentially addresses the content of the other student’s response. | Unacceptable development: Fails to meet at least 50% of the length requirement. | |
| Comment 2: Grammar and Mechanics and Length Requirement. | 3 Points | 2.5 Points | 2 Points | 1.5 Points | 0 Points |
| Contains few if any grammar or mechanics issues. Meets or exceeds the minimum length requirement. | Contains a few grammar and/or mechanics issues, but these do not affect overall clarity. Meets the minimum length requirement. | Contains grammar and/or mechanics issues that occasionally affect clarity. Meets or falls within 10% of the minimum length requirement. | Inadequately meets standards for grammar and mechanics. Clarity is frequently affected. Meets or falls 15%+ short of the minimum length requirement. | Unacceptable level of errors in grammar or mechanics that greatly affect clarity. (No credit for this element if comment fails to meet at least 50% of the minimum length requirement.) |
- Survey of English Literature I. Authored by : Wendy Howard Gray. Provided by : Reynolds Community College. Located at : http://www.reynolds.edu/ . License : CC BY: Attribution


3.1: Lab 3- Spinal Cord and Spinal Nerves
Measurable Outcomes
- Correctly identify the structures which constitute comprise the spinal cord and its extensions.
- Explain the differences between the meninges.
- Differentiate the spinal plexuses.
- Determine the origin, pathway and target organs of the spinal nerves.
- Classify the structures of the spinal cord on the given histology slides.
- Demonstrate an adequate understand of the material in this section.
Background
The spinal cord is made of white matter encompassed by gray matter with a central canal running through it that serves as a path for cerebrospinal fluid (CSF) . The gray matter is divided into posterior (dorsal) grey horns which contain sensory neurons, and lateral and anterior (ventral) horns that contain the cell bodies of motor neurons. The surrounding white matter is divided into anterior (ventral) white columns , lateral white columns , and posterior (dorsal) white columns . The grey commissure is the gray matter posterior to the central canal where the neurons from either side of the spinal cord crossover. The same principle applies to the white commissure which lies anteriorly to the gray matter.
The spinal cord has several layers to protect it from damage. Beginning superficially and working our way deeper, the vertebral column encases the spinal cord and provides a hard shell for protection. Deep to the vertebrae are the meninges, consisting of the dura mater , arachnoid mater, and pia mater . Extensions from the pia mater, the denticulate ligaments, suspend the spinal cord in CSF and act as a shock absorber.
The spinal cord begins at the terminal end of the brain stem and extends to approximately the L1 vertebra adults and L2 vertebrae in children; it is located within the vertebral foramen and is divided into 4 distinct regions. The cervical segment extends from C1 to the C7 vertebrae. The thoracic segment extends from T1 to the T8 vertebrae. The lumbar segment corresponds with T9-T11 vertebrae. Finally, the sacral segment extends from T12 to L2. The cervical enlargement, C4-T1, is a bulbous structure from which many neurons of the upper extremities invaginate. Likewise, the lumbar enlargement, T9-T12, is a bulbous structure from which neurons that innervate the lower limbs originate.
Note: do not confuse the regions of the spine with the regions of the spinal cord, they are not the same.
There are 31 pairs of spinal nerves: 8 cervical pairs 12 thoracic pairs, 5 lumbar pairs, 5 sacral pairs and 1 coccygeal pair. However, nerves from every other area along the spinal cord do not do this; they first converge in a network called a plexus. With the exception of the thoracic region, nerves of the cervical, brachial, lumbar and sacral regions of the spinal cord branch from a network of nerves known as plexuses.
Vocabulary for Spinal Cord and Spinal Nerves can be found on page(s) 171-172 .