6: The Roman World from 753 BCE to 500 BCE
The story of the Roman world from the foundation of the city of Rome and to the fall of the Roman Empire in the West is, overall, a tale of two different transformations. The first of these is the dramatic transformation in cultural values and beliefs, a glimpse of which is reflected in the two stories above. The second is a similarly dramatic geographical transformation, which also brought about drastic clashes of cultures and a variety of changes throughout the entire Mediterranean world and beyond, that is, the transformation of a small village on the Tiber into one of the largest empires in all of world history, followed by a collapse of a part of that Empire, but a collapse from whose ashes arose what we now know as Europe.
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- 6.5: Geography and Topography of Rome and the Roman Empire
- As the title of one recent textbook of Roman history puts it, Roman history is, in a nutshell, the story of Rome’s transformation “from village to empire.”1 The geography and topography of Rome, Italy, and the Mediterranean world as a whole played a key role in the expansion of the empire but also placed challenges in the Romans’ path, challenges which further shaped their history.
-
- 6.6: Basic Chronology and Periods of Roman History
- According to Roman tradition, Rome was founded as a monarchy. That monarchy, however, was not long-lived, and its history is overshadowed by myth and legend. Historians of Rome have most often divided its history into two major periods, based on the type of government that Rome had at the time: the Republic (from the late sixth century BCE to the late first century BCE) and the Empire (from the late first century BCE to the fall of the Western half of the empire in the late fifth century CE).
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- 6.9: Fall of the Roman Republic
- The victory over Carthage in the Second Punic War allowed Rome to “close” the circle of the Mediterranean almost completely, acquiring control over all territories that had previously belonged to Carthage. The destruction of Carthage in the Third Punic War, while largely a symbolic gesture, further cemented Rome’s control over the entire Mediterranean. The late Republican historian Sallust, though, grimly saw the Roman victory in the Punic Wars as the beginning of the end of the Republic.
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- 6.10: The Early Empire
- The period from the consolidation of power by Augustus in 27 BCE to the death of the emperor Marcus Aurelius in 180 CE was one of relative peace and prosperity throughout the Roman Empire. For this reason, the Romans themselves referred to this time as the Pax Romana, or Roman peace. During this period, the Empire became increasingly more of a smoothly run bureaucratic machine when commerce prospered, and the overall territory grew to its largest extent in the early second century CE.
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- 6.11: The Third-Century Crisis, and Late Antiquity
- While the second century CE was a time when the Empire flourished, the third century was a time of crisis, defined by political instability and civil wars, which ultimately demonstrated that the Empire had become too large to be effectively controlled by one ruler. Furthermore, the increasing pressures on the frontiers, which required emperors to spend much of their time on campaigns, resulted in the decline of the importance of the city of Rome.
Thumbnail: The extent of the Roman Republic in 40 BC after Caesar's conquests. (Public Domain; Tataryn77 via Wikipedia).


What you’ll learn to do: analyze emotional and social development in middle adulthood
Traditionally, middle adulthood has been regarded as a period of reflection and change. In the popular imagination (and academic press) there has been reference to a “mid-life crisis.” There is an emerging view that this may have been an overstatement—certainly, the evidence on which it is based has been seriously questioned. However, there is some support for the view that people do undertake a sort of emotional audit, reevaluate their priorities, and emerge with a slightly different orientation to emotional regulation and personal interaction in this time period. Why, and the mechanisms through which this change is affected, are a matter of some debate. We will examine the ideas of Erikson, Baltes, and Carstensen, and how they might inform a more nuanced understanding of this vital part of the lifespan.
Contributors and Attributions
CC licensed content, Original
-
Introduction to Emotional and Social Development in Middle Adulthood.
Authored by
: Ronnie Mather for Lumen Learning.
Provided by
: Lumen Learning.
License
:
CC BY: Attribution
CC licensed content, Shared previously


8.13: Putting It Together- Retail Human Resources
So the structure of the staff from the CEO or president to the cashiers, stockers and maintenance staff are all important and necessary components of a well run retail business. Whether you are managing a single store or are part of a larger national chain store, similar tasks need to be completed on different scales.
Human resources needs to manage all of these positions, job descriptions and employment related details to make sure all of the laws regarding employment are properly followed. Securing a quality workforce is a challenge in this economic environment, with low unemployment. Employers need to be diligent in securing qualified staff, and then providing the support, training and resources to keep them.
This module is one of the most important in the entire course! Once you pick your location (from module 6) and set up shop, your staff will make your business run!
Contributors and Attributions
- Putting It Together: Retail Human Resources. Authored by : Freedom Learning Group. Provided by : Lumen Learning. License : CC BY: Attribution


8.21: Introduction to the Application of Cost-Volume-Profit Concepts
What you’ll learn how to do: Illustrate the application of cost-volume-profit concepts
Now that you have some basic knowledge of the components of CVP analysis, let’s go a bit deeper and show how we can apply those concepts to business decisions. Since slight changes in costs, sales or pricing can have a profound impact on the net profit of a company, it is important to be able to analyze the data when it is received.
The contribution margin becomes very important, as it is the amount of funds available from each product, after the variable expenses are covered, to cover the fixed costs of the company. Being able to pay the rent, utilities and administrative wages are crucial to company success!


1.12: Glossary
Accidentals – notes that are not normally found in a given key
Acoustics – the study of how sound behaves in physical spaces
Acoustical Engineer – a person who works in the area of acoustic technology
Acoustician – a person who studies the theory and science of acoustics
Amplitude – refers to how high the waveform appears to vibrate above zero when seen on an oscilloscope; louder sounds create higher oscilloscope amplitude readings
Bar – see measure
Beat – the basic unit of time in music
Brass – instruments traditionally made of brass or another metal (and thus often producing a “bright” or “brassy” tone) whose sound is generated by blowing into a mouthpiece that is attached to a coiled tube
Chord – the simultaneous sounding of three or more pitches; like intervals, chords can be consonant or dissonant
Chord Progression – a series of chords
Chromatic – musical pitches which move up or down by successive half-steps
Composition – the process whereby a musician notates musical ideas using a system of symbols or using some other form of recording
Conjunct – a melody that moves mostly by step, in a smooth manner
Consonant – (adjective) term used to describe intervals and chords that tend to sound sweet and pleasing to our ears; consonance (noun), as opposed to dissonance, is stable and needs no resolution.
Cycles per Second (cps) – a definition of frequency of vibration; replaced by Hertz in 1960
Disjunct – a melody with wide leaps and rapid changes in direction
Dissonant – (adjective) intervals and chords that tend to sound harsh to our ears; dissonance (noun) is often used to create tension and instability, and the interplay between dissonance and consonance provides a sense of harmonic and melodic motion in music
Dynamic – the variation in the volume of musical sound (the amplitude of the sound waves)
Equalization (EQ) – the process of raising or lowering different frequencies of sound, either in a recording, or within a tone (overtones)
Form – the structure of the phrases and sections within a musical composition (Does it repeat?)
Frequency – how quickly or slowly a medium (solid, liquid, gas) vibrates and produces a sound
Fundamental Pitch – the lowest pitch in the harmonic series
Guido of Arezzo – a medieval music theorist who developed a system of lines and spaces that enabled musicians to notate the specific notes in a melody
Improvisation – the process whereby musicians create music spontaneously using the elements of music as building blocks
Instrumentation – the instruments comprising a musical group (including the human voice)
Interval – the distance in pitch between any two notes
Harmony – any simultaneous combination of tones and the rules governing those combinations (the way a melody is accompanied is also another way to define harmony)
Hertz (Hz) – the unit of frequency defined as one cycle per second and named after Heinrich Hertz (1957-1894) in 1960
Homophonic – musical texture comprised of one melodic line accompanied by chords
Key – the set of pitches on which a composition is based
Keyboard – instruments that are characterized by keyboards, such as the piano, organ, vibraphone, and accordion
Measure – a unit of time that contains a specific number of beats defined by the meter/ time signature
Melody – a succession of single tones in musical compositions Meter – the way in which the beats are grouped together in a piece
Monophonic – musical texture comprised of one melodic line; a melodic line may be sung by one person or 100 people
Motive – the smallest musical unit of a melody, generally a single rhythm of two or three pitches
Music – sound and silence organized in time
Noise – a disorganized sound with no discernable pitch
Octave – the distance between two musical pitches where the higher pitch vibrates exactly twice as many times per second as the lower
Oscilloscope - an electronic device that displays a visual representation of the different types of sound waves
Overtones (also known as harmonics) – a musical tone heard above a fundamental pitch
Partials – the sounds of different frequency that naturally occur above a fundamental (primary) tone
Percussion – instruments that are typically hit or struck by the hand, with sticks, or with hammers or that are shaken or rubbed by hand
Performing Forces – see instrumentation
Phrase – smaller sub-sections of a melody
Pitch – a tone that is composed of an organized sound wave
Polyphony – musical texture that simultaneously features two or more relatively independent and important melodic lines
Polyrhythm – two or more different rhythms played at the same time
Range – the number of pitches, expressed as an intervallic distance
Register – the low, medium, and high sections of an instrument or vocal range
Rhythm – the way the music is organized with respect to time
Scale – a series of pitches, ordered by the interval between its notes
Sequence – a repetition of a motive or phrase at a different pitch level Seventh
Chord – a chord that has four pitches stacked in intervals of thirds
Sine Wave – the simplest sound wave that occurs in nature. A pure sine wave contains no partials and is perfectly smooth and rounded in appearance on an oscilloscope.
Sound – the mechanical movement of an audible pressure wave through a solid, liquid, or gas
Sound Waves – longitudinal waves (compression and rarefaction waves) that travel through a solid, liquid, or gas
Step – the distance between adjacent notes in a musical scale
Strings – instruments whose sound is produced by setting strings in motion
Syncopation – the act of shifting the normal accent, usually by stressing the normally unaccented weak beats or placing the accent between the beats themselves
Synthesizers – electronic instruments (often in keyboard form) that create sounds using basic wave forms in different combinations
Tempo –the speed at which the beat is played Texture – the ways in which musical lines of a musical piece interact
Timbre – the tone color or tone quality of a sound
Time signature – the numeric notation at the beginning of a line of music where the top number indicates how many beats are in each measure and the bottom number indicates which type of note will represent that beat
Tonic – the most important pitch of a key; the note from which the other pitches are derived
Triad – a chord that has three pitches stacked in intervals of thirds
Twelve-Bar Blues – a twelve-bar musical form commonly found in American music
Vocal – having to do with the human voice
Woodwinds – instruments traditionally made of wood whose sound is generated by forcing air through a tube, thus creating a vibrating air column


14.2: Brønsted-Lowry Acids and Bases
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Learning Objectives
By the end of this section, you will be able to:
- Identify acids, bases, and conjugate acid-base pairs according to the Brønsted-Lowry definition
- Write equations for acid and base ionization reactions
- Use the ion-product constant for water to calculate hydronium and hydroxide ion concentrations
- Describe the acid-base behavior of amphiprotic substances
The acid-base reaction class has been studied for quite some time. In 1680, Robert Boyle reported traits of acid solutions that included their ability to dissolve many substances, to change the colors of certain natural dyes, and to lose these traits after coming in contact with alkali (base) solutions. In the eighteenth century, it was recognized that acids have a sour taste, react with limestone to liberate a gaseous substance (now known to be \(\ce{CO2}\)), and interact with alkalis to form neutral substances. In 1815, Humphry Davy contributed greatly to the development of the modern acid-base concept by demonstrating that hydrogen is the essential constituent of acids. Around that same time, Joseph Louis Gay-Lussac concluded that acids are substances that can neutralize bases and that these two classes of substances can be defined only in terms of each other. The significance of hydrogen was reemphasized in 1884 when Svante Arrhenius defined an acid as a compound that dissolves in water to yield hydrogen cations (now recognized to be hydronium ions) and a base as a compound that dissolves in water to yield hydroxide anions.
Johannes Brønsted and Thomas Lowry proposed a more general description in 1923 in which acids and bases were defined in terms of the transfer of hydrogen ions, H + . (Note that these hydrogen ions are often referred to simply as protons , since that subatomic particle is the only component of cations derived from the most abundant hydrogen isotope, 1 H.) A compound that donates a proton to another compound is called a Brønsted-Lowry acid , and a compound that accepts a proton is called a Brønsted-Lowry base . An acid-base reaction is, thus, the transfer of a proton from a donor (acid) to an acceptor (base).
The concept of conjugate pairs is useful in describing Brønsted-Lowry acid-base reactions (and other reversible reactions, as well). When an acid donates \(\ce{H^{+}}\), the species that remains is called the conjugate base of the acid because it reacts as a proton acceptor in the reverse reaction. Likewise, when a base accepts \(\ce{H^{+}}\), it is converted to its conjugate acid . The reaction between water and ammonia illustrates this idea. In the forward direction, water acts as an acid by donating a proton to ammonia and subsequently becoming a hydroxide ion, \(\ce{OH^{−}}\), the conjugate base of water. The ammonia acts as a base in accepting this proton, becoming an ammonium ion, \(\ce{NH4^{+}}\), the conjugate acid of ammonia. In the reverse direction, a hydroxide ion acts as a base in accepting a proton from ammonium ion, which acts as an acid.
The reaction between a Brønsted-Lowry acid and water is called acid ionization . For example, when hydrogen fluoride dissolves in water and ionizes, protons are transferred from hydrogen fluoride molecules to water molecules, yielding hydronium ions and fluoride ions:
Base ionization of a species occurs when it accepts protons from water molecules. In the example below, pyridine molecules, \(\ce{C5NH5}\), undergo base ionization when dissolved in water, yielding hydroxide and pyridinium ions:
The preceding ionization reactions suggest that water may function as both a base (as in its reaction with hydrogen fluoride) and an acid (as in its reaction with ammonia). Species capable of either donating or accepting protons are called amphiprotic , or more generally, amphoteric , a term that may be used for acids and bases per definitions other than the Brønsted-Lowry one. The equations below show the two possible acid-base reactions for two amphiprotic species, bicarbonate ion and water:
\[\ce{HCO3^{–}(aq) + H2O(l) <=> CO3^{2–}(aq) + H3O^{+} (aq)} \nonumber \]
\[\ce{HCO3^{-}(aq) + H2O(l) <=> H2CO3(aq) + OH^{-} (aq)} \nonumber \]
The first equation represents the reaction of bicarbonate as an acid with water as a base, whereas the second represents reaction of bicarbonate as a base with water as an acid. When bicarbonate is added to water, both these equilibria are established simultaneously and the composition of the resulting solution may be determined through appropriate equilibrium calculations, as described later in this chapter.
In the liquid state, molecules of an amphiprotic substance can react with one another as illustrated for water in the equations below:
The process in which like molecules react to yield ions is called autoionization . Liquid water undergoes autoionization to a very slight extent; at 25 °C, approximately two out of every billion water molecules are ionized. The extent of the water autoionization process is reflected in the value of its equilibrium constant, the ion-product constant for water, \(K_w\):
\[\ce{2H2O(l) <=> H3O^{+}(aq) + OH^{-}(aq)} \label{autoionization} \]
with
\[K_w=[\ce{H3O^{+}}][\ce{OH^{-}}] \label{Kw} \]
The slight ionization of pure water is reflected in the small value of the equilibrium constant; at 25 °C, \(K_w\) has a value of \(1.0 \times 10^{−14}\). The process is endothermic, and so the extent of ionization and the resulting concentrations of hydronium ion and hydroxide ion increase with temperature. For example, at 100 °C, the value for \(K_w\) is about \(5.6 \times 10^{−13}\), roughly 50 times larger than the value at 25 °C.
Example \(\PageIndex{1}\): Ion Concentrations in Pure Water
What are the hydronium ion concentration and the hydroxide ion concentration in pure water at 25 °C?
Solution
The autoionization of water yields the same number of hydronium and hydroxide ions. Therefore, in pure water, [H 3 O + ] = [OH − ] = x . At 25 °C:
\[K_{ w }=\left[ H_3 O^{+}\right]\left[ OH^{-}\right]=(x)(x)=x^2=1.0 \times 10^{-14} \nonumber \]
So:
\[x=\left[ H_3 O^{+}\right]=\left[ OH^{-}\right]=\sqrt{1.0 \times 10^{-14}}=1.0 \times 10^{-7} M \nonumber \]
The hydronium ion concentration and the hydroxide ion concentration are the same, \(1.0 \times 10^{−7}\, M\).
Exercise \(\PageIndex{1}\)
The ion product of water at 80 °C is 2.4 \times 10^{−13}. What are the concentrations of hydronium and hydroxide ions in pure water at 80 °C?
- Answer
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\[[\ce{H3O^{+}}] = [\ce{OH^{-}}] = 4.9 \times 10^{−7}\, M \nonumber \]
Example \(\PageIndex{2}\): The Inverse Relation between [H 3 O + ] and [OH − ]
A solution of an acid in water has a hydronium ion concentration of \(2.0 \times 10^{−6} M\). What is the concentration of hydroxide ion at 25 °C?
Solution
Use the value of the ion-product constant for water at 25 °C (Equations \ref{autoionization} and \ref{Kw}) to calculate the missing equilibrium concentration.
\[\ce{2H2O(l) <=> H3O^{+}(aq) + OH^{-}(aq)} \nonumber \]
with \(K_w=[\ce{H3O^{+}}][\ce{OH^{-}}] \nonumber\).
Rearrangement of the K w expression shows that [OH − ] is inversely proportional to [H 3 O + ]:
\[K_{ w }=\left[\ce{H3O^{+}}\right]\left[\ce{OH^{-}}\right]=\left(2.0 \times 10^{-6}\right)\left(5.0 \times 10^{-9}\right)=1.0 \times 10^{-14} \nonumber \]
Compared with pure water, a solution of acid exhibits a higher concentration o f hydronium ions (due to ionization of the acid) and a proportionally lower concentration of hydroxide ions. This may be explained via Le Chatelier’s principle as a left shift in the water autoionization equilibrium resulting from the stress of increased hydronium ion concentration.
Substituting the ion concentrations into the K w expression confirms this calculation, resulting in the expected value:
\[K_w=[\ce{H3O^{+}}][\ce{OH^{-}}]=(2.0 \times 10^{−6})(5.0 \times 10^{−9})=1.0 \times 10^{−14} \nonumber \]
Exercise \(\PageIndex{2}\)
What is the hydronium ion concentration in an aqueous solution with a hydroxide ion concentration of 0.001 M at 25 °C?
- Answer
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\[\ce{[H3O+] = 1 \times 10^{−11}\, M} \nonumber \]
Example \(\PageIndex{3}\): Representing the Acid-Base Behavior of an Amphoteric Substance
Write separate equations representing the reaction of \(\ce{HSO3^{-}}\)
- as an acid with \(\ce{OH^{-}}\)
- as a base with \(\ce{HI}\)
Solution
- \(\ce{HSO3^{-}(aq) + OH^{-}(aq) <=> SO3^{2-}(aq)+H2O(l)}\)
- \(\ce{HSO3^{-}(aq) + HI(aq) <=> H2SO3(aq) + I^{-}(aq)}\)
Exercise \(\PageIndex{3}\)
Write separate equations representing the reaction of \(\ce{H2PO4^{-}}\)
- as a base with \(\ce{HBr}\)
- as an acid with \(\ce{OH^{-}}\)
- Answer
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- \(\ce{H2PO4^{-}(aq) + HBr(aq) <=> H3PO4(aq) + Br^{-}(aq)}\)
- \(\ce{H2PO4^{-}(aq) + OH^{-}(aq) <=> HPO4^{2-}(aq) + H2O(l)}\)


26: Galaxies
In the last chapter, we explored our own Galaxy. But is it the only one? If there are others, are they like the Milky Way? How far away are they? Can we see them? As we shall learn, some galaxies turn out to be so far away that it has taken billions of years for their light to reach us. These remote galaxies can tell us what the universe was like when it was young.
In this chapter, we start our exploration of the vast realm of galaxies. Like tourists from a small town making their first visit to the great cities of the world, we will be awed by the beauty and variety of the galaxies. And yet, we will recognize that much of what we see is not so different from our experiences at home, and we will be impressed by how much we can learn by looking at structures built long ago.
We begin our voyage with a guide to the properties of galaxies, much as a tourist begins with a guidebook to the main features of the cities on the itinerary. In later chapters, we will look more carefully at the past history of galaxies, how they have changed over time, and how they acquired their many different forms. First, we’ll begin our voyage through the galaxies with the question: is our Galaxy the only one?
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- 26.2: The Discovery of Galaxies
- Faint star clusters, clouds of glowing gas, and galaxies all appeared as faint patches of light (or nebulae) in the telescopes available at the beginning of the twentieth century. It was only when Hubble measured the distance to the Andromeda galaxy using cepheid variables with the giant 2.5-meter reflector on Mount Wilson in 1924 that the existence of other galaxies similar to the Milky Way in size and content was established.
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- 26.3: Types of Galaxies
- Most bright galaxies are either spirals or ellipticals. Spiral galaxies contain both old and young stars, as well as interstellar matter, and have typical masses in the range of 109 to 1012 MSun. Our own Galaxy is a large spiral. Ellipticals are spheroidal or slightly elongated systems that consist almost entirely of old stars, with very little interstellar matter. Elliptical galaxies range in size from giants, more massive than any spiral, down to dwarfs, with masses of only about 106 MSun.
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- 26.4: Properties of Galaxies
- The masses of spiral galaxies are determined from measurements of their rates of rotation. The masses of elliptical galaxies are estimated from analyses of the motions of the stars within them. Galaxies can be characterized by their mass-to-light ratios. The luminous parts of galaxies with active star formation typically have mass-to-light ratios in the range of 1 to 10; the luminous parts of elliptical galaxies typically have mass-to-light ratios of 10 to 20.
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- 26.5: The Extragalactic Distance Scale
- Astronomers determine the distances to galaxies using a variety of methods, including the period-luminosity relationship for cepheid variables; objects such as type Ia supernovae, which appear to be standard bulbs; and the Tully-Fisher relation, which connects the line broadening of 21-cm radiation to the luminosity of spiral galaxies. Each method has limitations in terms of its precision, the kinds of galaxies with which it can be used, and the range of distances over which it can be applied.
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- 26.6: The Expanding Universe
- The universe is expanding. Observations show that the spectral lines of distant galaxies are redshifted, and that their recession velocities are proportional to their distances from us, a relationship known as Hubble’s law. The rate of recession, called the Hubble constant, is approximately 22 kilometers per second per million light-years. We are not at the center of this expansion: an observer in any other galaxy would see the same pattern of expansion that we do. The expansion described by Hub
Thumbnail: Spiral Galaxy. NGC 6946 is a spiral galaxy also known as the “Fireworks galaxy.” It is at a distance of about 18 million light-years, in the direction of the constellations Cepheus and Cygnus. It was discovered by William Herschel in 1798. This galaxy is about one-third the size of the Milky Way. Note on the left how the colors of the galaxy change from the yellowish light of old stars in the center to the blue color of hot, young stars and the reddish glow of hydrogen clouds in the spiral arms. As the image shows, this galaxy is rich in dust and gas, and new stars are still being born here. In the right-hand image, the x-rays coming from this galaxy are shown in purple, which has been added to other colors showing visible light. (Credit left: modification of work by NASA, ESA, STScI, R. Gendler, and the Subaru Telescope (NAOJ); credit right: modification of work by X-ray: NASA/CXC/MSSL/R.Soria et al, Optical: AURA/Gemini OBs)


7.3.E: Problems on Set Families
1. Verify Examples (a),(b), and (c).
Prove Theorem 1 for rings.
Show that in Definition 1 "\(\emptyset \in \mathcal{M}\)" may be replaced by "\(\mathcal{M} \neq \emptyset\)."
[Hint: \(\emptyset=A-A\).]
\(\Rightarrow\) Prove that \(\mathcal{M}\) is a field \((\sigma\)-field if \(\mathcal{M} \neq \emptyset, \mathcal{M}\) is closed under finite (countable) unions, and
\[(\forall A \in \mathcal{M}) \quad -A \in \mathcal{M}.\]
[Hint: \(A-B=-(-A \cup B); S=-\emptyset\).]
Prove Theorem 2 for set fields.
Does Note 1 apply to semirings?
Prove Note 2.
Prove Theorem 3 in detail.
Prove Theorem 4 and show that the product \(\mathcal{M} \dot{ \times} \mathcal{N}\) of two rings need not be a ring.
[Hint: Let \(S=E^{1}\) and \(\mathcal{M}=\mathcal{N}=2^{S}.\) Take \(A, B\) as in Theorem 1 of §1. Verify that \(A-B \notin \mathcal{M}, {\mathcal{M}} \dot{ \times} \mathcal{N}\).]
\(\Rightarrow\) Let \(\mathcal{R}, \mathcal{R}^{\prime}\) be the rings \((\sigma\)-rings, fields, \(\sigma\)-fields) generated by \(\mathcal{M}\) and \(\mathcal{N}\), respectively. Prove the following.
(i) If \(\mathcal{M} \subseteq \mathcal{N},\) then \(\mathcal{R} \subseteq \mathcal{R}^{\prime}\).
(ii) If \(\mathcal{M} \subseteq \mathcal{N} \subseteq \mathcal{R},\) then \(\mathcal{R}=\mathcal{R}^{\prime}\).
(iii) If
\[\mathcal{M}=\left\{\text {open intervals in } E^{n}\right\}\]
and
\[\mathcal{N}=\left\{\text {all open sets in } E^{n}\right\},\]
then \(\mathcal{R}=\mathcal{R}^{\prime}\).
[Hint: Use Lemma 2 in §2 for (iii). Use the minimality of \(\mathcal{R}\) and \(\mathcal{R}^{\prime}\).]
Is any of the following a semiring, ring, \(\sigma\)-ring, field, or \(\sigma\)-field? Why?
(a) All infinite intervals in \(E^{1}\).
(b) All open sets in a metric space \((S, \rho)\).
(c) All closed sets in \((S, \rho)\).
(d) All "clopen" sets in \((S, \rho)\).
(e) \(\left\{X \in 2^{S} |-X \text { finite}\right\}\).
(f) \(\left\{X \in 2^{S} |-X \text { countable}\right\}\).
\(\Rightarrow\) Prove that for any sequence \(\left\{A_{n}\right\}\) in a ring \(\mathcal{R},\) there is
(a) an expanding sequence \(\left\{B_{n}\right\} \subseteq \mathcal{R}\) such that
\[(\forall n) \quad B_{n} \supseteq A_{n}\]
and
\[\bigcup_{n} B_{n}=\bigcup_{n} A_{n}; \text { and}\]
(b) a contracting sequence \(C_{n} \subseteq A_{n},\) with
\[\bigcap_{n} C_{n}=\bigcap_{n} A_{n}.\]
(The latter holds in semirings, too.)
[Hint: Set \(B_{n}=\bigcup_{1}^{n} A_{k}, C_{n}=\bigcap_{1}^{n} A_{k}\).]
\(\Rightarrow\) The symmetric difference, \(A \triangle B,\) of two sets is defined
\[A \triangle B=(A-B) \cup(B-A).\]
Inductively, we also set
\[\triangle_{k=1}^{1} A_{k}=A_{1}\]
and
\[\triangle_{k=1}^{n+1} A_{k}=\left(\triangle_{k=1}^{n} A_{k}\right) \triangle A_{n+1}.\]
Show that symmetric differences
(i) are commutative,
(ii) are associative, and
(iii) satisfy the distributive law:
\[(A \triangle B) \cap C=(A \cap C) \triangle(B \cap C).\]
[Hint for (ii): Set \(A^{\prime}=-A, A-B=A \cap B^{\prime}.\) Expand \((A \triangle B) \triangle C\) into an expression symmetric with respect to \(A, B,\) and \(C\).]
Prove that \(\mathcal{M}\) is a ring iff
(i) \(\emptyset \in \mathcal{M}\);
(ii) \((\forall A, B \in \mathcal{M}) A \triangle B \in \mathcal{M}\) and \(A \cap B \in \mathcal{M}\) (see Problem 10); equivalently,
(ii') \(A \triangle B \in \mathcal{M}\) and \(A \cup B \in \mathcal{M}\).
[Hint: Verify that
\[A \cup B=(A \triangle B) \triangle(A \cap B)\]
and
\[A-B=(A \cup B) \triangle B,\]
while
\[A \cap B=(A \cup B) \triangle(A \triangle B).]\]
Show that a set family \(\mathcal{M} \neq \emptyset\) is a \(\sigma\)-ring iff one of the following conditions holds.
(a) \(\mathcal{M}\) is closed under countable unions and proper differences \((X-Y\) with \(X \supseteq Y)\);
(b) \(\mathcal{M}\) is closed under countable disjoint unions, proper differences, and finite intersections; or
(c) \(\mathcal{M}\) is closed under countable unions and symmetric differences (see Problem 10).
[Hints: (a) \(X-Y=(X \cup Y)-Y,\) a proper difference.
(b) \(X-Y=X-(X \cap Y)\) reduces any difference to a proper one; then
\[X \cup Y=(X-Y) \cup(Y-X) \cup(X \cap Y)\]
shows that \(\mathcal{M}\) is closed under all finite unions; so \(\mathcal{M}\) is a ring. Now use Corollary 1 in §1 for countable unions.
(c) Use Problem 11.]
From Problem 10, treating \(\triangle\) as addition and \(\cap\) as multiplication, show that any set ring \(\mathcal{M}\) is an algebraic ring with unity, i.e., satisfies the six field axioms (Chapter 2, §§1-4), except \(V(b)\) (existence of multiplicative inverses).
A set family \(\mathcal{H}\) is said to be hereditary iff
\[(\forall X \in \mathcal{H})(\forall Y \subseteq X) \quad Y \in H.\]
Prove the following.
(a) For every family \(\mathcal{M} \subseteq 2^{S}\), there is a "smallest" hereditary ring \(\mathcal{H} \supseteq \mathcal{M}\) (\(\mathcal{H}\) is said to be generated by \(\mathcal{M}\)). Similarly for \(\sigma\)-rings, fields, and \(\sigma\)-fields.
(b) The hereditary \(\sigma\)-ring generated by \(\mathcal{M}\) consists of those sets which can be covered by countably many \(\mathcal{M}\)-sets.
Prove that the field \((\sigma\)-field in \(S\), generated by a ring \((\sigma\)-ring \(\mathcal{R},\) consists exactly of all \(\mathcal{R}\)-sets and their complements in \(S\).
Show that the ring \(\mathcal{R}\) generated by a set family \(\mathcal{C} \neq \emptyset\) consists of all sets of the form
\[\triangle_{k=1}^{n} A_{k}\]
(see Problem 10), where each \(A_{k} \in \mathcal{C}_{d}\) (finite intersection of \(\mathcal{C}\)-sets).
[Outline: By Problem 11, \(\mathcal{R}\) must contain the family (call it \(\mathcal{M}\)) of all such \(\triangle_{k=1}^{n} A_{k}\). (Why?) It remains to show that \(\mathcal{M}\) is a ring \(\supseteq \mathcal{C}\).
Write \(A+B\) for \(A \triangle B\) and \(A B\) for \(A \cap B;\) so each \(\mathcal{M}\)-set is a "sum" of finitely many "products"
\[A_{1} A_{2} \cdots A_{n}.\]
By algebra, the "sum" and "product" of two such "polynomials" is such a polynomial itself. Thus
\[(\forall X, Y \in \mathcal{M}) \quad X \triangle Y \text { and } X \cap Y \in \mathcal{M}.\]
Now use Problem 11.]
AUse Problem 16 to obtain a new proof of Theorem 2 in §1 and Corollary 2 in the present section.
[Hints: For semirings, \(C=\mathcal{C}_{d}.\) (Why?) Thus in Problem 16, \(A_{k} \in \mathcal{C}.\)
Also,
\[(\forall A, B \in \mathcal{C}) \quad A \triangle B=(A-B) \cup(B-A)\]
where \(A-B\) and \(B-A\) are finite disjoint unions of \(\mathcal{C}\)-sets. (Why?)
Deduce that \(A \triangle B \in \mathcal{C}_{s}^{\prime}\) and, by induction,
\[\triangle_{k=1}^{n} A_{k} \in \mathcal{C}_{s}^{\prime};\]
so \(\mathcal{R} \subseteq \mathcal{C}_{s}^{\prime} \subseteq \mathcal{R}.\) (Why?)]
Given a set \(A\) and a set family \(\mathcal{M},\) let
\[A \cap{\dot\} \mathcal{M}\]
be the family of all sets \(A \cap X,\) with \(X \in \mathcal{M};\) similarly,
\[\mathcal{N} \dot{\cup} (\mathcal{M} \dot{-} A)=\{\text { all sets } Y \cup(X-A), \text { with } Y \in \mathcal{N}, X \in \mathcal{M}\}, \text { etc. }\]
Show that if \(\mathcal{M}\) generates the ring \(\mathcal{R},\) then \(A \cap{\dot} \mathcal{M}\) generates the ring
\[\mathcal{R}^{\prime}=A \cap{\dot} \mathcal{R}.\]
Similarly for \(\sigma\)-rings, fields, \(\sigma\)-fields.
[Hint for rings: Prove the following.
(i) \(A \cap \mathcal{R}\) is a ring.
(ii) \(\mathcal{M} \subseteq \mathcal{R}^{\prime} \cup(\mathcal{R} \pm A),\) with \(\mathcal{R}^{\prime}\) as above.
(iii) \(\mathcal{R} \cup(\mathcal{R} \div A) \text { is a ring (call it } \mathcal{N})\).
(iv) By (ii), \(\mathcal{R} \subseteq \mathcal{N},\) so \(A \cap \mathcal{R} \subseteq A \cap \mathcal{N} \subseteq \mathcal{R}^{\prime}\right.\)
(v) \(A \cap \mathcal{R} \supseteq \mathcal{R}^{\prime}(\text { for } A \cap \mathcal{R} \supseteq A \cap \mathcal{M})\).
Hence \(\mathcal{R}^{\prime}=A \cap \mathcal{R}\).]


6.4: Comfort Measures
Nursing assistants (NAs) should report subjective and objective signs of clients’ pain to the nurse for further assessment. After assessing the client, the nurse may choose to administer medication with provider order and/or provide other nonpharmacological treatments. The nurse may delegate tasks to the NA such as the application of over-the-counter topical medications, ice, or heat. The NA may also assist with repositioning and massage.
Topical Medications
Topical medications are applied to the skin and are typically over-the-counter (OTC) medications, meaning no prescription is needed to obtain them. Topical analgesics may come as a cream, gel, spray, or patch. An example of a topical analgesic is “Icy-Hot” cream.
There are also other types of topical medications an NA may be delegated to apply, such as antifungal medications (e.g., Nystatin in powder or cream form) or barrier creams to reduce the risk of skin breakdown or assist in healing of opened areas. When applying topical medications, it is important to use diligent infection control measures to prevent the medication from becoming contaminated. See the “ Topical Medications ” Skills Checklist for steps on how to properly apply topical medications.
Ice and Heat Applications
Applying ice and heat can also be delegated from the registered nurse to the NA. To safely apply ice or heat, first place a thin barrier on the skin, such as a towel or washcloth, to avoid damaging the tissue. Ice may be placed in a plastic bag, or cold therapy may be available in a disposable package. In some situations, a reusable gel pack may be placed in the freezer between uses.
Heat applications may include using an electrical heating pad or a reusable microwavable pack. The NA should discuss the setting for the heating pad or the time the pack should be warmed in the microwave with the delegating nurse. The NA should feel the pack’s temperature before placing it on the resident.
Ice or heat applications are typically left on for 15-20 minutes. If the resident is unable to communicate, the NA should lift the pack, check the skin temperature, and look for any redness every five minutes to prevent damage to the skin. If the ice or heat applications are not disposable, ensure they are sanitized according to agency policy before providing them to the resident.
Positioning and Massage
Pain may arise when a client remains in one position too long or is placed in a position that causes pressure on a sensitive area such as a joint, tendon, or muscle. Residents who are unable to move on their own should be repositioned at least every two hours, and some may require more frequent repositioning due to pain or skin issues. Clients can be maintained in a position of comfort by placing pillows to prevent discomfort between joints and bony prominences or to support the body and prevent them from rolling out of the position. For information on proper positioning, see Chapter 8 .
Massage provides relaxation by reducing soreness and tension in muscles. It also increases circulation by promoting blood flow. However, a massage should never be provided over red or swollen areas. A massage given to a resident for pain relief should last about 3-5 minutes. For specifics on giving a massage, see the 5.17 “ Back Rub ” Skills Checklist in Chapter 5.
Other Comfort Measures
In addition to the previously described interventions to reduce pain, NAs can further help reduce clients’ pain by offering distractions, such as talking with the resident about pleasant or interesting things that the resident enjoys, looking at photos or magazines, playing board games, or listening to music. Deep breathing, mindfulness techniques, aromatherapy, and light range of motion (ROM) activities can also help calm the resident and ease their pain. Read more about providing ROM activities in Chapter 9 . See Figure 6.9 [1] for images of nonpharmacological treatments for pain.
Read more about pain management for older adults from the University of Iowa.
- “ Massage-hand-4.jpg ” by Lubyanka is licensed under CC BY-SA 3.0 , “ Biofeedback_training_program_for_post-traumatic_stress_symptoms.jpg ” by Army Medicine is licensed under CC BY 2.0 , “ Tai_Chi1.jpg ” by Craig Nagy is licensed under CC BY-SA 2.0 , “ Musicoterapia_lmidiman_flickr.jpg ” by Midiman is licensed under CC BY 2.0 , “ Cold_Hot_Pack.jpg ” by Mamun2a is licensed under CC BY-SA 4.0 , “ pexels-photo-1188511.jpeg ” by Mareefe is licensed under CC0 , “ STOTT-PILATES-reformer-class.jp g” by MHandF is licensed under CC BY-SA 3.0 , “ prayer-2544994_960_720.jpg ” by Himsan is licensed under CC0 , and “ gaming-2259191_960_720.jpg ” by JESHOOTS-com is licensed under CC0 ↵


5.0: Introduction
Every person in the world belongs to a culture . Culture shapes one’s personal identity, influences social relationships, and contributes to the overall richness of human societies. Basic elements of culture include language, symbols, societal norms and customs, beliefs, values, and cognitive elements (such as learning to cope, managing difficult situations, and qualities taught to children). Culture plays a significant role in health and wellness, as it can affect what types of medicines and treatments to use, who is allowed to provide care, and beliefs about what causes illness and injury.
The United States has long had a reputation as a multicultural nation, and according to the United States Census Bureau (2020), it continues to grow even more racially and ethnically diverse every year (Jensen, 2022) (Figure 5.2). Nurses will interact with patients who belong to diverse cultures, both distinct from each other and distinct from the nurses’ own cultural background. It is crucial for nurses to understand and accommodate cultural differences, ensuring the delivery of the best possible care to all patients, regardless of their cultural background. This chapter discusses how to gain a better understanding of cultural differences among the patients who nurses serve as well as ethical and cultural practices in nursing and how to incorporate diversity and inclusion as best practice standards.


1.1: The Joys of Teaching
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A teacher named Ashley reflects: She looked around the classroom, enjoying a blessed moment of quiet after the students left at the end of the day. "Ashley, the teacher, that's me", she said proudly to the empty room. "But why am I doing this?" she asked herself quietly— and realized she wasn't always sure of the answer. But then she remembered one reason: she was teaching for Nadia, who sat at the table to the left, always smiled so well and always (well, usually) tried hard. And another reason: she was teaching for Lincoln, tired old Lincoln, who needed her help more than he realized. She remembered twenty other reasons— twenty other students. And one last reason: she was also teaching for herself challenging herself to see if she really could keep up with twenty-two young people at once, and really accomplish something worthwhile with them. She was teaching so she could keep growing as a person, keep connecting with others, keep learning new ideas. That's why she was teaching.
Why teach?
Why be a teacher? The short answer is easy:
- to witness the diversity of growth in young people, and their joy in learning
- to encourage lifelong learning—both for yourself and for others
- to experience the challenge of devising and doing interesting, exciting activities for the young
There is, of course, more than this to be said about the value of teaching. Consider, for instance, the "young people" referred to above. In one class they could be six years old; in another they could be sixteen, or even older. They could be rich, poor, or somewhere in between. They could come from any ethnic background. Their first language could be English, or something else. There are all sorts of possibilities. But whoever the particular students are, they will have potential as human beings: talents and personal qualities— possibly not yet realized— that can contribute to society, whether as leaders, experts, or supporters of others. A teacher's job— in fact a teacher's privilege— is to help particular "young people" to realize their potential.
Another teacher reflects: Nathan paused for a deep breath before speaking to me. "Lt's not like I expected it to be," he said. "I've got five kids who speak English as a second language. I didn't expect that. I've got two, maybe three, with reading disabilities, and one of them has a part-time aide. I've had to learn more about using computers than I ever expected— they're a lot of curriculum materials online now, and the computers help the kids that need more practice or who finish activities early. I'm doing more screening and testing of kids than I expected, and it all takes time away from teaching. “But it’s not all surprises. I expected to be able to ‘light a fire’ under kids about learning to read. And that has actually happened, at least sometimes with some children!”The joys of teaching
“But it’s not all surprises. I expected to be able to ‘light a fire’ under kids about learning to read. And that has actually happened, at least sometimes with some children!”
As a teacher, you will be able to do this by laying groundwork for lifelong learning. You will not teach any one student forever, of course, but you will often work with them long enough to convey a crucial message: that there is much in life to learn— more in fact than any one teacher or school can provide in a lifetime. The knowledge may be about science, math, or learning to read; the skills may be sports, music, or art— anything. Whatever you teach, its immensity can be a source of curiosity, wonder and excitement. It can be a reason to be optimistic about life in general and about your students in particular. Learning, when properly understood, is never-ending, even though it often focuses on short-term, immediate concerns. As a teacher, you will have an advantage not shared by every member of society, namely the excuse not only to teach valuable knowledge and skills, but to point students beyond what they will be able to learn from you. As an old limerick put it (before the days of gender-balanced language), "The world is full of such a plenty of things, I'm sure we should all be as happy as kings."
Jennifer Fuller, a third teacher reflects: "OK", suddenly getting businesslike in her tone. "Here's my typical day teaching tenth grade: I get up at 6:30, have a quick breakfast, get to school by 7:45 if the traffic's not bad. Then I check my email— usually there's a little stuff from the principal or some other administrator, maybe one or two from parents concerned because their child is doing poorly in one of my classes, maybe one or two from students— "I'm going to be sick today, Ms Fuller!"— that sort of thing. Now it's 8:15 and I have two hours before my first class— this term I teach only biology, and I only teach periods 2, 3, and 5. Maybe I have marking to do before class, or maybe I have to get a lab demonstration ready. Or maybe we all have to troupe down to the library for a staff meeting (groan...). Whatever I don't finish in the morning, I have to finish after school. But that's also when I meet with the Ecology Club (I'm the faculty advisor), so I might have to finish stuff in the evening. I try not to do it then, but a lot of times I have to. But I always quit by 9:00— that's always when I watch TV for an hour, or just "vegetate " with a book."
Whatever you teach, you will be able to feel the satisfaction of designing and orchestrating complex activities that communicate new ideas and skills effectively. The challenge is attractive to many teachers, because that is where they exercise judgment and "artistry" the most freely and frequently. Your students will depend on your skill at planning and managing, though sometimes without realizing how much they do so. Teachers will need you to know how to explain ideas clearly, to present new materials in a sensible sequence and at an appropriate pace, to point out connections between their new learning and their prior experiences. Although these skills really take a lifetime to master, they can be practiced successfully even by beginning teachers, and they do improve steadily with continued teaching over time. Right from the start, though, skill at design and communication of curriculum is one of the major "perks" of the job.
The very complexity of classroom life virtually guarantees that teaching never needs to get boring. Something new and exciting is bound to occur just when you least expect it. A student shows an insight that you never expected to see— or fails to show one that you were sure he had. An activity goes better than expected— or worse, or merely differently. You understand for the first time why a particular student behaves as she does, and begin thinking of how to respond to the student's behavior more helpfully in the future. After teaching a particular learning objective several times, you realize that you understand it differently than the first time you taught it. And so on. The job never stays the same; it evolves continually. As long as you keep teaching, you will have a job with novelty.
Are there also challenges to teaching?
Here, too, the simple answer is "yes". Every joy of teaching has a possible frustration related to it. You may wish to make a positive difference in students' lives, but you may also have trouble reaching individuals. A student seems not to learn much, or to be unmotivated, or unfriendly, or whatever. And some teaching problems can be subtle: when you call attention to the wonderful immensity of an area of knowledge, you might accidentally discourage a student by implying that the student can never learn "enough". The complexity of designing and implementing instruction can sometimes seem overwhelming, instead of satisfying. Unexpected events in your classroom can become chaos rather than an attractive novelty. To paraphrase a popular self-help book, sometimes "bad things happen to good teachers" (Kushner, 1983). But as in the rest of life, the "bad things" of teaching do not negate the value of the good. If anything, the undesired events make the good, desired ones even more satisfying, and render the work of teaching all the more valuable. As you will see throughout this book, there are resources for maximizing the good, the valuable, and the satisfying. You can bring these resources to your work, along with your growing professional knowledge and a healthy dose of common sense. In this sense you will not need to "go it alone" in learning to teach well. You will, however, be personally responsible for becoming and remaining the best teacher that you can possibly be; the only person who can make that happen will be you. Many of the resources for making this happen are described in this book in the chapters ahead.
This page has been edited by Alice Hale (Chabot College) with the Libretexts remixing tool.


4.A: Diffraction (Answers)
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Check Your Understanding
4.1. \(\displaystyle 17.8°, 37.7°, 66.4°\); no
4.2. \(\displaystyle 74.3°, 0.0083I_0\)
4.3. From \(\displaystyle dsinθ=mλ\), the interference maximum occurs at \(\displaystyle 2.87°\) for \(\displaystyle m=20\). From Equation 4.1, this is also the angle for the second diffraction minimum. (Note: Both equations use the index m but they refer to separate phenomena.)
4.4. \(\displaystyle 3.332×10^{−6}m\) or 300 lines per millimeter
4.5. \(\displaystyle 8.4×10^{−4}rad\), 3000 times broader than the Hubble Telescope
4.6. \(\displaystyle 38.4°\) and \(\displaystyle 68.8°\); Between \(\displaystyle θ=0°→90°\), orders 1, 2, and 3, are all that exist.
Conceptual Questions
1. The diffraction pattern becomes wider.
3. Walkie-talkies use radio waves whose wavelengths are comparable to the size of the hill and are thus able to diffract around the hill. Visible wavelengths of the flashlight travel as rays at this size scale.
5. The diffraction pattern becomes two-dimensional, with main fringes, which are now spots, running in perpendicular directions and fainter spots in intermediate directions.
7. The parameter \(\displaystyle β=ϕ/2\) is the arc angle shown in the phasor diagram in Figure 4.7. The phase difference between the first and last Huygens wavelet across the single slit is \(\displaystyle 2β\) and is related to the curvature of the arc that forms the resultant phasor that determines the light intensity.
9. blue; The shorter wavelength of blue light results in a smaller angle for diffraction limit.
11. No, these distances are three orders of magnitude smaller than the wavelength of visible light, so visible light makes a poor probe for atoms.
13. UV wavelengths are much larger than lattice spacing in crystals such that there is no diffraction. The Bragg equation implies a value for sinθ greater than unity, which has no solution.
15. Image will appear at slightly different location and/or size when viewed using \(\displaystyle 10%\) shorter wavelength but at exactly half the wavelength, a higher-order interference reconstructs the original image, different color.
Problems
17. a. \(\displaystyle 33.4°\);
b. no
19. a. \(\displaystyle 1.35×10^{−6}m\);
b. \(\displaystyle 69.9°\)
21. 750 nm
23. 2.4 mm, 4.7 mm
25. a. \(\displaystyle 1.00λ\);
b. \(\displaystyle 50.0λ\);
c. \(\displaystyle 1000λ\)
27. 1.92 m
29. \(\displaystyle 45.1°\)
31. \(\displaystyle I/I_0=2.2×10^{−5}\)
33. \(\displaystyle 0.63I_0,0.11I_0,0.0067I_0,0.0062I_0,0.00088I_0\)
35. 0.200
37. 3
39. 9
41. \(\displaystyle 5.97°\)
43. \(\displaystyle 8.99×10^3\)
45. 707 nm
47. a. \(\displaystyle 11.8°, 12.5°, 14.1°, 19.2°\);
b. \(\displaystyle 24.2°, 25.7°, 29.1°, 41.0°\); c. Decreasing the number of lines per centimeter by a factor of x means that the angle for the x-order maximum is the same as the original angle for the first-order maximum.
49. a. using \(\displaystyle λ=700nm,θ=5.0°\);
b. using \(\displaystyle λ=460nm,θ=3.3°\)
51. a. 26,300 lines/cm;
b. yes;
c. no
53. \(\displaystyle 1.13×10^{−2}m\)
55. 107 m
57. a. \(\displaystyle 7.72×10^{−4}rad\);
b. 23.2 m;
c. 590 km
59. a. \(\displaystyle 2.24×10^{−4}rad\);
b. 5.81 km;
c. 0.179 mm;
d. can resolve details 0.2 mm apart at arm’s length
61. \(\displaystyle 2.9μm\)
63. 6.0 cm
65. 7.71 km
67. 1.0 m
69. 1.2 cm or closer
71. no
73. 0.120 nm
75. \(\displaystyle 4.51°\)
77. \(\displaystyle 13.2°\)
Additional Problems
79. a. 2.2 mm;
b. \(\displaystyle 0.172°\), second-order yellow and third-order violet coincide
81. 2.2 km
83. 1.3 cm
85. a. 0.28 mm;
b. 0.28 m;
c. 280 m;
d. 113 km
87. 33 m
89. a. vertically;
b. \(\displaystyle ±20°, ±44°\);
c. \(\displaystyle 0, ±31°, ±60°\);
d. 89 cm;
e. 71 cm
91. 0.98 cm
93. \(\displaystyle I/I_0=0.041\)
95. 340 nm
97. a. 0.082 rad and 0.087 rad;
b. 480 nm and 660 nm
99. two orders
101. yes and N/A
103. 600 nm
105. a. \(\displaystyle 3.4×10^{−5°}\);
b. \(\displaystyle 51°\)
107. 0.63 m
109. 1
111. \(\displaystyle 0.17 mW/cm^2\) for \(\displaystyle m=1\) only, no higher orders
113. \(\displaystyle 28.7°\)
115. a. 42.3 nm;
b. This wavelength is not in the visible spectrum.
c. The number of slits in this diffraction grating is too large. Etching in integrated circuits can be done to a resolution of 50 nm, so slit separations of 400 nm are at the limit of what we can do today. This line spacing is too small to produce diffraction of light.
117. a. 549 km;
b. This is an unreasonably large telescope.
c. Unreasonable to assume diffraction limit for optical telescopes unless in space due to atmospheric effects.
Challenge Problems
119. a. \(\displaystyle I=0.00500I_0,0.00335I_0\);
b. \(\displaystyle I=0.00500I_0,0.00335I_0\)
121. 12,800
123. \(\displaystyle 1.58×10^{−6}m\)


2.4: Properties of Blood as a Buffer and Blood Glucose
Part I: Blood pH Homeostasis
Acidity and alkalinity describe a property of chemicals based upon relative concentration of hydrogen ions in a solution. The pH scale measures this value and ranges from 0 to 14. A pH of 7.0 is considered neutral. A pH value greater than 7 is basic, and a pH less than 7.0 is acidic.
The pH scale is defined as the negative log of the hydrogen ion concentration of a solution (figure 1). This means each pH value on the scale represents a ten-fold difference in hydrogen ion molarity than the next value. For instance, a solution with pH of 8.0 is one-hundred times more basic than a solution with a pH of 6.0. Similarly, a solution with a pH of 5.0 is ten times more acidic than a solution with a pH of 6.0.
In biological systems, it is important to keep the pH of a solution within a narrow range of values. To accomplish this, buffers are used. Buffers resist changes in the pH of a solution when hydrogen ions or hydroxide are added (or removed). Buffers dissociate in solution and neutralize extra hydrogen ions or hydroxide ions by participating in reactions with them.
Normal blood pH is 7.4, and arterial pH may only vary between 7.35 and 7.45 without being pathological. The Carbonic Acid-Bicarbonate buffer system is the most important buffer for maintaining the pH homeostasis of blood. In this system, gaseous metabolic waste carbon dioxide reacts with water to form carbonic acid, which quickly dissociates into a hydrogen ion and bicarbonate (see below).
CO 2 + H 2 O ⇌ H 2 CO 3 ⇌ H+ + HCO 3 –
Besides the carbonic acid-bicarbonate buffer system, there are other buffers in whole blood, including the phosphate buffer system. Additionally, some proteins have buffering capacity, such as hemoglobin and blood serum albumin (a common carrier protein in blood). These have a lesser effect than the carbonic acid-bicarbonate system on maintaining blood pH homeostasis.
In this week’s activity, you will test whether five solutions behave as buffers:
- Saline (a salt water solution)
- Phosphate Buffered Saline (PBS), which is a solution of disodium hydrogen phosphate, sodium chloride and potassium chloride commonly used the lab
- 5% blood serum albumin (a protein found in blood serum)
- Blood Plasma (Sheep), diluted 10X with PBS (the liquid part of blood, which contains all the water, ions and proteins minus any formed elements)
- Whole Blood (Sheep) diluted 10X with PBS (containing all the components in “live” blood, including the cells)
Part II: Blood Glucose Homeostasis
Blood sugar homeostasis is important 1.) to consistently provide body cells with the necessary glucose to sustain metabolic reactions and 2.) to protect cells against damage that can occur when circulating blood glucose levels are too high for too long. For healthy individuals, the American Diabetes Association recommends a fasting (no food or drink, except water, for 8 hours) plasma glucose level of less than 100 mg/dL and, 2 hours after meals, a concentration less than 140 mg/dL.
In order to tightly control blood glucose levels, α- and β-cells of the endocrine pancreas secrete two hormones – insulin and glucagon. When eating a meal, the surge in blood sugar is detected directly by receptors on the pancreatic islet β-cells. These cells then secrete insulin, which binds to insulin receptors on various body tissues. Occupied insulin receptors signal body cells to increase the number of glucose transporters, special proteins that shunt glucose from the blood, through cell plasma membranes, and into the cell. The increase in transporters results in quick internalization of blood glucose by the cells.
When blood glucose levels are too low, e.g., less than 70 mg/dL or lower, the body may not have enough circulating blood glucose to sustain the body’s chemical reactions. Symptoms of low blood sugar (hypoglycemia) can be severe and include: nervousness, shaking, fatigue, blurry vision, trouble thinking, and even the loss of consciousness.
Low blood sugar is detected by the α- cells of the pancreas, which increase glucagon secretion. Glucagon activates liver enzymes, which then convert the glucose storage molecule, glycogen, into glucose. Glucagon also initiates the endogenous synthesis of glucose from other biomolecules like amino acids. The newly released or synthesized glucose passes into the blood stream and raises blood glucose levels.
Diabetes is a condition in which the body fails to respond to insulin, resulting in the body’s inability to control glucose homeostasis. Typically, in Type I diabetes, pancreatic β-cells are destroyed by an autoimmune reaction resulting in low or absent insulin in the body. Type II diabetes is also called “insulin resistance.” Generally, in this disease, the body manufactures insulin, but there is a problem that prevents insulin receptors from sending signals that increase the presence of glucose transporters in the plasma membranes of cells.
In Lab this week, your TA may test your Blood Glucose using a Contour Blood Glucose Monitoring System. A blood sample will be obtained from the side of your middle or ring finger using an Accu-Chek Safe-T-Pro Lancet. It delivers a quick, almost painless pinprick and only a small amount of blood is needed.
Laboratory Methods
Exercises
The following text describes the laboratory methods for analysis of blood buffering and blood glucose.
In this experiment, students will determine the buffering capabilities of a variety of solutions by measuring the pH of the solutions when they are treated with a weak base. Each group of students will measure the pH changes that occur in Saline, Phosphate Buffered Saline (PBS), 5% Albumin in PBS, Blood Plasma diluted 1/10 with PBS, and Whole Blood diluted 1/10 with PBS.
Laboratory Objectives
- Students will practice pipetting technique.
- We will use iWorx and calibrate the electrodes with LabScribe.
- The calibrated electrodes will be used to determine the pH changes that occur with addition of NaOH to the test solutions.
- Analyze the change in pH for each solution and determine if it is a buffer.
- Finally, we will measure each student’s blood glucose level with a blood glucose monitor.
Equipment Required
- PC Computer
- iWorx TA (IXTA) data acquisition unit
- ISE-100 combination pH electrodE
- Saline
- PBS
- 5% albumin in PBS
- 1/10 blood plasma in PBS
- 1/10 whole blood in PBS
- Beakers
- 10-100μL or 20-100 μL pipette
- Distille d water
- Kimwipes®
- 0.1 M NaOH
Practice using the micropipette
To draw up a specific amount of a solution, set the dial on the micropipette to the appropriate volume, then depress the plunger, and immerse the pipette tip in the solution. The micropipette plunger has a first “soft” stop. When the plunger is pushed to the first stop, it allows the pipette to draw up the programmed amount as the plunger is gently returned to the original position. To discharge the drawn-up solution, the plunger is pushed all the way down to the second “hard” stop.
To practice, place a plastic tip on the pipette, push the plunger to the first stop, submerge the pipette tip into the distilled water and gently allow the plunger to return to its original position. Look at the plastic tip and note how much distilled water has been taken into the tip. Discharge the distilled water back into the container of distilled water and repeat. Did you get the same amount of distilled water drawn into the tip as the first time? Continue practicing until you feel confident that you are operating the pipette properly.
PART I. Set up the computer
- Turn On iWorx Unit Box on Lab Table at the switch at the back of the box. Make sure Green Light is lit and all equipment is attached to the iWorx box.
- Log into the computer using your ISU ID.
- Click the folder icon in the lower left task bar.
- Click “this PC” in the left side task bar.
- Double click the Biol 256L Course Materials P-Drive under Network Locations.
- Double click the “Week3_BiologicalBuffers” file.
- Click OK to the Hardware Found Box, if it appears.
PART II: Calibrate the pH Electrode
Note : electrodes are delicate and expensive sensors, which can easily crack. Do not tap or drop it. When placing it in a beaker, do so carefully.
- Remove the ISE-100 pH electrode from its bottle of buffer by unscrewing the cap a little so that you can easily pull out the electrode. Make sure top portion of the bottle is removed.
- Replace screw cap of bottle if totally separated and place back in dry storage beaker where you found the electrode. Rinse the electrode with distilled water while holding the electrode over the large beaker used for the collection of waste liquids .
- Place the tip of the ISE-100 pH electrode in a small beaker containing enough room temperature distilled water to submerge the tip. Keep the electrode in distilled water for a few seconds.
- Obtain the calibration buffers: One beaker will contain pH 7 buffer and the other will contain pH 10 buffer. Each beaker should be filled with enough buffer to cover the tip of the ISE-100 pH electrode, but NO MORE is necessary!
- Remove the electrode from the distilled water and gently blot any extra drops of water using Kimwipes. Submerge the end of the electrode in the beaker of pH 7 buffer.
- Click Record (the red button on the upper toolbar) on the LabScribe Main window to begin recording. After a few seconds, the trace will reach a stable baseline. Type pH 7 in the Mark box to the right of the Mark button (at the top- center of the screen). Press the Enter key on the keyboard to mark the stable baseline of the recording. This will mark the output of the ISE-100 pH electrode in pH 7 buffer. You may continue recording while changing the beakers of buffers.
- Remove the ISE-100 pH electrode from the beaker of pH 7 buffer. Hold the electrode over the beaker used for collecting waste liquid and rinse it with distilled water. Blot any extra drops of water with Kimwipe.
- Position the electrode in the beaker of pH 10 buffer.
- As you continue to record, the trace will reach a stable baseline, allow it to record for several seconds. Type pH 10 in the Mark box. Press the Enter key on the keyboard to mark the stable baseline of the recording. Click Stop on the LabScribe Main toolbar to stop recording .
- Remove the electrode from the beaker of pH 10 buffer. Hold the electrode over the beaker used for collecting waste liquid, and rinse it with distilled water from a wash bottle. Blot any extra drops of water and place the electrode in a clean beaker of room temperature distilled water.
Units Conversion
- Scroll to the beginning of the calibration data for the ISE-100 pH electrode.
- To show the data collected at pH 7 and pH 10 on the Main window at the same time, you can use either the Double Time Display icon to adjust the Display Time . Click Double Time several times until your pH 7 mark and the pH 10 mark are on the same screen or the Double Cursor icon will allow two red cursors to appear on the Main window.
- Place one red cursor on a flat section of data collected when the ISE-100 pH electrode was in the pH 7 buffer and the second red cursor on a flat section of data collected when the electrode was in the pH 10 buffer .
- Click on the Auto Scale icon in the tool bar above the graph screen.
- To convert the voltages at the positions of the cursors to pH values, use the Simple Units Conversion dialogue window . To access this dialogue window, click on the grey arrow (the upper left corner of the screen, see orange circle on figure 4, above) to the left of the channel title, pH, to open the channel menu.
- Select Units from the channel menu , and select Simple from the units submenu .
- On the Units Conversion window, (see picture below) make sure 2 point calibration is selected in the pull-down menu in the upper-left corner of the window.
- Put a check mark in the box next to Apply units to all blocks. Notice that the voltages from the positions of the cursors are automatically entered into the value equations.
- Enter the two buffers used in the calibration recording in the corresponding boxes on the right side of the conversion equations. Enter the name of the units, pH, in the box below the buffer values.
- Click on the OK button in the lower right corner of the window to activate the Units Conversion.
PART III: Test the Potential Buffers
Important: Click on the single-cursor mode icon for the rest of this experiment.
Solutions to test: Saline, Phosphate Buffered Saline (PBS), 5% Bovine Serum Albumin (BSA) in PBS, 10X sheep blood plasma in PBS, 10X sheep whole blood in PBS
For each solution to be tested:
- Click on the single cursor mode icon.
- Place approximately 10mL of the test solution in a small beaker. Label each buffer solution with a removable paper label which you will remove during clean up at the completion of the lab.
- Immerse the electrode in the test solution and click Record . Wait a few minutes for the pH to stabilize and mark this point as the Start for Solution X (name the solution) press ENTER.
- Add approximately 50��L of NaOH to the test solution. Gently swirl the solution and wait a few seconds for the pH to stabilize. Mark this point as 1 aliquot. Press ENTER.
- If the pH has changed less than 0.5 units, add another 50��L of NaOH and mark 2 aliquots and press ENTER once the solution has stabilized. Continue adding 50��L of NaOH and marking until you observe a change of 0.5 units or greater. Stop adding NaOH if you have added 15 aliquots of 50��L without a change in pH of at least 0.5 units.
- In Data Table 3.1 of your Lab Report , record the number of 50��L aliquots of NaOH required to cause the pH to go up at least 0.5 pH units. If you observed no change in pH after 15 aliquots were added, note “15+” in the data table.
- Repeat the procedure with the other test solutions making sure to rinse the electrode with clean distilled water and blotting it dry with a clean Kimwipe between solutions.
- Once you have tested all the test solutions, rinse the electrode again with distilled water and blot it with a Kimwipe. Gently insert the electrode into its original bottle of buffer and gently screw on the cap. Make sure the electrode is submersed in the buffer and stays upright! If the electrode dries out the equipment will be damaged. Please see the below figure.
- Finish the Week 3 Properties of Blood Worksheet.
- Note: Because the plasma and whole blood are diluted tenfold, their buffering ability is diluted as well. Therefore, assume these were ten times less effective than if undiluted plasma or blood were used.
Lab Clean Up
When the buffer part of lab is complete, please remove small labels from beakers and place in the trash. Rise the beakers several times with water and return them to their original locations to dry. Please leave the electrode in the same condition is was found: place electrode back in its small beaker with lid on (please make sure buffer solution is in the container because the electrodes must not dry out), and place the electrode storage bottle upright inside a larger beaker .
Blood glucose testing
When buffer work in lab has completed, TAs will offer students the opportunity to participate in a blood glucose test. Students will record their last meal and blood glucose value on the lab report; however, this part of the lab is volunteer only, since students must draw blood. TAs may offer one point extra credit for participation in this activity. Students who decide to participate must sign the consent form at the TA podium.


21.4: Progressivism in the White House
Progressive groups made tremendous strides on issues involving democracy, efficiency, and social justice. But they found that their grassroots approach was ill-equipped to push back against the most powerful beneficiaries of growing inequality, economic concentration, and corruption—big business. In their fight against the trusts, Progressives needed the leadership of the federal government, and they found it in Theodore Roosevelt in 1901, through an accident of history.
In 1900, a sound economic recovery, a unifying victory in the Spanish-American War, and the annexation of the Philippines had helped President William McKinley secure his reelection with the first solid popular majority since 1872. His new vice president was former New York Governor and Assistant Secretary of the Navy, Theodore Roosevelt. But when an assassin shot and killed President McKinley in 1901 (Figure 21.4.1) at the Pan-American Exposition in Buffalo, New York, Theodore Roosevelt unexpectedly became the youngest president in the nation’s history. More importantly, it ushered in a new era of progressive national politics and changed the role of the presidency for the twentieth century.
BUSTING THE TRUSTS
Roosevelt’s early career showed him to be a dynamic leader with a Progressive agenda. Many Republican Party leaders disliked Roosevelt’s Progressive ideas and popular appeal and hoped to end his career with a nomination to the vice presidency—long considered a dead end in politics. When an assassin’s bullet toppled this scheme, Mark Hanna, a prominent Republican senator and party leader, lamented, “Now look! That damned cowboy is now president!”
As the new president, however, Roosevelt moved cautiously with his agenda while he finished out McKinley’s term. Roosevelt kept much of McKinley’s cabinet intact, and his initial message to Congress gave only one overriding Progressive goal for his presidency: to eliminate business trusts. In the three years prior to Roosevelt’s presidency, the nation had witnessed a wave of mergers and the creation of mega-corporations. To counter this trend, Roosevelt created the Department of Commerce and Labor in 1903, which included the Bureau of Corporations, whose job it was to investigate trusts. He also asked the Department of Justice to resume prosecutions under the Sherman Antitrust Act of 1890. Intended to empower federal prosecutors to ban monopolies as conspiracies against interstate trade, the law had run afoul of a conservative Supreme Court.
In 1902, Roosevelt launched his administration’s first antitrust suit against the Northern Securities Trust Company, which included powerful businessmen, like John D. Rockefeller and J. P. Morgan, and controlled many of the large midwestern railroads. The suit wound through the judicial system, all the way to the U.S. Supreme Court. In 1904, the highest court in the land ultimately affirmed the ruling to break up the trust in a narrow five-to-four vote. For Roosevelt, that was enough of a mandate; he immediately moved against other corporations as well, including the American Tobacco Company and—most significantly—Rockefeller’s Standard Oil Company.
Although Roosevelt enjoyed the nickname “the Trustbuster,” he did not consider all trusts dangerous to the public welfare. The “good trusts,” Roosevelt reasoned, used their power in the marketplace and economies of scale to deliver goods and services to customers more cheaply. For example, he allowed Morgan’s U.S. Steel Corporation to continue its operations and let it take over smaller steel companies. At the same time, Roosevelt used the presidency as a “bully pulpit” to publicly denounce “bad trusts”—those corporations that exploited their market positions for short-term gains—before he ordered prosecutions by the Justice Department. In total, Roosevelt initiated over two dozen successful anti-trust suits, more than any president before him.
Roosevelt also showed in other contexts that he dared to face the power of corporations. When an anthracite coal strike gripped the nation for much of the year in 1902, Roosevelt directly intervened in the dispute and invited both sides to the White House to negotiate a deal that included minor wage increases and a slight improvement in working hours. For Roosevelt, his intervention in the matter symbolized his belief that the federal government should adopt a more proactive role and serve as a steward of all Americans (Figure 21.4.2). This stood in contrast to his predecessors, who had time and again bolstered industrialists in their fight against workers’ rights with the deployment of federal troops.
THE SQUARE DEAL
Roosevelt won his second term in 1904 with an overwhelming 57 percent of the popular vote. After the election, he moved quickly to enact his own brand of Progressivism, which he called a Square Deal for the American people. Early in his second term, Roosevelt read muckraker Upton Sinclair’s 1905 novel and exposé on the meatpacking industry, The Jungle . Although Roosevelt initially questioned the book due to Sinclair’s professed Socialist leanings, a subsequent presidential commission investigated the industry and corroborated the deplorable conditions under which Chicago’s meatpackers processed meats for American consumers. Alarmed by the results and under pressure from an outraged public disgusted with the revelations, Roosevelt moved quickly to protect public health. He urged the passage of two laws to do so. The first, the Meat Inspection Act of 1906, established a system of government inspection for meat products, including grading the meat based on its quality. This standard was also used for imported meats. The second was the Pure Food and Drug Act of 1906, which required labels on all food and drug products that clearly stated the materials in the product. The law also prohibited any “adulterated” products, a measure aimed at some specific, unhealthy food preservatives. For Sinclair, this outcome was a disappointment nonetheless, since he had sought to draw attention to the plight of workers in the slaughterhouses, not the poor quality of the meat products. “I aimed at the public’s heart, and by accident I hit it in the stomach,” he concluded with frustration.
Another key element of Roosevelt’s Progressivism was the protection of public land (Figure 21.4.3). Roosevelt was a longtime outdoorsman, with an interest that went back to his childhood and college days, as well as his time cattle ranching in the West, and he chose to appoint his good friend Gifford Pinchot as the country’s first chief of the newly created U.S. Forestry Service. Under Pinchot’s supervision, the department carved out several nature habitats on federal land in order to preserve the nation’s environmental beauty and protect it from development or commercial use. Apart from national parks like Oregon’s Crater Lake or Colorado’s Mesa Verde, and monuments designed for preservation, Roosevelt conserved public land for regulated use for future generations. To this day, the 150 national forests created under Roosevelt’s stewardship carry the slogan “land of many uses.” In all, Roosevelt established eighteen national monuments, fifty-one federal bird preserves, five national parks, and over one hundred fifty national forests, which amounted to about 230 million acres of public land.
In his second term in office, Roosevelt signed legislation on Progressive issues such as factory inspections, child labor, and business regulation. He urged the passage of the Elkins Act of 1903 and the Hepburn Act of 1906, both of which strengthened the position of the Interstate Commerce Commission to regulate railroad prices. These laws also extended the Commission’s authority to regulate interstate transportation on bridges, ferries, and even oil pipelines.
As the 1908 election approached, Roosevelt was at the height of popularity among the American public, if not among the big businesses and conservative leaders of his own Republican Party. Nonetheless, he promised on the night of his reelection in 1904 that he would not seek a third term. Roosevelt stepped aside as the election approached, but he did hand-pick a successor—Secretary of War and former Governor General of the Philippines William Howard Taft of Ohio—a personal friend who, he assured the American public, would continue the path of the “Square Deal” (Figure 21.4.4). With such a ringing endorsement, Taft easily won the 1908 presidential election, defeating three-time Democratic presidential nominee William Jennings Bryan, whose ideas on taxes and corporate regulations reminded voters of the more far-reaching Populist platforms of Bryan’s past candidacies.
Explore American Experience: TR at PBS for a wealth of information on Theodore Roosevelt, including details of his early life before the presidency and transcripts from several of his speeches.
THE TAFT PRESIDENCY
Although six feet tall and nearly 340 pounds, as Roosevelt’s successor, Taft had big shoes to fill. The public expected much from Roosevelt’s hand-picked replacement, as did Roosevelt himself, who kept a watchful eye over Taft’s presidency.
The new president’s background suggested he would be a strong administrator. He had previously served as the governor of the Philippines following the Spanish-American War, had a distinguished judicial career, and served as Roosevelt’s Secretary of War from 1904 to 1908. Republican leaders, however, were anxious to reestablish tighter control over the party after Roosevelt’s departure, and they left Taft little room to maneuver. He stayed the course of his predecessor by signing the Mann-Elkins Act of 1910, which extended the authority of the Interstate Commerce Commission over telephones and telegraphs. Additionally, during his tenure, Congress proposed constitutional amendments to authorize a federal income tax and mandate the direct election of U.S. senators. But even though Taft initiated twice as many antitrust suits against big business as Roosevelt, he lacked the political negotiating skills and focus on the public good of his predecessor, who felt betrayed when Taft took J.P. Morgan’s U.S. Steel Corporation to court over an acquisition that Roosevelt had promised Morgan would not result in a prosecution.
Political infighting within his own party exposed the limitations of Taft’s presidential authority, especially on the issue of protective tariffs. When House Republicans passed a measure to significantly reduce tariffs on several imported goods, Taft endorsed the Senate version, later known as the Payne-Aldrich Act of 1909, which raised tariff rates on over eight hundred products in the original bill. Taft also angered Progressives in his own party when he created the U.S. Chamber of Commerce in 1912, viewed by many as an attempt to offset the growing influence of the labor union movement at the time. The rift between Taft and his party’s Progressives widened when the president supported conservative party candidates for the 1910 House and Senate elections.
Taft’s biggest political blunder came in the area of land conservation. In 1909, Taft’s Secretary of the Interior, Richard Ballinger, approved the sale of millions of acres of federal land to a company for which he had previously worked over Gifford Pinchot’s objections. Pinchot publicly criticized the secretary for violating the principle of conservation and for his conflict of interest—a charge that in the public debate also reflected on the president. Taft fired Pinchot, a move that widened the gap between him and the former president. Upon his return from Africa, Roosevelt appeared primed to attack. He referred to the sitting president as a “fathead” and a “puzzlewit,” and announced his intention to “throw my hat in the ring for the 1912 presidential election.”
THE 1912 PRESIDENTIAL ELECTION
Although not as flamboyant or outwardly progressive as Roosevelt, Taft’s organizational skills and generally solid performance as president aligned with the party leadership’s concerns over another Roosevelt presidency and secured for him the Republican Party’s nomination. Angry over this snub, in 1912, Roosevelt and the other Progressive Republicans bolted the Republican Party and formed theProgressive Party. His popularity had him hoping to win the presidential race as a third-party candidate. When he survived an assassination attempt in Milwaukee, Wisconsin, in October 1912—the assassin’s bullet hit his eyeglass case and only injured him superficially—he turned the near-death experience into a political opportunity.  The moniker stuck, and Roosevelt’s Progressive Party would be known as the Bull Moose Party for the remainder of the campaign (Figure 21.4.5).
The Democrats realized that a split Republican Party gave them a good chance of regaining the White House for the first time since 1896. They found their candidate in the Progressive governor of New Jersey, Woodrow Wilson. A former history professor and president at Princeton University, Wilson had an academic demeanor that appealed to many Progressive reformers. Many Democrats also viewed Wilson as a Washington outsider who had made far fewer political enemies than Roosevelt and Taft.
Taft never truly campaigned for the post, did not deliver a single speech, and did not seem like a serious contender. In their campaigns, Roosevelt and Wilson formulated competing Progressive platforms. Wilson described his more moderate approach as one of New Freedom, which stood for a smaller federal government to protect public interests from the evils associated with big businesses and banks. Roosevelt campaigned on the promise of New Nationalism, a charge that he said required a vigorous and powerful federal government to protect public interests. He sought to capitalize on the stewardship approach that he had made famous during his previous administration.
Wilson won the 1912 election with over six million votes, with four million votes going to Roosevelt and three and one-half million for Taft. The internal split among Republicans not only cost them the White House but control of the Senate as well—and Democrats had already won a House majority in 1910. Wilson won the presidency with just 42 percent of the popular vote, which meant that he would have to sway a large number of voters should he have any aspirations for a second term.
In his 2002 article on the 1912 election, historian Sidney M. Milkis writes,
The Progressive Party’s “compromise” with public opinion in the United States points to its legacy for American politics and government. Arguably, the failure of the 1912 experiment and the Progressive Party’s demise underscore the incoherence of the Progressive movement. Nevertheless, it was neither the Democrats, nor the Republicans, nor the Socialists who set the tone of the 1912 campaign. It was the Progressives. Beyond the 1912 election, their program of political and social reform has been an enduring feature of American political discourse and electoral struggle. The Progressive Party forged a path of reform that left both social democracy and conservatism—Taft’s constitutional sobriety—behind. Similarly, T.R.’s celebrity, and the popularity of the Progressive doctrine of the people’s right to rule, tended to subordinate the more populist to the more plebiscitary schemes in the platform, such as the initiative, the referendum, and the direct primary, which exalted not the “grass roots” but mass opinion. Indeed, in the wake of the excitement aroused by the Progressive Party, Wilson, whose New Freedom campaign was far more sympathetic to the decentralized state of courts and parties than T.R.’s, felt compelled, as president, to govern as a New Nationalist Progressive.
It is interesting to think of how this most unusual election—one with three major candidates that pitted a former president against an incumbent and a major party contender—related to the larger Progressive movement. The cartoon below is only one of many cartoons of that era that sought to point out the differences between the candidates (Figure 21.4.6). While Roosevelt and the Progressive Party ultimately lost the election, they required the dialogue of the campaign to remain on the goals of Progressivism, particularly around more direct democracy and business regulation. The American public responded with fervor to Roosevelt’s campaign, partly because of his immense popularity, but partly also because he espoused a kind of direct democracy that gave people a voice in federal politics. Although Wilson and his New Freedom platform won the election, his presidency undertook a more activist role than his campaign suggested. The American public had made clear that, no matter who sat in the White House, they were seeking a more progressive America.
WILSON’S NEW FREEDOM
When Wilson took office in March 1913, he immediately met with Congress to outline his New Freedom agenda for how progressive interests could be best preserved. His plan was simple: regulate the banks and big businesses, and lower tariff rates to increase international trade, increasing competition in the interest of consumers. Wilson took the unusual step of calling a special session of Congress in April 1913 to tackle the tariff question, which resulted in the Revenue Act of 1913, also known as the Underwood Tariff Act. This legislation lowered tariff rates across the board by approximately 15 percent and completely eliminated tariffs on several imports, including steel, iron ore, woolen products, and farm tools. To offset the potential loss of federal revenue, this new law reinstituted the federal income tax, which followed the ratification of the Sixteenth Amendment. This first income tax required married couples who earned $4000 or more, and single people who earned $3000 or more, to pay a 1-percent, graduated income tax, with the tax rate getting progressively higher for those who earned more.
Late in 1913, Wilson signed the Federal Reserve Act to regulate the banking industry and establish a federal banking system (Figure 21.4.7). Designed to remove power over interest rates from the hands of private bankers, the new system created twelve privately owned regional reserve banks regulated by a presidentially appointed Federal Reserve Board. The Board, known informally as the Fed, regulated the interest rate at which reserve banks loaned or distributed money to other banks around the country. Thus, when economic times were challenging, such as during a recession, the Fed could lower this “discount rate” and encourage more borrowing, which put more currency in circulation for people to spend or invest. Conversely, the Fed could curb inflationary trends with interest hikes that discouraged borrowing. This system is still the basis for the country’s modern banking model.
The history of the Federal Reserve Act is explored in The Washington Post , reflecting back on the act one hundred years later.
In early 1914, Wilson completed his New Freedom agenda with the passage of the Clayton Antitrust Act. This law expanded the power of the original Sherman Antitrust Act in order to allow the investigation and dismantling of more monopolies. The new act also took on the “interlocking directorates”—competing companies that still operated together in a form of oligopoly or conspiracy to restrain trade. His New Freedom agenda complete, Wilson turned his attention to foreign affairs, as war was quickly encompassing Europe.
THE FINAL VESTIGES OF PROGRESSIVISM
As the 1916 election approached, Wilson’s focus on foreign affairs, as well as the natural effect of his small government agenda, left the 60 percent of the American public who had not voted for him the first time disinclined to change their minds and keep him in office. Realizing this, Wilson began a flurry of new Progressive reforms that impressed the voting public and ultimately proved to be the last wave of the Progressive Era. Some of the important measures that Wilson undertook to pass included the Federal Farm Act, which provided oversight of low-interest loans to millions of farmers in need of debt relief; the Keating-Owen Child Labor Act, which, although later deemed unconstitutional by the U.S. Supreme Court, prohibited the interstate distribution of products by child workers under the age of fourteen; and the Adamson Act, which put in place the first federally mandated eight-hour workday for railroad workers.
Wilson also gained significant support from Jewish voters with his 1916 appointment of the first Jewish U.S. Supreme Court justice, Louis D. Brandeis. Popular among social justice Progressives, Brandeis went on to become one of the most renowned justices on the court for his defense of freedom of speech and right to privacy issues. Finally, Wilson gained the support of many working-class voters with his defense of labor and union rights during a violent coal strike in Ludlow, Colorado, as well as his actions to forestall a potential railroad strike with the passage of the aforementioned Adamson Act.
Wilson’s actions in 1916 proved enough, but barely. In a close presidential election, he secured a second term by defeating former New York governor Charles Evans Hughes by a scant twenty-three electoral votes, and less than 600,000 popular votes. Influential states like Minnesota and New Hampshire were decided by less than four hundred votes.
Despite the fact that he ran for reelection with the slogan, “He Kept Us Out of the War,” Wilson could not avoid the reach of World War I much longer. For Wilson and the American public, the Progressive Era was rapidly winding down. Although a few Progressive achievements were still to come in the areas of women’s suffrage and prohibition, the country would soon be gripped by the war that Wilson had tried to avoid during his first term in office. When he took the oath for his second term, on March 4, 1917, Wilson was barely five weeks away from leading the United States in declaring war on Germany, a move that would put an end to the Progressive Era.
Section Summary
Theodore Roosevelt became president only by historical accident, but his activism in the executive branch spoke to the Progressive spirit in the nation and transformed the president’s office for the twentieth century. The courage he displayed in his confrontation of big business and willingness to side with workers in capital-labor disputes, as well as his commitment to the preservation of federal lands, set an agenda his successors had to match. Like Roosevelt, William Howard Taft pushed antitrust rulings and expanded federal oversight of interstate commerce. But estrangement from his predecessor and mentor left Taft in a difficult position for reelection. Roosevelt’s third-party challenge as a Progressive split the Republican vote and handed Woodrow Wilson the presidency in 1912.
A Progressive like his predecessors, Wilson was also a political creature who understood the need to do more in order to ensure his reelection. He, too, sought to limit the power of big businesses and stabilize the economy, and he ushered in a wave of Progressive legislation that grassroots Progressives had long called for. The nation’s entanglement in World War I, however, soon shunted the Progressive goals of democracy, efficiency, regulation, and social justice to the back burner. The nation’s new priorities included national security and making the world “safe for democracy.”
Review Questions
How did Roosevelt intercede in the Anthracite Coal Strike of 1902?
- He invited strikers and workers to the White House.
- He urged the owners to negotiate a deal.
- He threatened to send in the army to work the mines.
- He ordered the National Guard to protect the strikers.
A
Which of the following was a key Progressive item passed by Taft?
- the Pure Food and Drug Act
- the U.S. Forestry Service
- the Mann-Elkins Act
- the Payne-Aldrich Act
D
Which of the following was not an outcome of the Underwood Tariff Act?
- It reduced tariffs 15 percent across all imports.
- It eliminated tariffs for steel.
- It eliminated tariffs for iron ore.
- It established a federal banking system to oversee tariffs.
D
Explain the fundamental differences between Roosevelt’s “New Nationalism” and Wilson’s “New Freedom.”
The major difference between Roosevelt’s New Nationalism and Wilson’s New Freedom concerned the candidates’ beliefs about the necessary size of the federal government. Wilson believed that a small federal government could keep bad businesses in check while allowing the country to grow. Roosevelt, in contrast, believed that the country required a large and involved federal government to safeguard the interests of the American people.
Why did Wilson’s “New Freedom” agenda come in two distinct phases (1913 and 1916)?
Wilson’s actions were limited by his belief in his New Freedom platform, which promised voters a small government. Still, he took a number of steps in the first year of his presidency to shore up the economy and push back against destructive trusts. With those goals accomplished, he largely left the Progressive agenda alone. As the 1916 election season approached, however, Wilson realized that his hands-off policy was not endearing him to voters, and he ended his first term in a flurry of Progressive legislation that reminded the voting public of all he could do for them.
Critical Thinking Questions
Which of the primary features of grassroots Progressivism was the most essential to the continued growth and success of the reformist movement? Why?
Describe the multiple groups and leaders that emerged in the fight for the Progressive agenda, including women’s rights, African American rights, and workers’ rights. How were the philosophies, agendas, strategies, and approaches of these leaders and organizations similar and different? What made it difficult for all Progressive activists to present a united front?
How did President Theodore Roosevelt’s “Square Deal” epitomize the notion that the federal government should serve as a steward protecting the public’s interests?
How did the goals and reform agenda of the Progressive Era manifest themselves during the presidential administrations of Roosevelt, Taft, and Wilson?
What vestiges of Progressivism can we see in our modern lives—politically, economically, and socially? Which of our present-day political processes, laws, institutions, and attitudes have roots in this era? Why have they had such staying power?
Glossary
- New Freedom
- Woodrow Wilson’s campaign platform for the 1912 election that called for a small federal government to protect public interests from the evils associated with bad businesses
- New Nationalism
- Theodore Roosevelt’s 1912 campaign platform, which called for a powerful federal government to protect the American public
- Progressive Party
- a political party started by Roosevelt and other Progressive Republicans who were unhappy with Taft and wanted Roosevelt to run for a nonconsecutive third term in 1912
- Square Deal
- Theodore Roosevelt’s name for the kind of involved, hands-on government he felt the country needed