What is the theme of the story Three Men in a Boat?

The major recurring theme of the novel is English history. Many of the places that the three travellers encounter on their journey along the Thames, the old villages and inns and so on, are simply steeped in historical fact and legend. The narrator, Jerome, or J, seldom loses an opportunity to muse upon days and scenes gone by (it seems he is fitted by nature to do so in any case, being a self-confessed daydreamer and idler). He also nostalgically envisages the past as being a time of less fret and haste and anxiety than his own world of the late nineteenth century. He certainly has a vivid imagination as he conjures up historical events and personages.
Very often Jerome's historical musings are worked into the comedy of the book, especially when juxtaposed with events and characters of his own day. For instance, on noting how many public houses Queen Elizabeth I ('Queen Bess') is supposed to have frequented along the river, he falls to speculating how people of the future might come to see and wonder over the pubs that his fellow-traveller Harris, a noted drinker, did not visit. He also notes how the present time needs someone like Julius Caesar of old to exercise strong-arm tactics against those people whom Jerome sees as spoiling the enjoyment of the river for others by demanding money from sightseers, and so on.
However, on other occasions Jerome's imaginative excursions into England's past take on a wholly romantic and indeed sentimental glow, as for instance when he grandly envisions the signing of the Magna Charta, concluding as follows:

And King John has stepped upon the shore, and we wait in breathless silence till a great shout cleaves the air, and the great cornerstone in England's temple of liberty has, now we know, been firmly laid.

Two themes that stand out to me are the themes of happiness and where happiness can be found.
The initial reason that the men decide to go on their boat trip is that they are feeling sick, restless, and unhappy. What is great about the story in general is that it doesn't provide readers with a "key" to happiness. The men are unhappy with their lives in London, and they are unhappy and constantly bicker while on the boat ride. This story doesn't send readers the message that happiness is found away from the city, or on vacation, or out with friends. Instead the story gives readers the idea that happiness is more of a mindset. If you can be content with your current situation and appreciate all that is around you, happiness will follow.
The other theme is a theme that contrasts country life and city life. Various forms of media tend to portray country life as so much more wholesome, happy, and simple than city life. Currier and Ives paintings portray this notion nicely as do paintings from Thomas Kinkade. What's great about Three Men in a Boat is that it does not perpetuate this myth. The men in the story believe that a boat trip away from the stresses of the city will bring them happiness and relief; however, over the course of their trip, they discover that country living is every bit as stressful, demanding, and difficult as city life.
https://thomaskinkade.com/?v=7516fd43adaa

Chapter 4 onwards serves as a turning point in The Great Gatsby. Why did Nick Carraway choose this point?

To say that Chapter 4 represents a turning point in the novel means that it marks some significant change in the plot or narrative. Nick begins this chapter by listing the usual guests at Gatsby's parties, and Gatsby and Nick spend some time alone together. Gatsby tells his ludicrously romantic story, which Nick can scarcely believe until Gatsby produces apparent evidence of this history: a photograph. Nick and Gatsby go into the city, and Gatsby introduces Nick to Meyer Wolfsheim. Later, Jordan explains the history between Gatsby and Daisy and how Daisy ended up marrying Tom Buchanan. 
This chapter, then, really initiates the present story line between Gatsby and Daisy and sets into motion all the events which follow.  The chapter also begins to confirm some of our—and Nick's—suspicions about Gatsby's illegal activities, given the crowd he runs with and his sudden fortune. In other words, Gatsby becomes both more sympathetic and morally problematic in this chapter.  Perhaps Nick "chooses" this time in the story because he began to become aware of Gatsby's complexity at this time, too. It is also possible that Nick problematizes Gatsby here so readers can understand the man better as we continue to read his story. Nick doesn't want us to think Gatsby is a saint, but compared to most of the other characters in the story, he is somehow "great," and this sets him apart.

Explain how and why slavery expanded over time.

Slavery started in America from the beginning of its settlement by Europeans. It went through various phases until its end at the conclusion of the Civil War.
In 1619, a Dutch ship brought the first slaves to America. The slave trade grew because slaves were seen as a cheaper alternative to the use of indentured servants. Millions of Africans were imported from Africa in the seventeenth and eighteenth centuries, and they were employed on rice, indigo, and tobacco farms in the South.
After America achieved independence from England in 1783, the US Constitution (1789) recognized and legitimized the existence of slavery and counted them as 3/5 of a person for purposes of representation and taxation. Nevertheless, by 1804, states in the North had outlawed slavery; the African slave trade was abolished 1808.
Slavery might have died out in the South had it not been for the invention of the cotton gin in 1793. In 1793, Eli Whitney invented a device to facilitate the removal of seeds from cotton. This was a boon to slavery because it made cotton production—with slave labor—much more profitable.
The number of slaves in the South increased greatly in the fifty years before the Civil War (1861–1865). Southern leaders thought their economy—even their culture—depended on slavery. They were determined to keep it and spread it wherever they could. The South's loss in the Civil War finally put an end to the odious institution of slavery in the US.

Slavery, especially in the United States, expanded due to many factors. The first factor was the large supply of arable farmland in the country, especially in the South. As demand grew for textile products worldwide, Southern planters saw an opportunity to take the cheap land and turn it into a platform for cash crops. In order to work thousands of acres without mechanized equipment, they used slaves. Before 1808, they could buy the slaves from Africa; after this year, however, the United States stopped importing slaves. The slave owners could only rely on the progeny of their slaves. By 1820, a good field hand could be as expensive as a new luxury car today if compared in today's dollars.
The cotton gin also allowed for the expansion of slavery. It allowed one slave to do the work of many and made the industry even more profitable. This allowed for more acres to be utilized in monoculture and the slave industry to grow even further. Slavery also put pressure on the United States to expand as well, as planters sought cheap land in the American Southeast and Texas.

Contrast the solar system model of the atom with Schrodinger's Wave Equation. I wrote this so far: Schrodinger's Wave Equation is that the electrons move around the nucleus as a wave, while the solar system model has problems which are the accelerating electrons giving off light, leading them to spiral into the nucleus very quickly. I need 3 other facts integrated in my answer about either the solar system model or the Schrondinger wave equation.

The solar system model of an atom, usually called the "planetary" model, describes an atom as composed of a single positively charged nucleus and several electrons. The electrons orbit around the nucleus similarly to the planets of the solar system orbiting the Sun, hence the name "planetary." It is important to note that the number of the electrons is such that their total negative charge exactly equals the positive charge of the nucleus, so the atom as a whole is electrically neutral. Also, note that the size of the nucleus is about hundred thousand times smaller than the distance between the nucleus and the orbiting electrons, so the atom itself is mostly filled with empty space (the volume taken up by the electrons is negligible).
This model of an atom works well for some applications, but it is not consistent with the classical theory of electromagnetism. As you have pointed out, the electrons that undergo circular motion around the nucleus are accelerating (because they are constantly changing their velocity), so they will radiate or emit light. This light will carry off their energy, so they will eventually slow down. If the speed of an electron decreases, the radius of its orbit also has to decrease. As a result, the electron will "fall" into the nucleus, and the atom will collapse.
This, of course, does not happen (because then matter as we know it would not exist!) but the classical mechanics of electromagnetism cannot explain the structure of the atom. A different theory, known as quantum mechanics, is needed to explain why the electrons have stable orbits. The Schrodinger equation is the central equation of quantum mechanics. In this theory, each particle, including an electron, is modeled as a wave. The position of each electron at a given moment of time is not known precisely, but it is described as a probability function, called a wave function.These wave functions are characterized by certain integer numbers (called quantum numbers) that describe the energy of the electrons, and each number is associated with what traditionally would be the orbit. (There is an orbit for n = 1, an orbit for n = 2, and so on. The energy of the electron in each orbit depends on n.) In a quantum mechanical model, each electron forms a wave around the nucleus, in the sense that there is a probability that it can be found at a given place on the "orbit" (keep in mind that there is no actual wave-like motion going on). 
Please see the linked article that summarizes the atomic models and discusses the history of the development of the atomic theory.
http://www.abcte.org/files/previews/chemistry/s1_p6.html

Compare and contrast unilineal cultural evolution theory with historical particularism. Explain each theory, the anthropologists associated with them, their research methods, and what, if any, flaws these theories have.

Unilineal evolution theory is a concept which became formally defined in the nineteenth century but whose fundamental assumptions were derived from the ideas of social and cultural modernity of the eighteenth-century European Enlightenment. The idea of the “modern,” like the sociological concept of unilineal evolution that it inspired, posits the existence of a singular, teleological course of social evolution, in which both the beginning and end points of historical progress are fixed entities which can be scientifically demonstrated. Because it was Europe that saw the birth of rationalism, the scientific and industrial revolutions, and the belief in a stadial evolution of history, Europe served as the model by which the progress of all other world civilizations could be assessed.
Unilineal evolution theory was influenced by the works of many different European intellectuals. August Comte argued that from its most prehistoric antecedents to the present day, civilization evolves along a linear path and moves through predictable stages, from the theological (religious) to the metaphysical (philosophic) to ultimately the scientific. Karl Marx and Frederick Engels similarly argued for the linear evolution of society, except that they maintained this evolution occurred as a result of massive shifts in the “means of production” upon which a given society’s socioeconomic base was founded. For them, the means of production first permitted a hunter-gatherer way of life, then a slave-owning society, feudalism, and modern bourgeois capitalist society. Marxism anticipated a next and final stage of social evolution, that of the proletariat revolution that would produce a communist society, which was not yet in existence during Marx and Engels’s lives.
Sociologist Émile Durkheim made similar arguments for the evolution of society, but he instead focused his research on the evolution of religion. In his famous The Elementary Forms of Religious Life, Durkheim argued that, prior to the emergence of modern-day Christianity, with its many different divisions and groupings, there must have existed in past times some form of primordial religion, out of which the basic building blocks of what makes religion possible could be identified. Durkheim argued that from this primordial religion (which he traced to the totemic religions of the Australian Aborigines), religious practice evolved to the pagan, the animistic, and eventually the complex religions of his own day and age. What all of these philosophers had in common was that they believed in a singular, predictable path of social evolution that could be used as a common standard to judge the relative level of modernity of all the world’s peoples.
The problems associated with this way of thinking were that, as European intellectuals essentially founded the method of rational knowledge production, Europe itself was placed atop an artificial civilizational hierarchy. Of course, no European thinker wanted to identify his own society as somehow inferior to those of the far-off regions of the world. This was particularly salient given that that industrial revolution in the nineteenth century had generated unparalleled material wealth and splendor, which many Europeans found to be sorely lacking in other, non-industrial, undeveloped parts of the world. Thus, “modernity,” with its corresponding social science theory of unilineal evolution, was a Eurocentric concept that was used to justify European colonization of the planet and the brutal exploitation of indigenous people and natural wealth from Africa, Asia, and the New World.
Historical particularism is a concept that stands in contrast to unilinear evolution by positing that historical progression is not fixed and incontrovertible essence but is rather a product of the specific evolution of any given civilization. In the historical discipline, contribution to this theory, and to this way of thinking in general, came from individuals such as the German historian Leopold von Ranke, Thomas Macaulay, and George Bancroft in the nineteenth century and G. R. Elton in the twentieth. These historians emphasized the importance of using archival sources in the construction of historical narratives.
It was out of social science theories like historical particularism that new methods for the study of history and civilization were developed. The idea that culture, individual people, science, technology, the environment, and material commodities themselves could serve as historical objects for analysis emerged as a way to explain the course of social evolution for certain societies in such a way that did not simply assume divergence from the “correct” European path. More recently, Dipesh Chakrabarty has taken the implications of historical particularism to promote the field of postcolonialism. Postcolonial theory takes historical particularism to its extreme by arguing that the colonized peoples that Europeans encountered during their imperial projects influenced the course of European history just as much as Europeans changed the colonies. Thus, he reinforces the conclusion that history is not an inevitable and predictable procession but is rather contingent on material and social forces that cannot be readily explained or defined.

Unilinear Cultural Evolution Theory, popular through the nineteenth century, is the idea that all societies progress along the same general timeline: cultures start off as primitive groups (nomadic hunter-gatherers) and develop to become civilized communities (technological, literate, and rooted in a permanent location). This was an amalgamation of many anthropologists’ perspectives of the day, including those of Lewis Henry Morgan and Edward B. Tylor.
One problem with this was that the researchers were judging all societies by their own western European ideals of civilization, which (they believed) had reached its pinnacle with the ancient Greek and Roman societies and that society began to decline thereafter. They assumed that the progress of social evolution could be compared to Darwin’s theory of biological evolution: simple structures naturally become more complex.
Historical Particularism, introduced by Franz Boaz in the twentieth century, suggests that we can’t judge every society’s development by one standard. Geography, climate, regional history, and individual behavior all play a role in how a society develops and how unique communities could define “civilization.”
The Unilinear theory relied on second-hand information about different cultures, such as reports from traveling missionaries and merchants. Boaz felt that first-hand field work was necessary to really understand how individual cultures develop.
Visit the links below for more information about each theory, its proponents, and their methods.
https://anthropology.ua.edu/anthropological-theories/?culture=Social%20Evolutionism

In "A Modest Proposal," Swift's speaker outlines several benefits to his idea. Briefly explain two of the benefits he outlines.

In "A Modest Proposal," Swift satirizes the not-so-benign neglect of Ireland by its British colonial overlords. In the guise of a learned scientific paper, Swift puts forward the idea that the British can solve a number of problems in relation to the administration of Ireland by the simple expedient of allowing the natives to breed children for meat.
The author claims that his modest proposal will solve the problem of poverty. In Swift's time, poverty in Ireland was endemic and grinding, exacerbated by the indifference of British administrators. In the "Proposal," the author claims that allowing Irish people to breed children for meat will greatly reduce poverty in the Emerald Isle. With such a regular supply of food available, a prosperous new industry will emerge. People will be able to sell their children for meat, thus giving them a respectable living, instead of being forced to beg on the streets as they currently do.
Furthermore, the author goes on to say, his proposal will substantially reduce hunger. Even if the poor folk of Ireland are unable or unwilling to sell their children for meat, they can always eat them themselves. Neither they nor their families need ever go hungry again. Once more, Swift's biting satire has a serious target. Famines and chronic food shortages were a constant feature of Irish life, especially in the countryside, where the vast majority lived.

What made countries so powerful in the 1900s?

The Industrial Revolution made countries powerful in the 1900's.  In many respects, the Industrial Revolution was a separator between powerful states and ones that would woefully lag behind.  Geography and political stability were important factors in whether a country could industrialize or not.  Countries that saw an increase in manufacturing because of the utilization of machines were advantaged in a number of ways.  First, it was easier to mass produce weapons that were on the cutting edge of battlefield technology.  Second, the increase in wealth, and by extension, tax revenues allowed industrialized nations to invest in their defense industries.  A third reason that industrialization made nations powerful is because it helped them to expand their empires.  Industrialized nations looked to other lands to acquire natural resources and markets.  These lands provided both economic and military benefits to those nations.