Introduction
In this study, I investigate the tensions that surround the place of persuasion (and, more broadly, control) in marketing. Persuasion has variously been seen as an embarrassment to the discipline, a target for anti-marketing sentiment, the source of marketing’s value in the modern organisation, a mysterious black box inside the otherwise rational and logical endeavour of enterprise, and a rather insignificant part of the marketing programme. I will argue that this multifarious reputation for persuasion within marketing stems from the influence of two quite oppositional paradigms—the scientific and the magico-rhetorical—that ebb and flow across the discourses of its discipline and practice.
The scientific endeavour can be characterised as an effort to strip human investigation, and subsequent practice, of any confounding subjective influence, to objectively lay bare the workings of the natural world without becoming ensnared in the illusions of ideology, religion, myth, and received wisdom. Fundamental to all of these harbingers of error is that they are embedded in language. The careless use of language has been seen as the enemy of the objective discovery of truth since the birth of the modern scientific method (Stark, 2009). The early experimentalists of the Royal Society, for example, sought to eradicate figurative language and cultivate a plainness of style that focused not upon “The Artiface of Words, but a bare knowledge of things” (Sprat, cited in Longaker, 2015, p. 16). This attitude has also suffused much of the intellectual history of economics, commerce and management, where the patina of objective, ‘scientific’ discourse is important in persuading actors of the unbiased, incontrovertible logic of theories, policies and decisions (McCloskey, 1985; Miller, 1990; Greatbatch and Clark, 2005). Yet, as my own language here implies, the valorising of a plain and factual style, shorn of rhetorical figuration and emotional appeals, is itself a clear rhetorical strategy. Persuasive language does not have to appear florid and overflowing with figuration—it can instead adopt an empirical tone, relying upon the rhetoric of tables and matrices, to seduce readers into believing that the ‘logic of science’ is operating across its discourse. When academic and practitioner voices speak of banishing persuasion and rhetoric, then, they are often simply taking the opportunity to implement a
particular rhetorical strategy of their own, a strategy which at many level is concerned with the manufacturing and maintenance of control.
In order to examine the place of persuasion within marketing theory, one inevitably will have to explore the relationship that the discipline has with scientific discourse (and scientific methodology as a discourse strategy). Yet, as I have already indicated, there is another discourse paradigm that has just as much influence over the development and self-construction of the marketing discipline—the magical worldview. Here, language is something that can enchant, cast a glamour, control from afar, and influence without recourse to logic or facts. Knowing the right set of words (the appropriate incantation) can give you power over others and reduce the confusion of everyday life. Such a power is naturally attractive to us all—but marketing practitioners, who deal constantly with the effort to find the right combination of words to invoke their brand’s benefit as effectively as possible are perhaps closer than any other contemporary profession to the allure of the magical paradigm of language. Marketing theorists, who seek to formalise and explain the practice to themselves, their students, and (hopefully) professionals, are inevitably exposed to the assumptions of magical influence that I will show are common across the discipline. They might react to these assumptions, try to exorcise them, construct their theories in order to leave no room for them—but they inevitably become open to infection by them just as they are at the mercy of the assumptions of scientific discourse. I intend to show that at the root of both the scientific and magical paradigms of language is the same basic concern—control. Marketing is obsessed with control—it is its very lifeblood. Accordingly, it should come as no surprise that marketing theory and practice constantly flip-flop between scientific and magical approaches to language. However, the relationship between the two is not a simple binary one, and it is the tradition of rhetoric which gives important clues as to how they bind together. The study and practice of rhetoric (the classical art of persuasion) has similarly been entwined within variegated constructions of rationality and irrationality throughout its theory and practice. I will demonstrate that marketing is an institutionalised contemporary manifestation of the rhetorical enterprise, particularly as the Sophists conceived of it, and as such can greatly profit from a careful consideration of the history of its mother discipline and the way in which society has at turns embraced and demonised it. This is particularly important at this stage of marketing’s evolution. Concerns regarding marketing’s authenticity, transparency, manipulative intentions, and effectiveness are rife both within and without the discipline. Marketing academics, with varying degrees of alarmist language, worry about the future of both the academic discipline and the profession (Thomas, 2006; Merlo, 2011; Varey, 2013; Clark et al., 2013; Verhoef and Leeflang, 2009) while report after report demonstrates the crisis of trust that brands face online due to annoying and intrusive control-oriented marketing practices (Daly, 2016). Theories (or proto-theories) such as the Service-Dominant logic (Vargo and Lusch, 2004)
can be seen as attempts to re-define marketing in the face of such threats, yet they do this at the cost of making marketing less and less relevant. What is needed, instead, is an honest approach to the centrality of control to the marketing enterprise, one which can bring nuance and insight to the consideration of control rather than simply trying to act as if it is not (or should not be) there. This is what this study attempts to do by making a case for understanding marketing as a Sophistic enterprise, one which is focused upon the control (or management) of attention (or what I will call regard) through a persuasive, interactive engagement with stakeholders in an agonistic (i.e. competitive) environment. In order to argue this case, the reader must be taken through a number of stages and exposed to some quite diverse areas of scholarship and practice. I will now outline the course of the argument that I will be developing over the next nine chapters.
Synopsis
The first part of the book establishes the extent to which rhetoric has already figured as an object of marketing scholarship. In order to do this, and to prepare the reader of the development of my argument in later chapters, I start with an overview of the history of Western rhetoric. What writing there has been to date on the place of rhetoric within marketing practice and theory has tended to have to skimp heavily when supplying the historical and developmental context to rhetoric. This acts as a disadvantage for the further acceptance of rhetorical perspectives in the discipline because it leaves most readers with only a cursory understanding of what rhetoric really is and how much depth there exists in the scholarship that has grown up around it for more than two thousand years. If all we know of rhetoric is that Aristotle said that there were three different types of persuasive argument (ethos, logos, and pathos) and that it also has something (though we might not be sure what) to do with metaphors and figures of speech, then it is not surprising that we might not appreciate how much insight rhetoric can give us into the whole gamut of marketing thought. While there are many worthy primers of rhetoric available to the interested reader (Conley, 1990; Murphy et al., 2014; Kennedy, 1994; Smith, 2003; to name but a few), there are none that seek to summarise the story of the discipline for a marketing audience. Consequently, I will endeavour to lay out the important aspects of the study and practice of rhetoric as they will relate to my later, more involved, arguments regarding control, scientism, and magical thinking. Those readers who are already familiar with the rhetorical tradition are urged to jump straight to Chapter 2. It is here that I review the different ways in which marketing scholars have already engaged with aspects of rhetoric. For in linking rhetoric and marketing I am thankfully not starting ab initio. Even before Tonks’ (2002) clarion call for rhetoric to have a “central location in making sense of marketing management” (p. 806) there had been a growing weight of research investigating the part that traditional
rhetorical approaches to persuasion could have in explaining the power of textual and visual tactics in advertising and public relations (Bush and Boller, 1991; McQuarrie and Mick, 1992, 1996, 1999; Scott, 1994; Stern, 1988, 1990; Tom and Eves, 1999). This tradition has continued and broadened in recent years, with scholars such as Brown (2002, 2004, 2005, 2010), Hackley (2001, 2003) and myself (Miles, 2013, 2014a, 2014b) using rhetorical framings to discuss the ways in which marketing speaks about itself and how academics and practitioners use discourse to construct various aspects of what it means to be doing marketing. Chapter 2, therefore, brings us ‘up to date’ with the small but significant ‘rhetorical turn’ in marketing.
If, so far, marketing scholarship has not been overly receptive to arguments that it should be interpreted as an instantiation of rhetoric it is worth investigating just how it is that marketing does actually see itself. Chapter 3, therefore, begins by examining the foundation myths of marketing, looking at where scholars think the discipline comes from and how it has been thought to have developed in its formative years. Central to this examination is a consideration of the way that marketing has sought to define itself as a science and the sometimes quite vociferous debates that have flared up around this issue, particularly between those promoting a ‘relativistic’ interpretation of marketing truth and those supporting a far more empirical, ‘realist’ one. These debates are important for the stage that they set for my later analysis of the Sophistic character of the marketing enterprise, but they can also be analysed as attempts to run away from considering marketing’s true nature as a discipline of rhetorical control. This leads me directly to a discussion of the centrality of control in any consideration of marketing practice and theory. I start this discussion by tracing an alternative history of marketing in what Beniger (1986) has called the “crisis of control” (p. 219) accompanying the Industrial Revolution. I will argue that modern marketing developed as a technology of control designed to stimulate and direct consumer demand and that these origins have continued to direct its evolution, despite the manifold extensions and re-focussings that the practice and discipline have undergone in the following decades. Marketing’s ability to control consumption is dependent also upon the intermediary position of the marketing practitioner. The description of marketers as ‘middlemen’, though common in the late nineteenth and early twentieth century has largely fallen by the wayside. However, I will argue that the phrase holds an important key to the way in which the modern profession can be seen as reflecting a truly ancient dynamic. This is a cue for our first return to Plato and his dealings with early marketers (or retailers and traders) in order to worry away at the origins of this middle position of the marketer. Marketing historians have often reached for Plato when they have wished to underscore the esteemed history of the discipline, and I will consider the rhetorical ramifications for such an appeal. This will also serve as context for my oppositional reading of Plato’s description of marketing middle men which occurs in Chapter 4. Chapter 3 finishes with a consideration of marketing
scholarship’s unquenchable desire to increase its scope as far as possible and relates this to the issue of exchange, a concept which has been repeatedly put forward as the one motif which can unify all marketing thought.
Chapter 4 builds upon the discussion of exchange that finishes the previous chapter and uses it to present an initial conception of how marketing can be considered an instantiation of the rhetorical discipline. I begin by exploring the ramifications of understanding marketing as an attempt to control the flow of value. I adopt the idea of the marketer as an intermediary but also return to Plato’s discussion of the origins of the marketer in order to provide a detailed, Sophistic, oppositional reading of how the urmarketer functions in society. This allows me to offer an initial definition of marketing as rhetoric, a definition which is then qualified, expanded upon, and altered over the course of the chapter and its examination of the ways in which Plato deals with the infecting, liminal, dangerous presence of marketing in his ideal city-states. The chapter culminates with an argument, following Lanham (2006), for basing an understanding of marketing as rhetoric upon the provision of services to facilitate the exchange of attention.
Having argued for the broadly rhetorical nature of marketing, in Chapter 5 I make the case for considering marketing as particularly Sophistic. Once again, I return to Plato and the issue of the middle position of the marketer and demonstrate how that philosopher treated the Sophists in a very similar way—as infecting, dangerous outsiders who threatened the balance of society and the morals of those who composed it. On this basis I examine the legacy of Sophism, asking what made it unique as a rhetorical approach and what made it so threatening to Plato and Aristotle. This leads to a discussion of the way in which marketers are seen in modern society, and how the sorts of accusations and negative sentiment that are routinely thrown at marketing are similar to the ways in which Plato and his philosophical descendants saw both the marketers of their time and the Sophists. I argue that the reason for this similarity comes down to the fact that marketers (both ancient and modern) and Sophists were both performing very similar roles in society based upon controlling attention and the appreciation of value. Finally, I consider the question of why, if the links between rhetoric and marketing are so clear, has there been so little effort made by scholars of rhetoric to engage with marketing?
Much of Chapters 4 and 5 is concerned with the consequences of millennia of public and scholarly unease with marketing and rhetoric, with attempts to control others for commercial, political, or personal gain. A lot of this unease comes from the ways in which rhetoric and marketing remind people of magic. Magic is also about controlling people and things, destiny and luck. And it has a significant part to play in the practice of early rhetoric, particularly Sophistic rhetoric. There are, also, very close connections between marketing and magic, both in terms of the ways that consumers think of products and consumption and the ways that scholars outside marketing have occasionally attempted to explain its power and purpose. The next three chapters of the book deal with how magic, rhetoric, and
marketing come together. Firstly, Chapter 6 reviews the Western scholarly engagement with magic, the way that it has been defined around attempts at control, and the importance of language in our understandings of what it is. This then allows us to move on in Chapter 7 to a detailed consideration of how the Sophistic approach to language was one based upon a consideration of the magical power of speech. This chapter argues that the deep roots of early rhetoric in ritual and magical performative language constituted a significant part of the threat seen by Plato and Aristotle in the Sophists’ teachings and public demonstrations. Consequently, much of the systematisation of rhetoric, its bureaucratisation, can be seen as a series of attempts to expunge magic (as conveyed in ritual patternings, highly figurative language, vivid imagery) from public disputation. Although the ‘magical’ aspect of rhetoric never truly disappeared, authorities concerned with managing political, legal, and ceremonial disputation and declamation have often tended to take serious measures to keep it on the outside of the establishment. I argue that the practice of marketing can be seen as the last refuge of the magical roots of magic, and it marks, ironically, a (qualified) triumph after many millennia of marginalisation of this tradition. Chapter 8 then considers a number of instances in non-marketing and marketing scholarship where marketing or consumption have been identified with magic or sorcery. Examining the work of Williams (1980), Williamson (2002) and Jhally (1989), amongst a number of others, I argue that scholars working outside the marketing academy have often used the accusation of magical practice against marketing as a way of damning it, or publicly shaming it and the capitalist system that they argue utilises it to spread a glamour in front of the reality of the production and consumption process. As a counter to this, I also examine the consumer culture theory literature that seeks to uncover the magical thinking behind consumption experiences. I argue that as insightful as it is, this strand of marketing scholarship turns away from any real engagement with the magical nature of marketing itself, rhetorically positioning the consumer as the only agent in the creation of consumption magic. While it, therefore, recognises the continuing importance of magic in the modern market, it tells only half of the story. Instead, if we examine the relationship between magic, rhetoric, and marketing, we can fully appreciate the position of the marketer as both magician and rhetor.
The final chapter of the book, Chapter 9, returns to the establishment of a Sophistic understanding of marketing, and works towards presenting an improved version of the definition of marketing originally presented in Chapter 4. The chapter revisits and deepens major themes from the previous chapters in order to arrive at a more rounded conception of marketing as rhetoric. It considers the value of relativism, improvisation, magical thinking, and an agonistic perspective in understanding what makes marketing powerful, desirable, and unique. It also argues that, without a recognition of the centrality of control to what marketing does, a full understanding of marketing’s place in society will be always out of reach.
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A History of Rhetoric for Marketers
This chapter provides a grounding in the history of rhetoric so that the reader can later be brought to an understanding of exactly how modern marketing (both its theory and practice) represents the most sophisticated, influential, and articulated flourishing of the rhetorical tradition. The fact that, by and large, both marketing and modern rhetorical studies do not recognise this connection can be argued to be a, rather ironic, function of marketing’s own rhetorical success. In order to lay out the case for this position, we will initially have to concern ourselves with definitions of rhetoric and an overview of its history. In looking at how rhetoric has evolved over time we can develop some appreciation of how its practice, purpose, and public status have altered in response to changes in society and culture. In particular, I wish to emphasise the ways that rhetoric has been expected to be used professionally—for what purposes and by whom has rhetoric been employed?
In constructing this history, I have tried to write it from the perspective of the key concepts that develop around the art of persuasion. While this means that I will inevitably have to cover some historical material, to give an idea of how certain concepts became popular or unpopular and to trace the evolution of the discipline, I will be trying to present this historical material in a way that is grounded as much as possible in considerations of the main rhetorical concepts that will be important for the reader’s full appreciation of the later arguments that I will be constructing regarding the relationship between marketing and rhetoric. The marketing scholarship on rhetoric, which I will be examining in detail in Chapter 2, has generally not attempted to provide readers with an understanding of the historical development of rhetoric. Journal articles tend to quickly fill in some sense of Aristotle’s legacy in the systematisation of rhetoric and then move on to the more important business of finding rhetoric in marketing communication executions or interpreting marketing writing in the light of narrow definitions. It is, therefore, important in a book that intends to argue that marketing is fundamentally and completely rhetorical that a wider, more detailed overview of the long development of thinking around Western rhetoric is provided for the reader. What follows, however, is just that—an overview designed to sketch out some aspects of the evolution of the field and provide the interested reader with some jumping off points for their own further
reading. The reader who is well versed in the rhetorical tradition might skip ahead to Chapter 2, where I examine the ways in which this tradition has been applied in marketing scholarship.
Western rhetoric was born in ancient Greece, though the exact nature of its origins is shrouded in obscurity and argument (perhaps not unfittingly). The discipline does have its oft-repeated foundation myth, however, and this identifies the inventors of rhetoric as Corax and Tisias, who are alleged to have authored a treatise on the art of public speaking around 476 BCE in the city-state of Syracuse (in what we now call Sicily). Syracuse had recently transformed from a tyranny to a democracy and, as a result, many private citizens found that they had to represent themselves in claims to recover land that the earlier tyrants had stolen from them (Kennedy, 1994; Murphy et al., 2014). Corax and Tisias, so the story goes, sought to take advantage of the great demand for instruction in persuasive discourse that attended this flourishing of litigation. This timely exploitation of a marketing niche brought them to produce the first codification of the techne (or art) of persuasive oratory (though this work is now lost to us). Tisias was the pupil of Corax, and it is this relationship that provides the frame for perhaps the most famous story regarding the Sicilian pair to come down to us. It is said that Corax sued Tisias for unpaid tuition fees. Corax’s argument was that Tisias will inevitably pay, for if he won then the court must judge his education to be successful and thus worthy of payment, whereas if he lost the court would force Tisias to pay anyway. Of course, Tisias used exactly the same argument to argue for his own success—the court could not expect him to pay if he lost to Corax for that would prove that Corax’s own teaching was useless. The court is thought to have given up and walked away from the whole mess. The move towards democracy in Athens meant that similar opportunities were available in the significantly larger and more influential market there. The courts of Athens in the fifth century BCE were boisterous affairs. With no judges or lawyers, prosecuting and defending parties had to convince a jury of at least 201 members (often significantly more) of the truth of their arguments. This meant that everything hinged upon the effectiveness of speeches and, as a consequence, the demand for custom-written addresses to the court provided by a logographos was intense. At the same time, political decisions in Athens were made in a similar way. Radical democracy meant that any Athenian citizen could speak in the assembly, but in practice the power to influence the assembly lay in the hands of effective speakers who “represented the views of shifting factions within the state” (Kennedy, 1994, p. 16). Such speakers, sometimes called demagogues, could stir the assembly to ill-considered decisions that often might go against the long-term interests of the city-state.
The Sophists and the Birth of Rhetoric
It is in this environment that the thinkers we now know as the Sophists flourished (their name coming from the Greek for ‘wise’, sophos). Murphy
et al. (2014) note that “while the term applied originally to any wise person, it soon came to denote those who engaged in the art of rhetoric in the courts, the legislature, and/or the public forum” (p. 28). Sophists might earn their living from the teaching of argumentation, the writing of speeches for others, or from the public display of their oratorical skills. Now, all three of these vocational directions will lead at some point to the Sophist having to construct an effective argument for a case that might be called (to use Aristotle’s terminology) the weaker. So, a speechwriter will compose a plea for a client whose case might be full of holes, a teacher might build an exemplary argument for a patently absurd case in order to teach the use of particular tropes and strategies, and an orator who lives on the generosity of the crowd will sometimes seek to display his admirable skills in ways that are greatly entertaining precisely because they clearly make the weaker case the stronger. Modern marketers are, of course, familiar with the pressures; sometimes the realities of the profession mean that marketing skills are used to valorise a shoddy product or weak brand. Your campaign can still win a Cleo even if it is for a nutritionally suspect soft drink that others are convinced contributes to teen obesity levels. Indeed, in the same way that modern marketing is routinely lambasted for being at the root of a host of social ills (Critser, 2003; Chomsky, 2012; Klein, 2009; Malkan, 2007; Moss, 2013; Schlosser, 2002), the Sophists attracted a reputation for a dangerous lack of consideration towards the truth and for being concerned with victory in argument at any cost (called eristic argument). The nature of Sophistic argument and how it relates to what will later flower into the discipline of rhetoric is important to my thesis linking rhetoric and marketing, so I will spend a little time delineating the principal perspectives that surround it and we will return to it in later sections.
Much of the way that Sophistic practice is now understood has come down to us from the discourse of those who have sought to attack it. In particular, the works of Plato and Aristotle have powerfully influenced later understanding of the Sophists, tainting them with the “stigma of deception” (Tindale, 2004, p. 40). Platonic dialogues such as Euthydemus, Gorgias, Hippias Major, and Protagoras characterise their eponymous Sophists as unconcerned with objective or ultimate truth (aletheia), instead focused upon the importance of opinion (doxa) and how it can be swayed by appeal to an audience’s sense of what is most likely or probable (eikos). For Plato, such an approach is diametrically opposed to his own project of finding the truth of the good life because it leads to a mercenary style of relativism. The root of Sophistic eikos can be found in Protagoras ‘measure maxim’. Protagoras (484–411 BCE), along with Gorgias, is the most famous of the Sophists and was the first to settle in Athens. His ‘measure maxim’ asserts that “man is the measure of all things, of things that are as to how they are, and of things that are not as to how they are not” (quoted in Murphy et al., 2014, p. 31). The meaning here is that man cannot perceive the truth behind appearances; all we can do is to pay attention to our own subjective
A History of Rhetoric for Marketers
experiences, to the way that things seem to us. Consequently, it follows that in deciding upon any issue we should ask ourselves ‘what is the more probable’? In doing so, each of us will look upon our own experience and make a judgement. Such a position was not just antithetical to Plato, of course. Many aspects of Athenian culture assumed the existence of absolute truths and the “rampant individualism” (ibid.) displayed in the teaching of the Sophists (almost every one of them metics, or foreign-born immigrants to Athens) generated much anxiety in the city-state while at the same time contributing “to a more pluralistic and tolerant society than would exist at any other time in Greece” (Smith, 2003, p. 47).
One of the most obvious methodological differences between the Sophists and Plato is the former’s focus on public argument, often instantiated in lengthy speeches, which contrasts with the latter’s belief in “interior reasoning” (Tindale, 2010, p. 33). Disputing in public meant that Sophists relied upon the audience. This meant, from Plato’s perspective, that they cared “not for truth but only for persuading their audience” (ibid.). The Socratic elenchus (the question and answer pattern Plato has Socrates use in the dialogues) is far better suited to intimate argumentation between a few friends. It is also more adapted to the hunting down of small detail around specialised aspects of topics. The long speeches that were the Sophists’ tool in trade were primarily concerned with portraying the bigger picture, the wide sweep of a topic, in order to win over a large audience. Perhaps the most famous example of the power of Sophistic speech-making is Gorgias’ Encomium to Helen. Gorgias represents the final important element in Sophistic style and that is the power of poetic oratory. The Encomium provides four reasons why Helen should be considered blameless in the events surrounding her kidnapping by Paris. By Gorgias’ time, Helen’s part in the horror of the Trojan War had been much mulled over by generations of poets, playwrights, and philosophers and one’s view of her guilt or innocence was a litmus test for where one stood “in the emerging Greek sense of morality” (Murphy et al., 2014, p. 233). The Encomium is famous for two reasons. Firstly, it is a clear application of Gorgias’ poetic style to argumentative purposes—Gorgias plays with patterns of length, rhyme, and sound throughout the piece to great effect. Secondly, it contains a description of how Gorgias saw the operation of persuasion through the power of words that has become canonical in regard to the practice of rhetoric. In the Encomium Gorgias considers four reasons as to why Helen voyaged to Troy (abandoning Sparta and her husband, Menelaus). The third possibility, and the one that he spends the most time considering, is that “speech persuaded her, and deceived her soul” (ibid., p. 234). For Gorgias, speech (logos) “is a powerful lord” that can alter the “opinion of the soul” as if by the arts of witchcraft or magic”. The persuader is therefore a “user of force” and can rely upon the power of speech as having “the same effect on the condition of the soul as the application of drugs to the state of bodies” (ibid.). As Conley (1990) remarks, this means that “the relationship between speaker and audience is, so to speak, ‘asymmetric’ as
it is the speaker who casts a spell over the audience and not the other way around” (p. 6). In addition, we should note that Gorgias’ Encomium is itself an example of the power of logos to bewitch—it “both pays homage to the power of logos to create impressions and at the same time uses it to do so” (Tindale, 2004, p. 47). It advertises the power of which it speaks through its continuing power to enchant even in the twenty-first century.
I will be giving the Sophists significantly more attention in later stages of this study. Their legacy is, I will argue, central to a nuanced understanding of the rhetorical and magical nature of marketing. For now, though, we need to move on to consider the way in which competing and later Greek philosophers reacted to Sophistic rhetoric by constructing a systematised, bounded approach to persuasive argumentation that sought to cleanse public discourse of some of the more apparently irrational and dangerous aspects of Sophistic practice.
Plato and Anti-Rhetoric
It is no wonder that, despite their moral relativism and sceptical perspectives, Sophists such as Gorgias, Protagoras, Antiphon and Isocrates had such tremendous influence over the education of Athenian youth. Their emphasis on the cultivation of effective, persuasive speech had great practical value in the radical democracy of Athens. They were also very much part of the market—the sold their skills as teachers, speechwriters, speech-makers, and authors of teaching texts. Plato, who spent so much time across his dialogues attempting to ridicule and undermine the Sophist tradition, was certainly not a speech-maker. For him, the end of discourse was the philosophical discovery of absolute truth. The fact that we now use the word ‘sophistry’ in an entirely pejorative way to describe deceptive, fallacious arguments is in no little degree due to the influential early characterisations of Sophistic discourse provided by Plato. The speech-making of the Sophists was seen by Plato as trapped in the material world, the world of appearance and opinion, and as such was incapable of reaching the absolute truth that lies behind the senses. Plato “established dichotomies that the Sophists rejected: inquiry is preferred to persuasion; reason is preferred to emotion; one-on-one communication is preferred to mass persuasion” (Smith, 2003, p. 57). We shall see these tensions repeat themselves throughout the current study—they are not ancient matters far removed from our modern lives but instead sit at the heart of contemporary marketing thinking (as well as public reactions to it). Plato was suspicious of rhetoric and poetry precisely because he was suspicious of the audience. Unlike the Sophists, who thrived upon the challenges of an audience-led civic life in democratic Athens, Plato was no supporter of the crowd. His conception of the ideal state as outlined in the Laws and the Republic has the public audience “slotted into well-defined positions and not allowed to defy the philosopher king” (Smith, 2003, p. 59). If rhetoric was to be used, then it was to be restricted to ensuring the “consent of the governed
History of Rhetoric
by the governors” (ibid.). For Plato, the fact that Sophists were willing to teach all citizens the means of securing adherence to their position was not only a reckless and irresponsible abandonment of intellectual duty but it was also based upon an incorrect understanding of what the duty of a citizen should be. Perhaps one of the most fundamental problems that Plato had with the Sophist approach to logos is that it fosters a power asymmetry in discourse. This might be ironic in a broader sense, when we consider that Plato envisaged a state where each citizen had an allotted place and was led to knowledge of absolute truth (and hence the good life) by the forces of the philosopher king. However, in regard to the methodology of argumentation, Plato’s position is quite clearly concerned with equality between disputants. In Gorgias, Plato argues that the rhetor is successful only because he is talking to those who are ignorant of the matters in hand. While it might be true, as his interlocutor Gorgias contends, that a good rhetor could persuade a patient to accept a course of treatment far more effectively than a doctor might, this is only because the patient is ignorant and therefore will be swayed by the language tricks of the rhetor. Conversely, the rhetor has no power to convince the doctor regarding medical topics. The Sophist takes advantage of the ignorance of his audience, while the philosopher (i.e. one schooled in the methodology of Socrates) seeks to lead his interlocutor through a dialectic that will uncover for both of them the real truth. Similarly, in the Phaedrus Plato describes the way in which Sophistic logos can seduce the young (represented by the titular character) by aping the tricks of the Sophistic rhetor Lysias and bewitching Phaedrus with his speech on love only to point out that he has been successful through a use of linguistic and argumentative manipulation. As an antidote to this, Plato has Socrates expound upon the real art of rhetoric—by which, of course, he means a philosophical rhetoric that is anchored in, and convinces because of, the true knowledge of that which the rhetor speaks.
Perhaps the biggest irony regarding Plato’s position on rhetoric is that, while ridiculing the Sophists’ reliance upon the persuasive power of logos, he is such a masterful user of these techniques himself. Indeed, while Plato clearly has many important issues with Sophism, there is one area in which their methodology remains fundamental to Plato’s project. As Corey (2015) notes, the Sophists are adept at producing wonder, “of awakening interlocutors from their dogmatic slumber” (p. 231). While he might disagree with the Sophist approach to truth, Plato recognises that words have to be used in order to bring an audience, even if it is an intimate audience, to a realization that their common-sense views of the world need to be questioned, that what they thought to be true might not really make any sense. And it is this realization that can be “the starting point for philosophy” (ibid.).
Aristotle and the Art of Rhetoric
Plato’s Academy continued to exist and be influential in Athens (and so in Greek scholarship) for hundreds of years after his death. The Sophists
A History of Rhetoric for Marketers 15
left no comparable institution behind and their works have been largely lost to history. Consequently, Plato’s handling of the Sophists has (until comparatively recently) tended to be the one that has formed the accepted interpretation of the Sophists and their early approaches to rhetoric. However, in regard to the broader subject of rhetoric itself it certainly cannot be said that Plato’s view carried the day. His pupil, Aristotle, had a much more enthusiastic and nuanced understanding of the importance of rhetoric recognising it as an art “crucial for human survival” (Smith, 2003, p. 71). His work, On Rhetoric, quietly restores much of the Sophist thinking on the use of arguments of probability in persuasive civic discourse as well as powerfully establishing the contingent nature of argumentation. It also does an awful lot more, acting as a nexus (and testing ground) for much of Aristotle’s previous thinking on logic, psychology, civic duty, and morality. As a consequence, the work is a considerably complex one and in its taxonomic structure it is less clear and all-encompassing than many of Aristotle’s other works. As Murphy et al. (2014) note, this suggests that “rhetoric deals with human inter-relationships involving so many variables that not even an Aristotle can devise a ‘system’ to describe it scientifically” (p. 62). Despite this complexity, On Rhetoric has served directly or indirectly as the model for mainstream Western rhetorical studies to this day. It contains a number of concepts and distinctions that will be essential to my later arguments and expositions, so I will introduce these now.
The Genres (Eide) of Rhetoric
While rhetoric is the “detection of the persuasive aspects of each matter” (Aristotle, 1991, p. 70) and its “technical competence is not connected with any special, delimited kind of matter (p. 74), Aristotle makes it clear that there are three main areas of life in which rhetoric plays a fundamental part: the law courts (forensic rhetoric), political assemblies (deliberative rhetoric), and ceremonies (epideictic rhetoric). Each of these environments calls for a particular genre of rhetoric, with each genre having its own objective and temporal emphasis. So, forensic rhetoric focuses on the past (what has happened) and tries to prosecute or defend, deliberative rhetoric tries to urge or deter and is concerned with the future (what shall be done), while epideictic rhetoric (sometimes translated as rhetoric of ‘display’, or ‘demonstrative’ rhetoric) focuses on the present and attempts to praise or blame. As we shall see later, this typology is perhaps a little artificial—much political argument has always focused on what the opposition has done in the past, for example. However, I should note here that the inclusion of epideictic rhetoric is important for us as marketers as it covers the persuasion of an audience who are considering the worth of someone or something. Aristotle was concerned to describe rhetoric as a techne—a body of knowledge that has clear bounds and clear applications. Plato had argued that rhetoric was no such thing as it had no knowledge in and of itself but rather depended
A History
upon the lack of knowledge in its audience. Aristotle’s consideration of the types of rhetoric is part of his argument that the discipline has clear bounds of concern, and strategies for approaching the engineering of how an audience should value something are very much within those bounds. As I will elaborate upon below, when considering the relationship between rhetoric and marketing, the place of epideictic discourse is central.
The Proofs
Another way in which Aristotle frames rhetoric as a techne is through the establishment of the proofs as the basic concerns of the art of rhetoric. There are certain kinds of proof which are not to be contained within the art and these are the ones “that are not contrived by us” and therefore require no invention on our behalf, only exploitation. Examples of these proofs are witness statements, confessions under torture, contract agreements, etc. The proofs that are the concern of rhetoric are the “artistic” proofs, which are “furnished through the speech” (ibid.). These can be divided into three types: proofs that “reside in the character of the speaker” (ethos), proofs that are dependent upon “a certain disposition of the audience” (pathos), and proofs which are located “in the speech itself” (logos). The three forms of rhetorical proof are not meant to be mutually exclusive and a speech might use all three with each coming to the fore at various moments.
The Primacy of the Audience
The three artistic proofs clearly highlight the way in which Aristotle’s conception of rhetoric is based upon an interactive relationship with the audience. Arguments from ethos work because a speaker has discerned what personal qualities a particular audience will value and therefore makes an effort to demonstrate (or simply claim the ownership) of such qualities in their speech. The same ethos arguments will not work for every audience— for some audiences, in some situations, making a point of your Harvard degree at the start of your speech might make your words appear more trustworthy, while for other audiences in other situations it might instead cast suspicion on your motivations or your character. Similarly, arguments from pathos depend upon a careful reading of a particular audience to determine which emotions its members might be more easily led to and, from those, which emotions would be more useful in generating a sympathetic reception to the rest of your argument. Much of On Rhetoric is devoted to a description of different emotions, their antecedents, and the rhetorical uses that they can be put to when addressing different groups of people. For Aristotle, rhetorical persuasiveness is contingent upon a careful, strategic consideration of the audience to be addressed. His rhetoric is a ‘market-oriented’ one, we might say. Certainly, On Rhetoric plainly elevates audience research and insight to an essential component of the rhetorical enterprise. Related to
this is the topic of kairos (often translated as ‘timeliness’), which is an idea that informs much Sophistic rhetoric. As Kinneavy and Eskin (2000) note, Aristotle’s understanding of rhetoric places a high regard on “situational context” (p. 439), on knowing what type of argument, what metaphor, what stylistic device is appropriate at a particular moment. This almost improvisatory aspect of rhetoric is something that I will return to in later discussions of interactivity and marketing strategy.
The Tools of Rhetorical Argumentation
As well as decisions regarding the appropriate choice of rhetorical genres and proofs, the successful speaker must master the effective use of what Conley (1990) calls the “instruments of demonstration” (p. 15)—the enthymeme and the example. These are the substance of the proofs of logos and, given that they are used to demonstrate, or appear to demonstrate, they establish the link between rhetoric and the more formal dialectic. So, the enthymeme is the rhetorical equivalent of a deductive syllogism, while the example (or paradigm) is the rhetorical version of logical induction. Importantly, both rhetorical instruments work on what the audience knows (or will accept) as probable or likely. The syllogism is a way to universal truth, whereas the enthymeme is a way to a particular audience’s acceptance of what is likely. In form, the enthymeme is a truncated syllogism because it relies upon the audience to supply one of the premises. The speaker, therefore, does not have to set out all the premises but can compress his logic, taking advantage of the ‘common sense’ of the audience to fill the gaps. The most compressed form of enthymeme is the maxim that is really the conclusion from a syllogism without any accompanying premises. Aristotle warned that maxims work persuasively only if the speaker judges the prejudices of the audience well—but when they do work they can build a strong rapport with the audience due to the evident sharing of ‘common sense’ that they demonstrate. On Rhetoric provides a long list of common lines of enthymemetic argument, or topoi, so that speakers could pick and choose the most appropriate for their particular purposes. Aristotle also demonstrates a number of fallacious enthymemes that should be avoided by those who wish to succeed in rhetoric and which should be attacked if apparent in an interlocutor’s arguments.
The Place of Style
The last two sections of On Rhetoric deal with style and composition. As we have seen, these are topics which were much valued in Sophist rhetorical education, although Aristotle’s treatment of them is quite individual. For a start, Aristotle comments that if he were simply writing about what is appropriate in rhetoric he would leave the subject of style well alone, “but since the entire enterprise connected with rhetoric has to do with opinion, we must carry out the study of style not in that it is appropriate but in
A History of Rhetoric for Marketers
that it is necessary” (Aristotle, 1991, p. 216). It is necessary “because of the baseness of the audience” (p. 217). People are moved by words and their patterning and as the aim of rhetoric is to move an audience towards a particular acceptance of a position, it makes sense to study this adjunct to argumentation. One can certainly detect in Aristotle something that looks like embarrassment here, and he is at pains to make it clear that the sort of style he is talking about is certainly not the artificial, overly poetic one that Plato ridiculed in the Sophists. For Aristotle, style must be always appropriate and clear, giving the “impression of speaking not artificially but naturally” (p. 218). At the same time, one of the purposes of style is to draw attention to the speech, to make it “sound exotic; for men are admirers of what is distant, and what is admired is pleasant” (ibid.). The principal stylistic figure that Aristotle expounds upon in On Rhetoric is the metaphor, which is useful to the persuasiveness of a speech because, as well as bringing “clarity, pleasantness, and unfamiliarity” (p. 219), it serves to make the “inanimate animate” and infuse vividness and actuality into the terms of an argument. In general, across all the figures and patterns that Aristotle discusses, his key advice is the use of proportion and appropriateness. Word and figure choice should be a strategic matter of balance—one’s metaphors must be clear but unfamiliar, one’s words must be exotic yet simple, one’s rhythm should be pleasing to the ear yet restrained. It is not hard to feel the cautionary spectre of Gorgias being invoked through such admonishments. Certainly, later authors (particularly of the Roman school) will pay a lot more attention to the myriad detail of stylistic figurations than Aristotle does. This also applies to the subject of speech organization. Aristotle initially states that the only structure a speech really needs to have is a presentation (where one states the subject matter) and a proof (where one demonstrates it). However, as if seemingly embarrassed by this excessive simplicity in the face of so many other teachers of rhetoric making of organization such a complicated and involved topic, Aristotle concedes that, although “these [divisions] are the proper ones”, “the maximum number are introduction, presentation, proof, and epilogue” (p. 246). We will consider the matter of rhetorical organization in a little more depth when discussing Cicero.
The Influence of Aristotle
Aristotle’s On Rhetoric is today a fixture of many introductory speech and writing units on US university curricula, helping to ensure that the distinctions between ethos, logos, and pathos, as well as concepts such as the enthymeme and the three genres serve, as a foundation for the consideration of persuasive speech and writing in the English-speaking world (Gaines, 2000). However, the text itself has not enjoyed an unbroken tenure as the epitome of rhetorical system-making across the centuries. Conley (1990) states that “the Rhetoric failed to exercise much influence in the centuries after Aristotle’s death” (p. 17), having mostly indirect impact upon the works
History
of Cicero and Quintilian during the Roman period which became so influential into the Middle Ages and the Renaissance. Smith (2003), however, notes that “most of the theory that comes after him extends what Aristotle had to say; in very few cases are wholly new conceptualizations developed” (p. 106). The translation of On Rhetoric into Latin in the thirteenth century did little to immediately spark a return to Aristotelian fundamentals, despite enthusiastic recommendation from Roger Bacon. It was only with the sixteenth century that debate around the ideas in Aristotle’s text began to make it central to the European understanding of speech and persuasion.
Isocrates and the Improving Power of Logos
Before moving on to discuss the rhetoric of the Roman era, we should briefly consider the figure of Isocrates, who ran his school at the same time as Aristotle set up his own Lyceum. Isocrates can best be seen as Aristotle’s main competitor in the provision of education in Athens. He believed in a balanced approach to education, the paideia, and his inclusion of gymnastics, science, philosophy, mathematics, and rhetoric in his curriculum has served as an influential model for general education ever since. For Isocrates, the act of rhetoric was “the final phase of a total process of personal growth and development” (Murphy et al., 2014, p. 52). Learning how to speak more effectively in public is something that for Isocrates will significantly aid in a man’s social standing and his own character, for “the stronger a person desires to persuade hearers, the more he will work to be honourable and good and to have a good reputation among the citizens” (quoted in Kennedy, 1994, p. 47). This improving power of rhetoric was encouraged by Isocrates through the study and copying of speeches that he had composed on virtuous subjects. He reasoned that the more one considered and argued for the virtues, the more one would become virtuous. Chief amongst the virtuous topics that Isocrates composed essays upon was the cause of Panhellenism, an idea which offered to bring together all of the Greek feuding city-states. Isocrates locates the practice of persuasive logos firmly within a frame of idealised civic duty. In this sense, Conley (1990) argues that he “tried to bridge the gap between morality and technical skill that had been created by his sophistic predecessors and Plato alike” (p. 18). Alongside his general impact upon the development of education, Isocrates’ teachings had a definite influence upon the early Roman conception of rhetoric, particularly through his focus on kairos, his ornate style, and impressive use of amplifications (or makrologia, where sentences are prolonged in various ways in order to underline the importance of particular words).
Stasis and the Orator-Leader
Roman rhetoric is characterised by the presentation of “highly specific, pragmatic systems” of oration (Murphy et al., 2014, p. 111). In this sense,
it is influenced by the tradition of rhetorical handbooks that flourished throughout the times of Plato and Aristotle. Most of these handbooks have not survived, though a few of the more influential, such as the Rhetorica ad Alexandrum, have. However, their decidedly practical orientation formed the model for the works of Cicero and Quintilian as well as the anonymous Rhetorica ad Herennium, which became the first work to attempt to create an exhaustive listing of the rhetorical figures and which became the basis of rhetorical education well into the sixteenth century.
It is interesting to note that, as Athens turned from being a radical democracy towards more tyrannical forms of government, so the necessity for public displays of deliberative (political) rhetoric diminished. In the Hellenistic period, it was in the law courts that most rhetoric happened and, as was natural given the move away from democracy, the arbiter who was to be persuaded became not a large group of citizens but a very small number of judges. Not surprisingly, therefore, the next significant innovation in rhetoric comes from a re-consideration of the demands of forensic rhetoric. Hermagoras’ theory of stasis (c. 150 BCE) had a great effect upon the early Roman rhetoricians, particularly Cicero, with whom the term is most closely associated in modern times, and the author of the Rhetorica ad Herennium.
Stasis, meaning ‘stance’, refers in rhetorical theory to “the stand taken by a speaker toward an opponent” (Kennedy, 1994, p. 98) and concerns the ability to locate the “relevant points at issue in a dispute and to discover the applicable arguments drawn from the appropriate ‘places” (Conley, 1990, p. 32). Stasis theory essentially comes down to walking through a series of questions to determine what is the best defence in any particular case. These questions relate to issues of fact, definition, justification, quality (including mitigating circumstances), jurisdiction, and procedure (Smith, 2003; Murphy et al., 2014).
Any fan of modern police procedurals or court room dramas will be familiar with the arguments that result from a consideration of the stasis system; “as the records of his ankle tracker clearly show, my client was in Texas at the time of the murder in New York” (an issue of fact), “yes, my client stabbed the deceased but she did it in the heat of the moment and therefore this is not a malicious, premeditated murder” (and issue of definition), “while it is true that Dr. White administered the fatal dose of morphine to the President, he did this in order to save the whole country from entering an unjust and illegal war that would have claimed the lives of thousands of our armed forces personnel” (an issue of justification), “my client ran the red light, it is true, but having just failed his PhD viva he was in no fit mental state to consider the rules of the road and he throws himself upon your mercy” (an issue of quality), “my client is a sovereign citizen of the Oceanic state of Linux and does not recognise the authority of this court in matters relating to taxation” (an issue of jurisdiction), “my client was not read her Miranda rights at the time of arrest and so was held illegally” (an issue of procedure).
Another random document with no related content on Scribd:
mean solar days, or about 365¼ of the average interval which elapses between noon and noon, that is, between the times when the sun is highest in the heavens. Our year is made to consist of 365 days, and the odd quarter is allowed for by adding one day to every fourth year, which gives what we call leap-year This is the same as adding ¼ of a day to each year, and is rather too much, since the excess of the year above 365 days is not ·25 but ·24224 of a day The difference is ·00776 of a day, which is the quantity by which our average year is too long. This amounts to a day in about 128 years, or to about 3 days in 4 centuries. The error is corrected by allowing only one out of four of the years which close the centuries to be leap-years. Thus, . . 1800 and 1900 are not leap-years, but 2000 is so.
213. The day is therefore the first measure obtained, and is divided into 24 parts or hours, each of which is divided into 60 parts or minutes, and each of these again into 60 parts or seconds. One second, marked thus, 1″,[33] is therefore the 86400ᵗʰ part of a day, and the following is the
MEASURE OF TIME.[34]
60 seconds are 1 minute 1
214. The second having been obtained, a pendulum can be constructed which shall, when put in motion, perform one vibration in exactly one second, in the latitude of Greenwich.[35] If we were inventing measures, it would be convenient to call the length of this pendulum a yard, and make it the standard of all our measures of length. But as there is a yard already established, it will do equally well to tell the length of the pendulum in yards. It was found by commissioners appointed for the purpose, that this pendulum in London was 39·1393 inches, or about one yard, three inches, and ⁵/₃₆ of an inch. The following is the division of the yard.
MEASURES OF LENGTH.
The lowest measure is a barleycorn.[36]
3 barleycorns are 1 inch 1 in 12 inches 1 foot 1 ft.
3 feet 1 yard 1 yd.
5½ yards 1 pole 1 po.
40 poles or 220 yards 1 furlong 1 fur 8 furlongs or 1760 yards 1 mile 1 mi
Also
6 feet 1 fathom 1 fth. 69⅓ miles 1 degree 1 deg. or 1°.
A geographical mile is ¹/₆₀th of a degree, and three such miles are one nautical league.
In the measurement of cloth or linen the following are also used: 2¼ inches are 1 nail 1 nl.
4 nails
215. MEASURES OF SURFACE, OR SUPERFICIES.
All surfaces are measured by square inches, square feet, &c.; the square inch being a square whose side is an inch in length, and so on. The following measures may be deduced from the last, as will afterwards appear 144 square inches are
Thus, the acre contains 4840 square yards, which is ten times a square of 22 yards in length and breadth. This 22 yards is the length which land-surveyors’ chains are made to have, and the chain is divided into 100 links, each ·22 of a yard or 7·92 inches. An acre is then 10 square chains. It may also be noticed that a square whose side is 69⁴/₇ yards is nearly an acre, not exceeding it by ⅕ of a square foot.
216 MEASURES OF SOLIDITY OR CAPACITY [37]
Cubes are solids having the figure of dice. A cubic inch is a cube each of whose sides is an inch, and so on. 1728 cubic inches are 1 cubic foot 1 c ft 27 cubic feet 1 cubic yard 1
This measure is not much used, except in purely mathematical questions. In the measurements of different commodities various measures were used, which are now reduced, by act of parliament, to one.This is commonly called the imperial measure, and is as follows:
MEASURE OF LIQUIDS AND OF ALL DRY GOODS.
4 gills are 1 pint 1 pt. 2 pints 1 quart 1 qt. 4 quarts 1 gallon 1 gall 2 gallons 1 peck[38] 1 pk. 4 pecks 1 bushel 1 bu. 8 bushels 1 quarter 1 qr. 5 quarters 1 load 1 ld
The gallon in this measure is about 277·274 cubic inches; that is, very nearly 277¼ cubic inches.[39]
217. The smallest weight in use is the grain, which is thus determined.A vessel whose interior is a cubic inch, when filled with water,[40] has its weight increased by 252·458 grains. Of the grains so determined, 7000 are a pound averdupois, and 5760 a pound troy The first pound is always used, except in weighing precious metals and stones, and also medicines. It is divided as follows:
AVERDUPOIS WEIGHT
27¹¹/₃₂ grains are 1 dram 1 dr.
6 drams, or drachms 1 ounce[41] 1 oz.
16 ounces 1 pound 1 lb.
28 pounds 1 quarter 1 qr
4 quarters 1 hundred-weight 1 cwt
20 hundred-weight 1 ton 1 ton.
The pound averdupois contains 7000 grains. A cubic foot of water weighs 62·3210606 pounds averdupois, or 997·1369691 ounces.
For the precious metals and for medicines, the pound troy, containing 5760 grains, is used, but is differently divided in the two cases. The measures are as follow:
TROY WEIGHT
24 grains are 1 pennyweight 1 dwt. 20 pennyweights 1 ounce 1 oz. 12 ounces 1 pound 1 lb.
The pound troy contains 5760 grains. A cubic foot of water weighs 75·7374 pounds troy, or 908·8488 ounces.
APOTHECARIES’ WEIGHT.
20 grains are 1 scruple ℈ 3 scruples 1 dram ʒ 8 drams 1 ounce ℥ 12 ounces 1 pound lb
218. The standard coins of copper, silver, and gold, are,—the penny, which is 10⅔ drams of copper; the shilling, which weighs 3 pennyweights 15 grains, of which 3 parts out of 40 are alloy, and the rest pure silver; and the sovereign, weighing 5 pennyweights and 3¼ grains, of which 1 part out of 12 is copper, and the rest pure gold.
MEASURES OF MONEY.
The lowest coin is a farthing, which is marked thus, ¼, being one fourth of a penny
2 farthings are 1 halfpenny ½d 2 halfpence 1 penny 1d.
1 shilling 1s
20 shillings 1 pound[42] or sovereign £1
21 shillings 1 guinea. [43]
219. When any quantity is made up of several others, expressed in different units, such as £1. 14. 6, or 2cwt. 1qr. 3lbs., it is called a compound quantity. From these tables it is evident that any compound quantity of any substance can be measured in several different ways. For example, the sum of money which we call five pounds four shillings is also 104 shillings, or 1248 pence, or 4992 farthings. It is easy to reduce any quantity from one of these measurements to another; and the following examples will be sufficient to shew how to apply the same process, usually called R , to all sorts of quantities.
I. How many farthings are there in £18. 12. 6¾?[44]
Since there are 20 shillings in a pound, there are, in £18, 18 × 20, or 360 shillings; therefore, £18. 12 is 360 + 12, or 372 shillings. Since there are 12 pence in a shilling, in 372 shillings there are 372 × 12, or 4464 pence; and, therefore, in £18. 12. 6 there are 4464 + 6, or 4470 pence.
Since there are 4 farthings in a penny, in 4470 pence there are 4470 × 4, or 17880 farthings; and, therefore, in £18. 12. 6¾ there are 17880 + 3, or 17883 farthings. The whole of this process may be written as follows:
. 12 . 6¾
+ 3 = 17883
II. In 17883 farthings, how many pounds, shillings, pence, and farthings are there?
Since 17883, divided by 4, gives the quotient 4470, and the remainder 3, 17883 farthings are 4470 pence and 3 farthings (218).
Since 4470, divided by 12, gives the quotient 372, and the remainder 6, 4470 pence is 372 shillings and 6 pence.
Since 372, divided by 20, gives the quotient 18, and the remainder 12, 372 shillings is 18 pounds and 12 shillings.
Therefore, 17883 farthings is 4470¾d., which is 372s. 6¾d., which is £18. 12. 6¾.
The process may be written as follows:
A has £100. 4. 11½, and B has 64392 farthings. If A receive 1492 farthings, and B £1. 2. 3½, which will then have the most, and by how much?—Answer, A will have £33. 12. 3 more than B.
In the following table the quantities written opposite to each other are the same: each line furnishes two exercises.
£15 . 18 . 9½ 15302 farthings.
115ˡᵇˢ 1ᵒᶻ 8ᵈᵚᵗ 663072 grains.
3ˡᵇˢ 14ᵒᶻ 9ᵈʳ 1001 drams.
3ᵐ 149 yds 2ᶠᵗ 9 in
220. The same may be done where the number first expressed is fractional. For example, how many shillings and pence are there in ⁴/₁₅ of a pound? Now, ⁴/₁₅ of a pound is ⁴/₁₅ of 20 shillings; ⁴/₁₅ of 20 is 4 × 20 , or 4 × 4 (110), or 16 , 15 3 3 or (105) 5⅓ of a shilling. Again, ⅓ of a shilling is ⅓ of 12 pence, or 4 pence. Therefore, £⁴/₁₅ = 5s. 4d.
Also, ·23 of a day is ·23 × 24 in hours, or 5ʰ·52; and ·52 of an hour is ·52 × 60 in minutes, or 3ᵐ·2; and ·2 of a minute is ·2 × 60 in seconds, or 12ˢ; whence ·23 of a day is 5ʰ 31ᵐ 12ˢ.
Again, suppose it required to find what part of a pound 6s 8d is. Since 6s. 8d. is 80 pence, and since the whole pound contains 20 × 12 or 240 pence, 6s. 8d. is made by dividing the pound into 240 parts, and taking 80 of them. It is therefore £⁸⁰/₂₄₀ (107), but ⁸⁰/₂₄₀ = ⅓ (108); therefore, 6s. 8d. = £⅓
221, 222. I have thought it best to refer the mode of converting shillings, pence, and farthings into decimals of a pound to the Appendix (See Appendix On Decimal Money). I should strongly recommend the reader to make himself perfectly familiar with the modes given in that Appendix. To prevent the subsequent sections from being altered in their numbering, I have numbered this paragraph as above.
223. The rule of addition[46] of two compound quantities of the same sort will be evident from the following example. Suppose it required to add £192. 14. 2½ to £64. 13. 11¾. The sum of these two is the whole of that which arises from adding their several parts. Now
¾d. + ½d. = ⁵/₄d. = £0 . 0 . 1¼ (219)
11d. + 2d. = 13d. = 0 . 1 . 1
13s + 14s = 27s = 1 7 0
£64 + £192 = = 256 . 0 . 0
The sum of all of which is £257. 8 . 2¼
This may be done at once, and written as follows:
£192.14. 2½
64 13 11¾
£257. 8. 2¼
Begin by adding together the farthings, and reduce the result to pence and farthings. Set down the last only, carry the first to the line of pence, and add the pence in both lines to it. Reduce the sum to shillings and pence; set down the last only, and carry the first to the line of shillings, and so on. The same method must be followed when the quantities are of any other sort; and if the tables be kept in memory, the process will be easy
224. S is performed on the same principle as in (40), namely, that the difference of two quantities is not altered by adding the same quantity to both. Suppose it required to subtract £19 . 13. 10¾ from £24. 5. 7½. Write these quantities under one another thus:
£24. 5. 7½
19 13 10¾
Since ¾ cannot be taken from ½ or ²/₄, add 1d. to both quantities, which will not alter their difference; or, which is the same thing, add 4 farthings to the first, and 1d. to the second. The pence and farthings in the two lines then stand thus: 7⁶/₄d. and 11¾d. Now subtract ¾ from ⁶/₄, and the difference is ¾ which must be written under the farthings. Again, since 11d. cannot be subtracted from 7d., add 1s. to both quantities by adding 12d. to the first, and 1s. to the second. The pence in the first line are then 19, and in the second 11, and the difference is 8, which write under the pence. Since the shillings in the lower line were increased by 1, there are now 14s. in the lower, and 5s. in the upper one. Add 20s. to the upper and £1 to the lower line, and the subtraction of the shillings in the second from those in the first leaves 11s. Again, there are now £20 in the lower, and £24 in the upper line, the difference of which is £4; therefore the whole difference of the two sums is £4. 11. 8¾. If we write down the two sums with all the additions which have been made, the process will stand thus:
£24 . 25 . 19⁶/₄ 20 . 14 . 11¾
Difference £4 . 11 . 8¾
225. The same method may be applied to any of the quantities in the tables. The following is another example:
From 7 cwt. 2 qrs. 21 lbs. 14 oz. Subtract 2 cwt. 3 qrs. 27 lbs. 12 oz.
After alterations have been made similar to those in the last article, the question becomes: From 7 cwt 6 qrs 49 lbs 14 oz
Subtract 3 cwt 4 qrs 27 lbs 12 oz
The difference is 4 cwt. 2 qrs. 22 lbs. 2 oz.
In this example, and almost every other, the process may be a little shortened in the following way Here we do not subtract 27 lbs. from 21 lbs., which is impossible, but we increase 21 lbs. by 1 qr or 28 lbs. and then subtract 27 lbs. from the sum. It would be shorter, and lead to the same result, first to subtract 27 lbs. from 1 qr. or 28 lbs. and add the difference to 21 lbs.
226. EXERCISES.
A man has the following sums to receive: £193. 14. 11¼, £22. 0. 6¾, £6473. 0. 0, and £49. 14. 4½; and the following debts to pay: £200 19. 6¼, £305. 16. 11, £22, and £19. 6. 0½. How much will remain after paying the debts?
Answer, £6190. 7. 4¾.
There are four towns, in the order A, B, C, and D. If a man can go from A to B in 5ʰ 20ᵐ 33ˢ, from B to C in 6ʰ 49ᵐ 2ˢ and from A to D in 19ʰ 0ᵐ 17ˢ, how long will he be in going from B to D, and from C to D?
Answer, 13ʰ 39ᵐ 44ˢ, and 6ʰ 50ᵐ 42ˢ.
227. In order to perform the process of M , it must be recollected that, as in (52), if a quantity be divided into several parts, and each of these parts be multiplied by a number, and the products be added, the result is the same as would arise from multiplying the whole quantity by that number
It is required to multiply £7. 13. 6¼ by 13. The first quantity is made up of 7 pounds, 13 shillings, 6 pence, and 1 farthing. And
1 farth. × 13 is 13 farth. or £0 . 0 . 3¼ (219)
6 pence × 13 is 78 pence, or 0 . 6 . 6 13 shill × 13 is 169 shill or 8 9 0
7 pounds × 13 is 91 pounds, or 91 . 0 . 0
The sum of all these is £99 . 15 . 9¼
which is therefore £7. 13. 6¼ × 13.
This process is usually written as follows:
£ 7 . 13 . 6¼ 13
£99 . 15 . 9¼
228. D is performed upon the same principle as in (74), viz. that if a quantity be divided into any number of parts, and each part be divided by any number, the different quotients added together will make up the quotient of the whole quantity divided by that number. Suppose it required to divide £99. 15. 9¼ by 13. Since 99 divided by 13 gives the quotient 7, and the remainder 8, the quantity is made up of £13 × 7, or £91, and £8. 15. 9¼. The quotient of the first, 13 being the
divisor, is £7: it remains to find that of the second. Since £8 is 160s., £8 15. 9¼ is 175s. 9¼d., and 175 divided by 13 gives the quotient 13, and the remainder 6; that is, 175s. 9¼d. is made up of 169s. and 6s. 9¼d., the quotient of the first of which is 13s., and it remains to find that of the second. Since 6s. is 72d., 6s. 9¼d. is 81¼d., and 81 divided by 13 gives the quotient 6 and remainder 3; that is, 81¼d. is 78d. and 3¼d., of the first of which the quotient is 6d. Again, since 3d. is ¹²/₄, or 12 farthings, 3¼d. is 13 farthings, the quotient of which is 1 farthing, or ¼, without remainder. We have then divided £99. 15. 9¼ into four parts, each of which is divisible by 13, viz. £91, 169s., 78d., and 13 farthings; so that the thirteenth part of this quantity is £7. 13. 6¼. The whole process may be written down as follows; and the same sort of process may be applied to the exercises which follow:
Here, each of the numbers 99, 175, 81, and 13, is divided by 13 in the usual way, though the divisor is only written before the first of them.
EXERCISES.
2 cwt. 1 qr. 21 lbs. 7 oz. × 53 = 129 cwt. 1 qr. 16 lbs. 3 oz. 2ᵈ 4ʰ 3ᵐ 27ˢ × 109 = 236ᵈ 10ʰ 16ᵐ 3ˢ
£27 10 8 × 569 = £15666 9 4
£7 . 4 . 8 × 123 = £889 . 14
£166 × ₈/₃₃ = £40 . 4 . 10⁶/₃₃
£187 . 6 . 7 × ³/₁₀₀ = £5 . 12 . 4¾ ²/₂₅
4s 6½d × 1121 = £254 11 2½ 4s 4d × 4260 = 6s 6d × 2840
229. Suppose it required to find how many times 1s. 4¼d. is contained in £3. 19. 10¾. The way to do this is to find the number of farthings in each. By 219, in the first there are 65, and in the second 3835 farthings. Now, 3835 contains 65 59 times; and therefore the second quantity is 59 times as great as the first. In the case, however, of pounds, shillings, and pence, it would be best to use decimals of a pound, which will give a sufficiently exact answer Thus 1s. 4¼d. is £·067, and £3. 19. 10¾ is £3·994, and 3·994 divided by ·067 is 3994 by 67, or 59⁴¹/₆₇. This is an extreme case, for the smaller the divisor, the greater the effect of an error in a given place of decimals.
EXERCISES.
How many times does 6 cwt. 2 qrs. contain 1 qr. 14 lbs. 1 oz.? and 1ᵈ 2ʰ 0ᵐ 47ˢ contain 3ᵐ 46ˢ?
Answer, 17·30758 and 414·367257.
If 2 cwt. 3 qrs. 1 lb. cost £150. 13. 10, how much does 1 lb. cost?
Answer, 9s. 9d. ¹³/₃₀₉
A grocer mixes 2 cwt. 15 lbs. of sugar at 11d. per pound with 14 cwt. 3 lbs. at 5d. per pound. At how much per pound must he sell the mixture so as not to lose by mixing them?
Answer, 5d. ¾ ¹⁵³/₉₀₅
230. There is a convenient method of multiplication called P Suppose I ask, How much do 153 tons cost if each ton cost £2. 15. 7½? It is plain that if this sum be multiplied by 153, the product is the price of the whole. But this is also evident, that, if I buy 153 tons at £2. 15. 7½ each ton, payment may be made by first putting down £2 for each ton, then 10s. for each, then 5s., then 6d., and then 1½d. These sums together make up £2. 15. 7½, and the reason for this separation of £2. 15 . 7½ into different parts will be soon apparent. The process may be carried on as follows:
1. 153 tons, at £2 each ton, will cost
£306 0 0
2. Since 10s. is £½, 153 tons, at 10s. each, will cost £15³/₂, which is
76 10 0
3. Since 5s. is ½ of 10s., 153 tons, at 5s., will cost half as much as the same number at 10s. each, that is, ½ of £76 . 10, which is
38 5 0
4. Since 6d. is ⅒ of 5s., 153 tons, at 6d. each, will cost ⅒ of what the same number costs at 5s. each, that is, ⅒ of £38 . 5, which is
3 16 6
5. Since 1½ or 3 halfpence is ¼ of 6d. or 12 halfpence, 153 tons, at 1½d. each, will cost ¼ of what the same number costs at 6d. each, that is, ¼ of £3 . 16 . 6, which is
0 19 1½
The sum of all these quantities is 425 10 7½ which is, therefore, £2 . 15 . 7½ × 153.
The whole process may be written down as follows:
or what 153 tons would cost at
£153 0 0 £1 per ton.
£2 is 2 × £1 306 0 0 2 0 0
10s. is ½ of £1 76 10 0 0 10 0
10s is ½ of £1 76 10 0 0 10 0
5s is ½ of 10s 38 5 0 0 5 0
6d. is ⅒ of 5s. 3 16 6 0 0 6 1½d. is ¼ of 6d. 0 19 1½ 0 0 1½ Sum £425 10 7½
ANOTHER EXAMPLE.
0 1½
What do 1735 lbs. cost at 9s. 10¾d. per lb.? The price 9s. 10¾d is made up of 5s., 4s., 10d., ½d., and ¼d.; of which 5s. is ¼ of £1, 4s. is ⅕ of £1, 10d. is ⅙ of 5s., ½d. is ¹/₂₀ of 10d., and ¼d. is ½ of ½d. Follow the same method as in the last example, which gives the following: or what 1735 tons would cost at
£1735 0 0 £1 per ton.
5s is ¼ of £1 433 15 0 0 5 0 4s. is ⅕ of £1 347 0 0
4 0 10d. is ⅙ of 5s. 72 5 10
0 10 ½d. is ¹/₂₀ of 10d. 3 12 3½ 0 0 0½
¼d. is ½ of ½d. 1 16 1¾ 0 0 0¼ by addition £858 9 3¼ £0 9 10¾
In all cases, the price must first be divided into a number of parts, each of which is a simple fraction[47] of some one which goes before. No rule can be given for doing this, but practice will enable the student immediately to find out the best method for each case. When that is done, he must find how much the whole quantity would cost if each of these parts were the price, and then add the results together
EXERCISES.
What is the cost of
243 cwt. at £14 . 18 . 8¼ per cwt.?—Answer, £3629 . 1 . 0¾.
169 bushels at £2 . 1 . 3¼ per bushel?—Answer, £348 . 14 . 9¼.
273 qrs. at 19s. 2d. per quarter?—Answer, £261 . 12. 6.
2627 sacks at 7s. 8½d. per sack?—Answer, £1012 . 9 . 9½.
231. Throughout this section it must be observed, that the rules can be applied to cases where the quantities given are expressed in common or decimal fractions, instead of the measures in the tables. The following are examples:
What is the price of 272·3479 cwt. at £2. 1. 3½ per cwt.?
Answer, £562·2849, or £562. 5. 8¼. 66½lbs. at 1s. 4½d. per lb. cost £4. 11. 5¼.
How many pounds, shillings, and pence, will 279·301 acres let for if each acre lets for £3·1076?
Answer, £867·9558, or £867. 19. 1¼.
What does ¼ of ³/₁₃ of 17 bush. cost at ⅙ of ⅔ of £17. 14 per bushel?
Answer, £2·3146, or £2. 6. 3½.
What is the cost of 19lbs. 8oz. 12dwt. 8gr. at £4. 4. 6 per ounce?—Answer, £999. 14. 1¼ ⅙.
232. It is often required to find to how much a certain sum per day will amount in a year. This may be shortly done, since it happens that the number of days in a year is 240 + 120 + 5; so that a penny per day is a pound, half a pound, and 5 pence per year. Hence the following rule: To find how much any sum per day amounts to in a year, turn it into pence and fractions of a penny; to this add the half of itself, and let the pence be pounds, and each farthing five shillings; then add five times the daily sum, and the total is the yearly amount. For example, what does 12s. 3¾d. amount to in a year?This is 147¾d., and its half is 73⅞d., which added to 147¾d. gives 221⅝d., which turned into pounds is £221. 12. 6. Also, 12s. 3¾d. × 5 is £3. 1. 6¾, which added to the former sum gives £224. 14. 0¾ for the yearly amount. In the same way the yearly amount of 2s. 3½d. is £41. 16. 5½; that of 6¾d. is £10. 5. 3¾; and that of 11d. is £16. 14. 7.
233. An inverse rule may be formed, sufficiently correct for every purpose, in the following way: If the year consisted of 360 days, or ³/₂ of 240, the subtraction of one-third from any sum per year would give the proportion which belongs to 240 days; and every pound so obtained would be one penny per day But as the year is not 360, but 365 days, if we divide each day’s share into 365 parts, and take 5 away, the whole of the subtracted sum, or 360 × 5 such parts, will give 360 parts for each of the 5 days which we neglected at first. But 360 such parts are left behind for each of the 360 first days; therefore, this additional process divides the whole annual amount equally among the 365 days. Now, 5 parts out of 365 is one out of 73, or the 73d part of the first result must be subtracted from it to produce the true result. Unless the daily sum be very large, the 72d part will do equally well, which, as 72 farthings are 18 pence, is equivalent to subtracting at the rate of one farthing for 18d., or ½d. for 3s., or 10d. for £3. The rule, then, is as follows: To find how much per day will produce a given sum per year, turn the shillings, &c. in the given sum into decimals of a pound (221); subtract one-third; consider the result as pence; and diminish it by one farthing for every eighteen pence, or ten pence for every £3. For example, how much per day will give £224. 14. 0¾ per year? This is 224·703, and its third is 74·901, which subtracted from 224·703, gives 149·802, which, if they be pence, amounts to 12s. 5·802d., in which 1s. 6d. is contained 8 times. Subtract 8 farthings, or 2d., and we have 12s. 3·802d., which differs from the truth only about ¹/₂₀ of a farthing. In the same way, £100 per year is 5s. 5¾d. per day.
234. The following connexion between the measures of length and the measures of surface is the foundation of the application of arithmetic to geometry.
Suppose an oblong figure, , , , , as here drawn (which is called a rectangle in geometry), with the side 6 inches, and the side 4 inches. Divide and (which are equal) each into 6 inches by the points a, b, c, l, m, &c.; and and (which are also equal) into 4 inches by the points f, g, h, x, y, and z Join a and l, b and m, &c., and f and x, &c. Then, the figure is divided into a number of squares; for a square is a rectangle whose sides are equal, and therefore a f is square, since a is of the same length as f, both being 1 inch. There are also four rows of these squares, with six squares in each row; that is, there are 6 × 4, or 24 squares altogether. Each of these squares has its sides 1 inch in length, and is what was called in (215) a square inch By the same reasoning, if one side had contained 6 yards, and the other 4 yards, the surface would have contained 6 × 4 square yards; and so on.
235. Let us now suppose that the sides of , instead of being a whole number of inches, contain some inches and a fraction. For example, let be 3½ inches, or (114) ⁷/₂ of an inch, and let contain 2½ inches, or ⁹/₄ of an inch. Draw twice as long as , and four times as long as , and complete the rectangle The rest of the figure needs no description. Then, since is twice , or twice ⁷/₂ inches, it is 7 inches. And since is four times , or four times ⁹/₄ inches, it is 9 inches. Therefore, the whole rectangle contains, by (234), 7 × 9 or 63 square inches. But the rectangle contains 8 rectangles, all of the same figure as ; and therefore is one-eighth part of , and contains ⁶³/₈ square inches. But ⁶³/₈ is made by multiplying ⁹/₄ and ⁷/₂ together (118). From this and the last article it appears, that, whether the sides of a rectangle be a whole or a fractional number of inches, the number of square inches in its surface is the product of the numbers of inches in its sides. The square itself is a rectangle whose sides are all equal, and therefore the number of square inches which a square contains is found by multiplying the number of inches in its side by itself. For example, a square whose side is 13 inches in length contains 13 × 13 or 169 square inches.
236. EXERCISES.
What is the content, in square feet and inches, of a room whose sides are 42 ft. 5 inch. and 31 ft. 9 inch.? and supposing the piece from which its carpet is taken to be three quarters of a yard in breadth, what length of it must be cut off?—Answer, The content is 1346 square feet 105 square inches, and the length of carpet required is 598 feet 6⁵/₉ inches.
The sides of a rectangular field are 253 yards and a quarter of a mile; how many acres does it contain?—Answer, 23.
What is the difference between 18 square miles, and a square of 18 miles long, or 18 miles square?—Answer, 306 square miles.
237. It is by this rule that the measure in (215) is deduced from that in (214); for it is evident that twelve inches being a foot, the square foot is 12 × 12 or 144 square inches, and so on. In a similar way it may be shewn that the content in cubic inches of a cube, or parallelepiped,[48] may be found by multiplying together the number of inches in those three sides which meet in a point. Thus, a cube of 6 inches contains 6 × 6 × 6, or 216 cubic inches; a chest whose sides are 6, 8, and 5 feet, contains 6 × 8 × 5, or 240 cubic feet. By this rule the measure in (216) was deduced from that in (214).
SECTION II. RULE OF THREE.
238. Suppose it required to find what 156 yards will cost, if 22 yards cost 17s. 4d. This quantity, reduced to pence, is 208d.; and if 22 yards cost 208d., each yard costs ²⁰⁸/₂₂d. But 156 yards cost 156 times the price of one yard, and therefore cost 208 × 156 pence, or 208 × 156 pence (117) 22
Again, if 25½ French francs be 20 shillings sterling, how many francs are in £20. 15? Since 25½ francs are 20 shillings, twice the number of francs must be twice the number of shillings; that is, 51 francs are 40 shillings, and one shilling is the fortieth part of 51 francs, or ⁵¹/₄₀ francs. But £20 15s. contain 415 shillings (219); and since 1 shilling is ⁵¹/₄₀ francs, 415 shillings is ⁵¹/₄₀ × 415 francs, or (117) 51 × 415 francs.
239. Such questions as the last two belong to the most extensive rule in Commercial Arithmetic, which is called the R T , because in it three quantities are given, and a fourth is required to be found. From both the preceding examples the following rule may be deduced, which the same reasoning will shew to apply to all similar cases.
It must be observed, that in these questions there are two quantities which are of the same sort, and a third of another sort, of which last the answer must be. Thus, in the first question there are 22 and 156 yards and 208 pence, and the thing required to be found is a number of pence. In the second question there are 20 and 415 shillings and 25½ francs, and what is to be found is a
number of francs. Write the three quantities in a line, putting that one last which is the only one of its kind, and that one first which is connected with the last in the question.[49] Put the third quantity in the middle. In the first question the quantities will be placed thus:
22 yds. 156 yds. 17s. 4d.
In the second question they will be placed thus:
20s. £20 15s. 25½ francs.
Reduce the first and second quantities, if necessary, to quantities of the same denomination. Thus, in the second question, £20 15s. must be reduced to shillings (219). The third quantity may also be reduced to any other denomination, if convenient; or the first and third may be multiplied by any quantity we please, as was done in the second question; and, on looking at the answer in (238), and at (108), it will be seen that no change is made by that multiplication. Multiply the second and third quantities together, and divide by the first. The result is a quantity of the same sort as the third in the line, and is the answer required. Thus, to the first question the answer is (238)
208 × 156 pence, or, which is the same thing, 17s. 4d. × 156 22 22
240. The whole process in the first question is as follows:[50]
yds s d
22)32448(1474¾d. and ¹⁴/₂₂, or ⁷/₁₁ of a farthing, 22 or (219) £6 . 2 . 10¾-⁷/₁₁.
The question might have been solved without reducing 17s. 4d. to pence, thus:
£135 . 4 . 0(£6 . 2 . 10¾-⁷/₁₁
× 20 + 4 =
The student must learn by practice which is the most convenient method for any particular case, as no rule can be given.
241. It may happen that the three given quantities are all of one denomination; nevertheless it will be found that two of them are of one, and the third of another sort. For example: What must an income of £400 pay towards an income-tax of 4s. 6d. in the pound? Here the three given quantities are, £400, 4s. 6d., and £1, which are all of the same species, viz. money. Nevertheless, the first and third are income; the second is a tax, and the answer is also a tax; and therefore, by (152), the quantities must be placed thus:
£1 : £400 ∷ 4s. 6d.
242. The following exercises either depend directly upon this rule, or can be shewn to do so by a little consideration. There are many questions of the sort, which will require some exercise of ingenuity before the method of applying the rule can be found.
EXERCISES.
If 15 cwt. 2 qrs. cost £198. 15. 4, what does 1 qr. 22 lbs. cost?
Answer, £5 . 14 . 5 ¾ ¹⁸⁵/₂₁₇
If a horse go 14 m. 3 fur. 27 yds. in 3ʰ 26ᵐ 12ˢ, how long will he be in going 23 miles?
Answer, 5ʰ 29ᵐ 34ˢ(²⁴⁶²/₂₅₃₂₇).
Two persons, A and B, are bankrupts, and owe exactly the same sum; A can pay 15s. 4½d. in the pound, and B only 7s. (6¾)d. At the same time A has in his possession £1304. 17 more than B; what do the debts of each amount to?
Answer, £3340 . 8 . 3 ¾ ⁹/₂₅
For every (12½) acres which one country contains, a second contains (56¼). The second country contains 17,300 square miles. How much does the first contain? Again, for every 3 people in the first, there are 5 in the second; and there are in the first 27 people on every 20 acres. How many are there in each country?—Answer, The number of square miles in the first is 3844⁴/₉, and its population 3,321,600; and the population of the second is 5,536,000.
If (42½) yds. of cloth, 18 in. wide, cost £59. 14. 2, how much will (118¼) yds. cost, if the width be 1 yd.?
Answer, £332. 5. (2⁴/₁₇).
If £9. 3. 6 last six weeks, how long will £100 last?
Answer, (65¹⁴⁵/₃₆₇) weeks.
How much sugar, worth (9¾d). a pound, must be given for 2 cwt. of tea, worth 10d. an ounce?
Answer, 32 cwt. 3 qrs. 7 lbs. ³⁵/₃₉
243. Suppose the following question asked: How long will it take 15 men to do that which 45 men can finish in 10 days? It is evident that one man would take 45 × 10, or 450 days, to do the same thing, and that 15 men would do it in one-fifteenth part of the time which it employs one man, that is, in (450 ÷ 15) or 30 days. By this and similar reasoning the following questions can be solved.
EXERCISES.
If 15 oxen eat an acre of grass in 12 days, how long will it take 26 oxen to eat 14 acres?
Answer, (96¹²/₁₃) days.
If 22 masons build a wall 5 feet high in 6 days, how long will it take 43 masons to build 10 feet?
Answer, (6⁶/₄₃) days.
244. The questions in the preceding article form part of a more general class of questions, whose solution is called the D R T , but which might, with more correctness, be called the Rule of Five, since five quantities are given, and a sixth is to be found. The following is an example: If 5 men can make 30 yards of cloth in 3 days, how long will it take 4 men to make 68 yards? The first thing to be done is to find out, from the first part of the question, the time it will take one man to make one yard. Now, since one man, in 3 days, will do the fifth part of what 5 men can do, he will in 3 days make ³⁰/₅, or 6 yards. He will, therefore, make one yard in ³/₆6 or (3 × 5)/30 of a day From this we are to find how long it will take 4 men to make 68 yards. Since one man makes a yard in
3 × 5 of a day, he will make 68 yards in 3 × 5 × 68 days, 30 30 or (116) in 3 × 5 × 68 days; and 4 men will do this in one-fourth; 30 of the time, that is (123), in 3 × 5 × 68 days, or in 8½ days.
30 × 4
Again, suppose the question to be: If 5 men can make 30 yards in 3 days, how much can 6 men do in 12 days? Here we must first find the quantity one man can do in one day, which appears, on reasoning similar to that in the last example, to be 30/(3 × 5) yards. Hence, 6 men, in one day, will make
6 × 30 yards, and in 12 days will make 12 × 6 × 30 or 144 yards 5 × 3 5 × 3
From these examples the following rule may be drawn. Write the given quantities in two lines, keeping quantities of the same sort under one another, and those which are connected with each other, in the same line. In the two examples above given, the quantities must be written thus:
SECOND EXAMPLE.
Draw a curve through the middle of each line, and the extremities of the other There will be three quantities on one curve and two on the other Divide the product of the three by the product of the two, and the quotient is the answer to the question.
If necessary, the quantities in each line must be reduced to more simple denominations (219), as was done in the common Rule of Three (238).
EXERCISES.
If 6 horses can, in 2 days, plough 17 acres, how many acres will 93 horses plough in 4½ days?
Answer, 592⅞.
If 20 men, in 3¼ days, can dig 7 rectangular fields, the sides of each of which are 40 and 50 yards, how long will 37 men be in digging 53 fields, the sides of each of which are 90 and 125½ yards?
Answer, 75 2451 days. 20720
If the carriage of 60 cwt. through 20 miles cost £14 10s., what weight ought to be carried 30 miles for £5. 8. 9?
Answer, 15 cwt.
If £100 gain £5 in a year, how much will £850 gain in 3 years and 8 months?
Answer, £155. 16. 8.
SECTION III. INTEREST, ETC.
245. In the questions contained in this Section, almost the only process which will be employed is the taking a fractional part of a sum of money, which has been done before in several cases. Suppose it required to take 7 parts out of 40 from £16, that is, to divide £16 into 40 equal parts, and take 7 of them. Each of these parts is
£16 and 7 of them make 16 × 7, or 16 × 7 pounds (116). 40 40 40
The process may be written as below:
. 16s.
Suppose it required to take 13 parts out of a hundred from £56. 13. 7½. 56 . 13 . 7½ 13
736 . 17 . 1½ ( £7 . 7 . 4 ¼ ¹/₄₁
Let it be required to take 2½ parts out of a hundred from £3 12s. The result, by the same rule is £3 12s. × 2½ , or 123 £3 12s. × 5 ;
so that taking 2½ out of a hundred is the same as taking 5 parts out of 200.
Take 7⅓ parts out of 53 from £1 10s.
