In his Lectures on Physics, Richard Feynman asserts that “ten thousand years from now, there can be little doubt that the most significant event of the 19th century will be judged as Maxwell's discovery of the laws of electrodynamics”. Whether this prediction is borne out or not, it is impossible to deny the significance of Maxwell's achievement to the history, practice, and future of physics. That is why electrodynamics has a permanent place in the physics curriculum, along with classical mechanics, quantum mechanics, and statistical mechanics. Of these four, students often find electrodynamics the most challenging. One reason is surely the mathematical demands of vector calculus and partial differential equations. Another stumbling block is the non-algorithmic nature of electromagnetic problem-solving. There are many entry points to a typical electromagnetism problem, but it is rarely obvious which lead to a quick solution and which lead to frustrating complications. Finally, Freeman Dyson points to the “two-level” structure of the theory.1 A first layer of linear equations relates the electric and magnetic fields to their sources and to each other. A second layer of equations for force, energy, and stress are quadratic in the fields. Our senses and measurements probe the second-layer quantities, which are determined only indirectly by the fundamental first-layer quantities.

Introduction

Many contemporary technologies exploit the fact that electromagnetic waves can be guided along specified paths through space and transiently stored in low-loss enclosures. The special configurations of conductors and dielectrics used to do this are called waveguides and resonant cavities. In this chapter, we show that electromagnetic fields can be guided and stored because they adjust themselves to satisfy the required boundary (or matching) conditions at the surfaces (or internal interfaces) of a guide or cavity. The nature and characteristics of the waves are fixed by the geometry and topology of the guiding and storage structures. Besides the familiar transverse electromagnetic (TEM) waves, where E and B are both transverse to the direction of propagation, we will find transverse electric (TE) waves where only E is transverse and transverse magnetic (TM) waves where only B is transverse. By and large, our discussion focuses on the applications of waveguides and cavities to specific problems of physics. Textbooks of engineering electro magnetics discuss applications to communication and power transmission.

Guided waves were discovered in 1842 by the Swiss physicist Colladon, who reported that total internal reflection could be exploited to trap light inside the parabolic streams of water produced by drilling holes in a water-filled vessel. Fifty-five years later, Hertz sought and observed meter-scale waves guided by a conducting wire.

Introduction

An incident electromagnetic wave is said to scatter or diffract from a sample of matter when the field produced by the sample cannot be described using Fresnel's theory of reflection and refraction from a flat interface (Section 17.3). In this chapter, we focus on the class of problems where this occurs because the wavelength of the incident monochromatic field is not small compared to the curvature of a material boundary. From a Fresnel point of view, the total field in these cases results from the interference of many different “reflected” and “refracted” waves propagating in different directions. We will encounter other points of view as we proceed. Figure 21.1 shows some typical geometries of interest. There is no universal naming practice, but many authors say that “scattering” occurs from objects with smooth boundaries and “diffraction” occurs from objects with sharp edges.

The physics that produces scattering and diffraction is identical to the physics that produces the Fresnel equations. An incident electromagnetic wave sets the charged particles of a medium into motion. Each accelerated charge produces a retarded field which is felt by, and thus affects the motion of, every other charge in the medium. The motion of every charge and the field it produces must be consistent with the total field each charge experiences.

In this chapter . . .

In this chapter we will introduce you to a system of thinking about, and then describing, English words and sentences. We will see that most words can have different forms. Combined according to rules of grammar (morpho-syntax), words can form larger units such as phrases, clauses and sentences. Many words can also be segmented into smaller meaningful units, which are called morphemes. We will discover that the most important shared characteristic of these units is that they all have internal structure. As we will see, in order to work systematically with English words and sentences, we need to analyse both: the structure that lies behind words (morphology), and the organising principles according to which native speakers assemble words into sentences (syntax). And we will see that, without this internal structure, we would not be able to communicate with language, and this is, after all, its purpose. We will not give you stylistic or prescriptive rules, but together we will discover the conventions underlying the use of standard English for communication.

Introduction

This chapter describes how linguists realized they needed to study ongoing changes. In the early part of the twentieth century, language change was assumed to happen too slowly to be observable. In their grammars, linguists had unwittingly omitted the variations which indicated that changes were under way. The American linguist William Labov was the key figure in this twentieth-century linguistic breakthrough. He made a preliminary ingenious attempt to study current changes in a now-famous department store survey in New York. Later, he proceeded to other New York changes. He found he could reliably predict the percentage of the features he was investigating in the speech of different ethnic groups, sexes, ages and socio-economic classes, in different speech styles. In his later work, he has refined his early techniques and produced a solid methodological framework for future researchers. His later work in Philadelphia again proved groundbreaking. Meanwhile, in Northern Ireland, Jim and Leslie Milroy explored speech varieties in different social networks. These seminal studies, on each side of the Atlantic, kick-started work on ongoing changes, which are now a standard part of language change investigations.

In this chapter . . .

In this chapter we will introduce the main word classes: nouns, determiners, pronouns, adjectives, verbs, adverbs, prepositions and conjunctions. We said that in order to work systematically with English words and sentences, we need to analyse both the structure that lies behind words (morphology) and the organising principles according to which sentences are assembled (syntax). In accordance with this principle, we will introduce you to morphological, syntactic and semantic criteria for word-class identification. We will see that word meaning is of course important for words to fit into a sentence; but their form characteristics are equally important. Each of the sections begins with a discussion of the shared properties of the word class under consideration. Once we have identified the typical characteristics of a word class, we will introduce you to different sub-types within it, if there are any. Activities on the fuzziness of different word classes, and on how distributional criteria allow us to shed some light on this fuzziness, will be relegated to the end of the chapter. In this chapter you will learn to work out which word class any word in any given sentence belongs to.

1. Large streams from little fountains flow,

2. Tall oaks from little acorns grow.

3. David Everett, ‘Lines written for a school declamation’

Introduction

This chapter considers the linguistic progress of a sound change, where it starts, and how it makes its way through the language. Frequently used words often (but not inevitably) get affected early. But these words need also to be linguistically susceptible. Typically, the change follows an S-curve (slow-quick-quick-slow) pattern. It starts slowly, then speeds up; eventually it gradually fades away. But as the change happens, individual speakers tend to vary in their treatment of words: on one day, a speaker may use the new form, on another day the old. Neatness may happen in the long run, but not in the course of the change.

Language change spreads in two ways: outwardly through a community, and inwardly through a language. Let us now consider this inner linguistic burrowing. Like a seed, any change is likely to have small beginnings. But if it puts down firm roots, it can develop into a massive growth which affects the whole landscape. This spreading process is the topic of this and the next chapter. This chapter will deal with sound change, and the following with syntactic change.

Introduction

This chapter discusses reductions and abbreviations, known in more modern terms as grammaticalization and text messaging. The former used to be described as a previously autonomous word becoming an affix, as in spoon-full → spoonful. But this is oversimple. Grammaticalization covers the whole of language, taking in semantic attrition, grammatical reduction, and phonetic reduction, as well as some idioms. Meanwhile, phonetic cropping has long been in use for a few well-known sequences, such as PTO ‘please turn over’, RIP ‘rest in peace’. Recently such abbreviations have escalated in number, due to the use of text messaging in emails and on mobile phones.

Introduction

This chapter explains how language changes spread from person to person, a once mysterious process. As elsewhere, William Labov was the key innovator. His research papers on New York [r] and Martha's Vineyard diphthongs are considered linguistic ‘classics’, essential reading for anyone studying language change. He found that insertion of [r] in words such as bear, beard was considered a prestige feature, an item which speakers felt should be there in good speech. The lower middle class and upper working class had many more r-sounds in their careful speech than in their casual conversation. This over-insertion of [r] was a sure sign that a partially conscious change was in progress. Speakers were less aware of the ongoing change in Martha's Vineyard diphthongs. Subconsciously, those who wanted to remain on the island had been trying to sound more like some respected old fishermen, who represented traditional values: the change was less established in those who were planning to move away. These findings highlight the importance of social issues in the spread of change. In his most recent work, Labov has promoted the label ‘the curvilinear hypothesis’, which is a description of a diagram which shows changes radiating from speakers in the middle of the social scale.

This book has been written for people who are interested in language change, and enjoy reading about it. It is NOT written primarily for people who want to be tested on the topic in essays or exams. However, I have been told that some people have requested possible questions which might help them to see how much of the book they have remembered. So here, chapter by chapter, are some suggestions.

Chapter 1

1. Why in the eighteenth and nineteenth centuries were people so worried about language change?

2. Explain what is meant by the word ‘grammar’.

3. What is the difference between a prescriptive and a descriptive grammar?

Chapter 2

1. Suggest at least three types of clue which might help linguists to reconstruct the pronunciation of speakers in past centuries.

2. Outline two basic assumptions of comparative historical linguistics.

3. Name two other types of reconstruction, and explain what they involve.