Your essay assignment is to compare Democritus and the Sophists (Protagoras and Gorgias) on the distinction between nature and custom (or law). In Philosophy Before Socrates, McKirihan does not include Democritus in his discussion of this distinction [Chapter 20]. It is generally accepted that the Sophists introduced this distinction and did so as part of their activities as teachers of rhetoric in a new environment in which political power was much more democratic and traditional beliefs and morals were questioned and were changing. Thus the nature/custom distinction is usually associated entirely with the Sophists and with the 4th century responses to them by Plato and then by his student Aristotle. We will discuss those responses when the course turns to those authors, but you are now being asked to write not only on the Sophists but on Democritus as well with respect to nature and custom. Since McKirihan gives you no guidance in doing this for Democritus, and we had time only barely to touch upon the topic in our last class, I am writing this note to assist you.
The first thing to keep in mind is that these two terms, "nature" and "custom", are topics [?????]or places of discussion; i. e. they are given different meanings by different authors. Different meanings have different implications for what is considered a good life. All the philosophers cited in Chapter 20 are Sophists. They pretty much agree that truth is what wins the argument and is always subject to further argument and change. That's what it means to say that "man is the measure". This basic idea is familiar to you, in fact tends to dominate many minds, in the idea that truth is a matter of individual point of view. Another way of saying this is to say that there is no truth, only opinion. Sometimes it is suggested that we not try to impose our opinions on others, but this is naïve, not only because we need to choose in order to act (and life is action), but because every time we speak we assert a point of view ["assertion" is a synonym for "statement"]and at least implicitly try to persuade others of it. Moreover, we learn much in a good debate as assertions and counter-assertions lead to the discovery of more facts and more adequate interpretations. According to the Sophists, all this is a matter of rhetoric and persuasion; there is no independent, objective standard by which the views of persons can be measured.
This point against objectivity makes for a useful transition to Democritus. The atomistic philosophy is the very opposite of the sophistic and is as familiar to us as ideas about individual points of view. It is the idea of scientific objectivity. Democritus' claim is that by thinking about experience we can find the elements of all that exists and happens and get rid entirely of any subjectivity or personal point of view present in experiences before they have been analyzed. This is why he calls experience a bastard or illegitimate knowledge, contrasting it with the legitimate knowledge of atoms moving in the void. An atom is about as great a contrast as you can get with a personal point of view. It is stuff devoid of all quality except for shape and motion. As such, in itself it has nothing to do with perception or thought at all. Atoms are known by thought, but so far from having the quality of thought, thoughts are instead explained as motions of atoms: material events in the human nervous system (another familiar thought). 
Having briefly contrasted the two philosophies, I will write briefly about nature and custom in each.
In thinking about the Sophists' view, it is clear that "nature" cannot refer to the world around us, since on their view it is the product of our assertions, our words engaged in persuasive communication. In that respect, it is no different from the laws [custom, ?????]we formulate in our legislatures and cultural traditions. Paradoxically, what we usually call "nature", the natural world, is by custom or agreement among human beings - although that agreement is never unanimous. I illustrated this in class by reference to the persuasiveness of those who have convinced us that the earth is neither flat nor at rest, that the world is governed by laws of inertia and impressed mechanical forces, and then, changing their (and our) minds, that it is energy governed by quantum laws and the curvature of space, etc. What then is nature for the Sophist? It is the human nature that is the source of all custom, the desire to act that leads to the production of all our customs, i. e. of our beliefs about laws of nature as well as laws of behavior. Read McKirihan's long discussion of whether the good life consists in following nature or custom in terms of these distinctions.
For Democritus, however, nature is the world around us, and us too, as atoms moving in the void. We need customs to live together and opinions to act and survive as organisms in the world, but these customs are good only insofar as they are based on knowledge of nature: science is the source of wisdom. In place of the self-assertive ethic of the sophist, the atomist gives us the idea of health. The question in life is how to preserve oneself, i. e. one's nature (a configuration of atoms). Instead of the power of assertion of one's own desires, the atomist shows us the need to moderate desire by making one's nature stronger in the sense of less susceptible to the external causes that stimulate desire. Ethics and law are customs, but like science, they are good and true only when based on nature. The community exists by agreement, but its aims is self-preservation and self-determination.
I could say more on all of these topics. But my purpose is to give you some guidance, not to cover the subject. Use these notes to guide you in your interpretation of the Sophists and Atomists and of McKirihan's discussion in Chapter 20 of Nature and Custom.