That’s a famous line in Federalist No. 51, generally attributed to James Madison — but not quite. The line is actually, in context,

But the great security against a gradual concentration of the several powers in the same department, consists in giving to those who administer each department the necessary constitutional means and personal motives to resist encroachments of the others. The provision for defense must in this, as in all other cases, be made commensurate to the danger of attack. Ambition must be made to counteract ambition. The interest of the man must be connected with the constitutional rights of the place. It may be a reflection on human nature, that such devices should be necessary to control the abuses of government. But what is government itself, but the greatest of all reflections on human nature? If men were angels, no government would be necessary. If angels were to govern men, neither external nor internal controls on government would be necessary. In framing a government which is to be administered by men over men, the great difficulty lies in this: you must first enable the government to control the governed; and in the next place oblige it to control itself. A dependence on the people is, no doubt, the primary control on the government; but experience has taught mankind the necessity of auxiliary precautions.

The phrase is “reflections on human nature,” and I take it that “reflection” there means — to quote the Oxford English Dictionary —

9. a. Something which brings discredit on (also upon) a person or thing.
… 1711 J. Addison Spectator No. 189. ¶7 It is one of the greatest Reflections upon Human Nature that Paternal Instinct should be a stronger Motive to Love than Filial Gratitude.
1749 H. Fielding Tom Jones VI. xvi. vii. 60, I will not hear my Niece abused. It is a Reflection on my Family.
1819 Times 2 July 2/2 The honourable member … asserted, that it was a sad reflection on the house, that the Lords had paid greater attention to the security and protection of the subject than they (the House of Commons) had done….

Webster’s 1828 Dictionary likewise offers, as one decision of “reflection,” “Censure; reproach cast,” and gives as an example, “He died, and oh! may no reflection shed its pois’nous venom on the royal dead.”

Madison isn’t saying that government reflects human nature, in that the structure of government stems from human nature. (Maybe that’s true, and maybe it’s even what Madison believed, but it’s not what Madison is talking about in that particular phrase.) First, that’s not what “reflection on” generally means. Second, if we read the sentences as, “It may be a reflection [of] human nature, that such devices should be necessary to control the abuses of government” followed by “But what is government itself, but the greatest of all reflections [of] human nature?,” then it’s not clear why he would use the “It may be/But” construction. That construction isn’t generally used when one sets forth two neutral and related facts about life (separation of powers reflects human nature, and so does government).

Rather, Madison is saying, “Acknowledging the need for separation of powers does bring discredit on human nature (since if human nature weren’t flawed, we wouldn’t need separation of powers). But that’s just a special case of the broader point that acknowledging the need for government itself brings discredit on human nature (since if human nature weren’t flawed, we wouldn’t need government).” Here the “It may be/But” construction makes sense: It may be that my proposal carries within it an implicit indictment of human nature, but the very existence of government carries within it that indictment.

Yet search for “the greatest of all reflections on human nature” (whether through the Internet generally, through books, or through law review articles), and you’ll see plenty of references to the “of” version, e.g.,

Government and politics exist in a universe of real problems and real solutions. To quote James Madison, “What is government itself but the greatest of all reflections of human nature?”
Americans needed a new form of government based on this new acceptance of what people are really like. “But what is government,” James Madison, the father of the Constitution, wrote in 1788, “but the greatest of all reflections of human nature?”
A. The Constitution Was Intended to Be a Reflection of Human Nature
In arguing for the ratification of the Constitution in The Federalist, Madison portrayed the plan of government as “the greatest of all reflections of human nature.” The founding generation was both explicit and emphatic that the Constitution’s success would turn on how well the charter got our personal basics correct.
Yet as Socrates rhetorically inquired, and the Framers dogmatically insisted, whence could a constitution derive if not from the self, “what is government itself but the greatest of all reflections of human nature?”

The “reflection of human nature” reading has had some sticking power. (Indeed, that’s how I had recalled the phrase until I looked closely at it last week.) A few thoughts:

1. “What is government itself, but the greatest of all reflections of human nature?” is itself a plausible statement, indeed a not very controversial one. What’s more, it sounds more familiar to the modern ear than the “reflections on” reading. (The old sense of “reflection” is still sometimes used, but it’s pretty rare.) Many people thus naturally misread it, and don’t check themselves when they do it.

The use of “free reign” for “free rein” offers a good analogy, I think: “Free rein” refers to an activity — riding horses — with which few modern people are closely familiar; “free reign” thus sounds more natural, and many people use it without realizing that “free rein” is the original. (Of course, the analogy is limited: “free rein” is an English phrase, which can legitimately change over time, though the change hasn’t yet fully taken place, at least in edited writing. “Reflection on human nature” was a specific phrase of Madison’s, and when it’s attributed to Madison, it should be rendered accurately.)

2. The English of 200 years ago is generally accessible to us, but some locutions aren’t quite what they seem at first glance. Such misleading terms aren’t as common as they are in Shakespeare, which after all is 400 years old and not just 200. Still, there is some risk of such confusion, both with legal terms (e.g., “Suits at common law” in the Seventh Amendment) and even with lay terms, such as “reflections on.”

3. When you see something suspicious, look it up, and look closely at the context. The phrase is, after all, “reflections on,” not “reflections of” — a signal that there’s something potentially odd here. Don’t just assume that “reflections on” must be an old-fashioned way of saying “reflections of”; maybe it’s an old-fashioned way of saying something else.