Justice Antonin Scalia, writing for the majority in D.C. v. Heller, distinguishes between "unusual and dangerous weapons," which can be banned without violating the Second Amendment, and weapons "in common use...for lawful purposes," which can't. The distinction is necessary partly to shore up his argument that "nothing in our precedents forecloses our adoption of the original understanding of the Second Amendment"—i.e., that it protects an individual right to arms. In particular, Scalia argues that the 1939 decision U.S. v. Miller, which gun control supporters (including the Heller dissenters) portray as endorsing the militia-only, collective-right view of the Second Amendment, in fact "stands only for the proposition that the Second Amendment right, whatever its nature, extends only to certain types of weapons." The law at issue in Miller was a federal ban on sawed-off shotguns, and the Court said "it is not within judicial notice that this weapon is any part of the ordinary military equipment or that its use could contribute to the common defense." It therefore concluded that short-barreled shotguns are not covered by the Second Amendment, which applies only to the sort of weapons that citizens would bring with them for militia duty.

Scalia is right that Justice John Paul Stevens' reading of Miller—that the Second Amendment applies only to possession of guns while serving in the organized militia—is implausible. "Had the Court believed that the Second Amendment protects only those serving in the militia," Scalia writes, "it would have been odd to examine the character of the weapon rather than simply note that the two crooks were not militiamen." 

Nevertheless, for someone determined (as Scalia apparently is) to maintain existing federal gun laws, there are a couple of problems with accepting the Miller Court's view of which weapons are covered by the Second Amendment. First, the Court's assumption that short-barreled shotguns are not appropriate for military use was incorrect. Second, this test would mean that the Second Amendment covers machine guns, which also are banned by federal law.* Scalia acknowledges this difficulty:

Read in isolation, Miller's phrase "part of ordinary military equipment" could mean that only those weapons useful in warfare are protected. That would be a startling reading of the opinion, since it would mean that the National Firearms Act's restrictions on machineguns (not challenged in Miller) might be unconstitutional, machineguns being useful in warfare in 1939.

To avoid this uncomfortable result, Scalia latches onto another phrase in Miller:

We think that Miller's "ordinary military equipment" language must be read in tandem with what comes after: "[O]rdinarily when called for [militia] service [able-bodied] men were expected to appear bearing arms supplied by themselves and of the kind in common use at the time."

Machine guns obviously were not "in common use" at the time the Second Amendment was adopted. But that's not enough to avoid overturning the ban on automatic weapons, since, as Scalia himself emphasizes, constitutional rights do not apply only to colonial-era technology:

Some have made the argument, bordering on the frivolous, that only those arms in existence in the 18th century are protected by the Second Amendment. We do not interpret constitutional rights that way. Just as the First Amendment protects modern forms of communications, and the Fourth Amendment applies to modern forms of search, the Second Amendment extends, prima facie, to all instruments that constitute bearable arms, even those that were not in existence at the time of the founding.

Scalia needs to make this point because otherwise today's pistols and revolvers, quite different from the firearms available in the 18th century, would not be covered by the Second Amendment. But why stop there? Why isn't an M-16, eminently suitable for military use but also the sort of weapon militia members could keep in their homes and bring with them when their services were necessary (as Swiss and Israeli citizen-soldiers do), included as well? Apparently because machine guns are not "in common use...for lawful purposes" in the United States today. But maybe they would be if they were legal. This seems like circular reasoning to me.

* As a commenter noted, private citizens can legally possess machine guns manufactured before 1986 if they successfully complete an onerous and expensive licensing process. The sale of new machine guns to civilians is prohibited.