What an astonishing move by Rudolph Giuliani and Michael Mukasey in asking a federal appeals court to admit them as friends of the court on the side of the city in the stop, question and frisk case. The filing, made quietly Monday, comes amid growing alarm among courthouse cognoscenti that the city is failing to act aggressively enough in seeking to protect the ability of the police department to protect New York.

The two legendary lawmen — Mr. Giuliani, a former mayor and federal prosecutor; Mr. Mukasey, a former United States attorney general and federal judge here — filed their motion in federal appeals court for the Second Circuit. That’s the court the city is currently asking to stay Judge Shira Scheindlin’s ruling that the city’s stop, question and frisk policing practices are unconstitutional.

For weeks, court-watchers have looked on in alarm as Mayor Bloomberg and city lawyers in the office of the corporation counsel have seemed to be frozen like deer in the headlights in the face of the judge’s ruling. This is particularly so after the mayor went before the press in mid-August to declare Judge Scheindlin’s ruling “a very dangerous decision made by a judge who I think does not understand how policing works.”

At the time, the mayor — with Police Commissioner Kelly and the city’s chief lawyer, Michael Cardozo, behind him — vowed to appeal the ruling. Mr. Bloomberg warned that if it were allowed to stand the city would be “a more dangerous place.” Kelly defended the honor of the cops, characterizing the suggestion that they engage in racial profiling “recklessly untrue.”

If the mayor is so all-fired upset, though, it hasn’t been evident from the pace at which the city is pressing its appeal in court. Its filing suggests it may not be able “to perfect its appeal” until November and seeks an order “directing appellees to file their answering brief by January 13, 2014,” which gives the impression, in light of the political realities, that the city’s lawyers are not eager to get the stay they’re ostensibly seeking.

This has left the savviest court-watchers shaking their heads in amazement. Judge Scheindlin originally issued her ruling in mid-August. Though the ruling was widely anticipated, the city waited two weeks before asking that she stay her decision while the city appealed. The city argued that “irreparable harm was imminent.” Judge Scheindlin fussed for two more weeks before, in a sneering opinion, she denied the stay.

At this point, one would have thought that the city would have been ready — meaning that the corporation counsel and the mayor would have bestirred themselves personally to go into the federal courthouse and ask the judges who ride the Second Circuit for a stay. Instead, the city was pursuing something different, a motion for expedited appeal.

It included a leisurely schedule that failed to convince the appeals judge that the city regarded the crisis as all that urgent. The judge denied the request. On Sept. 17, Mr. Cardozo finally announced that the city would ask the Second Circuit for a stay — halting Judge Scheindlin’s order — “in the next few days.” Six days later, it filed a motion that seemed to suggest that hearings on the stay could take us into next year.

Meantime, the other side is moving like it means business. One can hear predictions that the special monitor’s hiring will eventually mean a legal bill in the millions, even tens of millions. In an important piece by Heather MacDonald, The Post reported that a panel of the most left-wing professors in the entire solar system is being appointed to second-guess the police.

Thugs in the city apparently comprehend how things are going. In the month following Scheindlin’s ruling, according to crime figures also first reported in The Post, shootings in the city “spiked nearly 13 percent — and gun seizures plummeted more than 17 percent.” The mayor was cautious. “Maybe it’s just a blip, maybe it’s a trend,” he said.

Or maybe the mayor figures the best way to make people appreciate his mayoralty is for things to fall apart after he leaves office. That’s the danger if, as the polls predict, we get a mayor who opposes the police on stop, question and frisk the way Bill de Blasio does. So a stay at the Second Circuit is the city’s best chance. No wonder Messrs. Giuliani and Mukasey are making a move.

This column first appeared in the New York Post.