FOR THE authorities charged with policing the Potomac River shorelines at Great Falls, the last weekend in June cannot pass too quickly. They know all too well that these are the most perilous times for drownings. Though cooler air and intermittent showers have helped to slow down what had been a frighteningly high rate of drownings this spring, all it takes in June is a shot of hot sun to bring out the biggest crowds of sunbathers, rock climbers, picnickers and others who either don't recognize or don't respect the deadly nature of this river stretch.

By July and August, park officials note, news of the spring drownings tends to scare more people away from the slippery rocks. Fewer people visit Great Falls because many more are at the beaches or on other vacations. That's why chief National Park spokesman Earl V. Kittleman said earlier this month that he was "praying for clouds, drizzle or rain . . . anything until we get past June weekends."

The dangers do not disappear, of course, when you rip that last June page off the calendar. The risk at this point is that people may drop whatever guard they had during the earlier rash of drownings. That is why there should be no letup in the efforts of police, park authorities and the public to crack down on those who ignore warnings and break the law.

Park rangers and park police can't begin to do this job alone. Everybody can and should be a spotter. And to help still more, how about erecting some watchtowers, modeled after those used by forest rangers? These could be designed so they don't ruin any views. They might be staffed by volunteer organizations.

One new regulation should help this year: anyone arrested entering this part of the Potomac from federal parkland will face a mandatory appearance in federal court. Also, stiffer penalties should be in the offing. The maximum is six months in jail and a $500 fine. Usually the penalty has been limited to a $25 summons. Punishment now will be up to U.S. magistrates, and tougher action may well result. Will this help? It's worth finding out.