The cold light of dawn is just beginning to break and the mists still hang heavily on the dank coves of Lake Occoquan when we spot it - the critter we had gotten up in the middle of the night to see. Naturalist Earl Hodnett turns off the boat's electric motor. Cameras click. Kids are silenced. But old chiseltooth doesn't even look up. It just squats on the bank munching on a branch.

Is this the animals that launched a million canoes? That made men leave home and brave untold dangers in search of its furry tail?

Yes, says Hodnett, who takes out a box of props and, with one eye on the critter on the bank, proceeds to tell us everything we always wanted to know about beavers - wanted to know badly enough to sign up months in advance for an Eager Beaver Cruise that embarks at 6 of a Saturday morning.

The reason these cruises start so early is that beavers hide out during the hours when most people are up. They aren't naturally nocturnal, explains Hodnett, but, people have forced nocturnal habits on them. The buck-toothed rodents, who look as if they'd be attractive only to other beavers were hunted almost to extinction by trappers catering to the fashion craze for beaver pelts. Since beavers were almost extinct in the Old World when the New World was discovered, North American beavers had to satisfy the world's demands for beaver hats and collars.

By way of illustration, Hodnett takes out a beaver hat, the kind Abe Lincoln, who didn't have a conservation lobby to contend with, used to wear. Adults stroke it. Kids try it on, beginning to understand why in the height of the beaver-hat craze - between 1853 and 1877 - the Hudson's Bay Company marketed almost 3 million beaver pelts, and one ambitious trapper earned $50,000 in a good year.

Then Hodnett brings out another reason for the beavers' popularity - a small vial of castoreum. He passes that around too, making kids wrinkle up their noses and say "yuk." Though the stuff smells like old tires, it is used in perfumes, Hodnett explains. The Indians and trappers reportedly, used it to treat everything from epilepsy to hysteria.

To show exactly where the odoriferous stuff comes from, Hodnett pulls the piece de resistance out of his box of tricks: a stuffed beaver. Showing the beaver's underside, he points out the source of his musky glandular secretion. Another gland, Hodnett explains, secretes a substance the beavers curry into their coats for waterproofing with a toenail that acts like a comb.

As if on cue, the real, live, unstuffed beaver on bank plunges its waterproof body into the water. It swims toward the boat, steering with its heavy, rudderlike tail and pushing back the water with its webbed hind feet. Hodnett shows the feet and tail of the stuffed beaver, but most people are too busy trying to take pictures or looking at the real thing. By the time most cameras are ready, however, the beaver has given the water a resounding slap with its tail and gone under. Beavers can swim half a mile underwater, but this one's destination is much less than that.

"Sometimes in these coves you can hear beaver tails slapping one right after another," says Hodnett, conjecturing that the beavers warn one another of approaching danger.

We can't see below the surface of the murky water, but we are told that the beaver is swimming toward the underwater entrance of his lodge. Near the lodge but hidden underwater is the beaver's food cache, a winter's supply of tasty twigs.

The secret of the beaver's success as a master builder, Hodnett explains, lies in its teeth. Beavers are born with their formicable incisors already cut. Even if beavers didn't need to fell trees with their teeth to build dams and lodges and cut food, they'd have to chew. If they didn't gnaw on something hard their incisors would get too big and their mouths would be propped open.

Beavers mate for life, Hodnett tells us, but keep their young around for only two years. Families consist of parents, newborn and yearlings. Two-year-olds are sent out into the wide world to make their own lodges, a prace that helps avoid inbreeding.

We wonder about the occupants of the lodge. Is it a single-family lodge? Is there a Mrs. Beaver inside straightening up or nursing her kits? Will she bring them out for a swimming lesson?

But we don't see the family in the lodge, who have probably sacked out for the day. Resigned to this, we head back to the dock, counting ourselves lucky to have seen at least one beaver that isn't stuffed or made into a hat.

The electric motor purrs. Canadian geese honk overhead. Beavers sleep peacefully, protected by conservation laws. People in the boats reel in fish. The sun rises higher in the sky. All's right with the world, and there's hot coffee for sale in the snack bar at the dock.