Everybody peered at the 20-inch-high birch tree in a plastic sack, and Rosalynn Carter, the President's wife, beamed at it as if it were a baby on the campaign trail.

Hannelore Schmidt, if town with her husband Helmut, the chancellor of West Germany, held the tree in her hand and looked sharply at it to see the little pricks around the leaf mar-girls.

As birches go - some of which are fairly spectacular trees - this one was unimpressive, but both the National Arboretum and nature lovers in general had reason to be moderately enchanted with it. The little sprig of green was Betula uber, the Virginian round-leaf birch, which was discovered only in 1914 and rather promptly lost to cultivation. It has only recently been discovered again in Virginia creek bottoms through efforts of the arboretum.

"It turned out we had been looking in the wrong creek bottoms," said John L. Creech, arboretum director. He had this plant on hand for Schmidt, who is passionately interested in preserving rare German plants that face extinction. Schmidt also is working on a handbook for school students there to interest them in the subject.

Carter was her hostess yesterday on the visit to the arboretum, where it took only six minutes to show them a display illustrating the arboretum's aims of conservation and breeding, and to get the tree into Schmidt's hands (she said she will have it planted at the botanic garden of Bonn).

The women then walked to the bonsai collection, marvelling at the age of the small gnarled trees and especially admiring the cryptomeria-lined approach to the collection. Then, in station wagons, they rode about the arboretum grounds in northeastern Washington, where Schmidt was qucik to admire the large educational signs.

She spotted a black-eyed susan in a wild garden and recognized it immediately as an American rudbeckia. Her educational background is in mathematics and biology but she has studied botany as well, and has been on collecting trips in the Galapagos and in Kenya.

Creech, who was pleased that Carter has been to te arboretum twice within the few months she has lived here, observed that an awful lot of people have no idea where the arboretum is (24th and R Streets NE), but he would like it to become as popular as the zoo. The dwarfed Japanese trees of the bonsai collection have drawn 70,000 visitors besides Rosalynn Carter, and Creech likes to think of the tiny trees as "our pandas," to draw the public in.

They passed some crape myrtles on the tour and were told a rare and not very good-looking one from a small island south of Honshu has been used in breeding varieties resistant to powdery mildew.

Creech pointed out that rather obscure plants that nobody would choose for garden ornaments may have unique and wonderful genes of value in breeding, to confer disease resitance or some other quality lacking in their showier relatives.

Hence the value of the little birch. It is no handsomer than the common river birch, and not nearly so handsome as some of the white-barked birches, but it is genetically distinct, and nobody can say what its value might be in some future breeding program.

The party stopped a few minutes to walk about a collection of naturally dwarf conifers - grouped for ornamental effect rather than botanical relationship - and widely admired for clear and foolproof labeling.

Schmidt kept looking at the ground - the conifers are not all that dwarf, really - but at last she reached down to pick a four-leaf clover. It comes of having sharp eyes for leaf forms. She gave it to Carter who was pleased.

Then back in the cars, past the pond with the good Japanese irises, past the fine white altheas (the sterile triploid "Diana" was admired by Schmidt) and a glimpse of some fine plantings of crabs and cherries, and over yonder the big holly and fire thorn collections are maintained. No time for the daylillies or peonies or box or viburnum collections.

But it was clear that Schmidt was having a dandy time and Carter was keeping in the background as much as she could, smiling a good bit. Both women were dressed in ordinary-length dresses suitable for going to the grocery store or the arboretum, and seemed as comfortable as anybody is entitled to be on a fine July day.