The National Symphony embarked on the second all-Tchaikovsky program of the week last night at the Kennedy Center. Under the eager baton of Mstislav Rostropovich, they captured, unfailingly, the spirit if not always the letter of the score.

There were relatively unfamiliar pieces on the first half of the program: to begin with, the rollicking "Cossack Dance" from the opera "Mazeppa," propelled with momentum and enthusiasm and let the details fall where they may.

The Suite No. 3 that followed was full of the sorts of lovely, broad lyricism that the orchestra is so good at. This is vintage Tchaikovsky, painted with the full sweep and drama that characterizes his symphonies, and why it isn't played more often is a mystery. The contrasts in the third movement between winds and strings had a sophisticated delicacy and coordination that was a delight. Throughout this movement, however, there was a feeling that every down-beat was anticipated, an unsettling sensation that sapped the music of much of its rhythmic backbone.

Pianist Andre Watts joined the orchestra after intermission for a performance of the Piano Concerto No. 1, and, together, Watts, Rostropovich and Tchaikovsky made a formidable trio. The incisiveness of Watts' impeccable pianism lent an edge to the orchestral playing that had not been there earlier. His remarkable strength gave the piece excitement, but his musicianship gave the second movement its poetry. Taken very slowly, with voices from the orchestra speaking intimately, this was the evening's finest hour.