We have not received from any friend notes of the New York Exhibition, but the following from a correspondent of the Philadelphia Ledger may give some idea of what occurred :

"The flower show was opened at the Metropolitan Opera House this forenoon. The house is floored over as for a ball, and every foot of space, from the back of the orchestra to the drop against the rear wall of the stage, has been utilized. At the back of the stage is an arrangement of mirrors so bedded in palms and moss that the perspective, or the illusion, is very fine, and the arbors seem to extend to vast distances. Hundreds of Florida and Honduras palms, of a size and beauty never before seen here, are a prominent feature. The number of roses on exhibition is 85,000; bulbous plants, 65,000; shrubs, about 20,000. On the main floor are half a dozen immense pyramids, nearly 30 feet high, built up of potted roses, azaleas and orchids. The celebrated hybrid perpetual rose, 'Her Majesty,' from Short Hills, N. J., has a table appropriated all to itself. The flower is a pale pink, measuring 6 1/2 inches across, and is supposed to be the largest flower in existence. It was fully open a week ago, when it was cut and preserved in a cold frame lor the exhibition; if the air is not too warm it is expected it will last until the end of the week.

At the Broadway entrance is a miniature Dutch garden, with an infinite variety of tulips and crocuses, while not far from the proscenium arch are to be seen orange trees in full bloom".