We are indebted to Thomas S. Kennedy, Esq., the energetic President of this Society, for an account of the last three weekly exhibitions, which we are compelled to condense more than we should if we could get them "one at a time." We ask the members of societies about New York to note the met, that these are weekly exhibitions, and then ask themselves if they are doing their duty, either to themselvea or the public. We wish the members of the Kentucky Society, and all others like them, the success they deserve. The proceedings and exhibitions of remote societies, aside from their own interest, afford our readers the means of judging of the local value of particular kinds of fruits, and their time of ripening in various parts of the country; and this, of itself, gives them a general interest.

The following articles were exhibited on Saturday, July 14th:

Carey, Peter, & Carey exhibited Jargonelle, Dearborn's Seedling, Osband's Summer, and Harvard Pears; Red Astrachan and Early Harvest Apples; with Apples for a name.

Jacob Johnston exhibited Early Harvest, Early Joe, Gravenstein, and Carolina Red June Apples.

Dr. J. C. Johnston exhibited a French Apple of fine size and tempting appearance, unknown in this locality.

James Stevens exhibited Bummer Queen Apples, Germantown and Dearborn's Seedling Pears, Imperial Gage Plums, and two plates of Plums for a name.

Lawrence Young exhibited Pears and Plums for a name.

Thomas S. Kennedy exhibited Herr'e Striped June Apples.

W. H. Duncan exhibited Dunne's Purple Plums.

H. S. Duncan exhibited Early Tillotson Peaches, Osband's Summer and Bloodgood Pears, Early Smith't Orleans Plums, Philadelphia Queen, Sweet Bough, and Carolina Red June Apples.

Wm. Heaver, of Cincinnati, exhibited ten varieties of Apples, viz: Early Joe, Duchess of Oldenburg, Early Bough, Early Strawberry, Summer rose, Bed Astraohan, Early Harvest, William's Favorite, (two samples, one grown on dwarf trees, and one variety not named.) Wm. Daitriek, of Indiana, Hoosier Bed Apple, Transcendent Grab, and Apples for a name. Biaaell & Salter, of New York, exhibited a beautiful specimen of German White Muscat Grapes.

Joseph Ashton, of Indiana, exhibited Dearborn's Seedling and Jargonelle Pears, and Pears for a name.

Flowers graced the tables in a few bouquets - -one of which, exhibited by Henry Nana, was exceedingly beautiful.

On Saturday, July 21, another exhibition was held, from which we gather the following: The largest display was with Pears, of which nine exhibitors had the following varieties, named in the order of their merit and quality, according to the specimens on the tables: Os-band's Summer, Tyson, Bloodgood, Dearborn's Seedling, Harvard, Jargonelle, Doyenne' d'Ete, Lawrence's Summer, (not quite ripe,) and Bartlett, (premature).

There were ten kinds of Peaches exhibited by five different growers, viz: Early York, July Seedling, Very's Seedling, Early Crawford, Early Tillotson, Cole's Early Red, Yellow Alberge, Yellow Rareripe, and Hill's Superb Jersey. The Superb Jersey was the most splendid exhibited.

In spite of the curculio, there was a very fine display of Plums. Six growers exhibited no less than ten different kinds of Plums, nearly all of which were perfect, although traces of lime on the fruit gave evidence of the watchful care that had been necessary to save them from destruction. The kinds were: Red Gage, Imperial Gage, Smith's Orleans, Bradshaw's Columbia, Lombard, McLaughlin, Duane's Purple, a red seedling from Indiana, Seedling Apricots, and several kinds of Chickasaw Plums, of which a very large red variety from Tennessee was regarded by the Society as worthy of special attention and careful cultivation.

There were nine kinds of Apples exhibited, some of which were of the very best quality, and worthy of more extended culture. The varieties were: Carolina Red June, Summer Queen, Gravensteiu, Black's Annette, Red Striped June, Indiana Seedling, Summer Hagloe, Keswick Codling, and an apple which was planted for the Summer Queen, but it proves to be superior to that variety in several respects, and, for the want of the true name, which is unknown, it has been called, for several years past, Cary's Favorite. On Saturday, July 28th, the following fruits were on the tables;

Peaches, 9 Exhibitors

Early York, (very fine,) Early Tillotson, Crawford's Early, (large,) Birkenmayer's July, Longworth's July, Hill's Superb Jersey, (monstrous,) Cooledge's Favorite, Grosse Mignonne, Vanzant's Superb, Yellow Alberge, Red Rareripe, Teton de Venus, and two unnamed Seedlings.

Apples, 8 Exhibitors

Keswick Codling, (worthless,) Summer Hagloe, Early Harvest Carnation, Alexander, (immense size,) Finley, (a splendid local fruit,) Summer Queen, Summer Pear-main, Gravenstein, Shaker's Summer, (local, very superior,) Transcendent Crab, and four unknown varieties.

Peart, 7 Exhibitors

Tyson, (delicious,) Flemish Beauty, Rostiezer, (not ripe,) Bartlett, White Doyennl, St. Ghislain, Doyenne d'Ete, Green Beurre.

Plums, 16 Exhibitors

Washington, Imperial Gage, Red Gage, Yellow Gage, Yellow Egg, Colombia, Duane's Purple, Bradshaw, McLaughlin, Reine Claude, Lombard, Smith's Orleans, and four varieties unknown.

Grapes

Black Hamburgh and Victoria Hamburgh, from Messrs. C. P. Bissell & Salter, of Rochester, N. Y. Mr. Kennedy informs us: "The fruits exhibited at the weekly shows are sold at auction, at 11o'clock, unless otherwise desired by the exhibitor, who has the privilege of withdrawing his contribution after the tale. No entrance or admittance fees are charged. The expenses of the exhibitions are paid by the retaining of twenty-five per cent of the gross sales by the Society; the balance of the sales is paid in cash to the owners of the fruits and bouquets, of which the florists in the vicinity always furnish a very fine collection. The prices generally obtained at these sales are quite satisfactory to the contributors. In the sale of the fruit on the foregoing list, one plateful, containing about eight or nine peaches, (Hill's Superb Jersey,) sold for $7 50. Other kinds of peaches sold for prices ranging from one dollar to three dollars per dozen.