The Philadelphia Society held its annual show at the Lamb tavern, October 4, 5, and 6. The Germantown Telegraph states, in the Report of the Committee of Arrangements, that the display of horses was unusually attractive, exhibiting the various breeds for the turf, road, and farm, in considerable numbers. The Durham cattle seem at last to be getting the better of prejudice in that quarter, and in their superior forms and deep milking qualities, have shamed nearly everything else from the ground, save a few fine Devons and capital grade Durham milkers. Of sheep and swine, there were very few present, which is the more to be regretted, as these animals exist in considerable numbers and of superior breeds throughout the neighboring counties of Montgomery, Delaware, Chester, and Lancaster. Of Agricultural Implements and Products there was a good show, and the Plowing-Match proved an interesting affair. Peter A. Browne, Esq., delivered the address, which we find at length in the Farmers' Cabinet. Among other things, he contends no less strenuously than justly for the establishment of Agricultural schools and Professorships. From another part of the address we subjoin a few suggestions.

First, then, it is feared that our agricultural friends have not yet paid all the attention that the subject demands, to a judicious rotation of crops, adapted to our climate; particularly in regard to roots.

Second. Much has been done, that is beyond all praise, in insuring the best breeds of cattle. While we hear pronounced with gratitude, the names of Mease, Powell, Brantz, Clay, Gowen, and Kelley, let us not forget that the task is not finished.

Third. Soiling, it is apprehended, has been too much neglected by most American husbandmen.

Fourth. Irrigation has also been too little attended to in the United States.

Fifth. Proper care and precaution have not been sufficiently bestowed upon the selection of seeds. This is a subject of the greatest importance.

Sixth. Much is yet to be learned in regard to the preservation and economical use of manure.

Seventh. The introduction, more generally, of labor-saving machinery, and particularly of the itinerant thrashing-machine, deserves to be mentioned.

Eighth. Gardening and raising fruit are much neglected by our farmers.

It is respectfully suggested that special committees might, with advantage, be raised upon these and other useful topics, to report at the next annual meeting.

Pennsylvania contains nearly thirty millions of acres. According to the census of 1840, she had a population of one million seven hundred and odd thousands, which is nineteen acres and a fraction for each inhabitant. In 1842, she raised, of grains of all kinds, upward of sixty millions of bushels; of potatoes, nearly thirteen millions of bushels; of hay, upward of two millions and a quarter of tons; of flax and hemp, upward of three thousand three hundred tons; of tobacco, four hundred and eighty thousand tons; of silk, upward of twenty-one thousand pounds; of sugar, nearly three millions and a half of pounds; and of wines, nearly eighteen thousand gallons.

The Henrico Society held its third annual show at Richmond, Virginia, November 1st. The proceedings are published in the Richmond Enquirer. The Executive Committee reports, that although there is a falling off in its receipts, there is an increased interest and attention to its proceedings by the planters. Mr. C. T. Botts, Editor of the Southern Planter, made the address, from which we subjoin an extract.

This society was organized and has been chiefly supported by a few public-spirited gentlemen in the neighborhood. Its beneficial effects are felt and seen by all of you. To form a proper appreciation of them, you have only to ride in any direction about the suburbs of the city. Rude grounds have been converted into productive gardens, and barren wastes into smiling fields. I recollect a lady's saying to me last summer, that she meant to make her husband become a member of this society, because it had done so much to beautify the rides and walks about the city. She declared the time had been when it gave her a fit of the horrors, (she was a nervous lady,) to order her carriage for an evening drive; but that now, there was nothing that she and her children enjoyed so much. But this is not all. Let him who has been familiar with your market for the last eight or ten years, compare its present abundant supplies of the finest fruits and vegetables, with the meager exhibition of former days; and, after all, let us be as sentimental as we will, a good market plays a very important part in the comedy of human happiness. Our merchants and mechanics too should remember, that these exhibitions are annually becoming more and more attractive, and that they are by no means inefficient in increasing the trade of the city. But, over and above all considerations of dollars and cents, let us, one and all, come forward and enrol our names as members of this association, which represents the great agricultural interest of the state, and which should be the pride and ornament of its metropolis.

Lake County Society.—The show of this society took place at Medina, Ohio, and a complete account of its proceedings may be found in the Painsville Telegraph. In addition to the usual show of stock, &c., an extensive procession was got up of wagons and carriages, preceded by bands of music. One of these held no less than 35 ladies, engaged in the laudable occupations of knitting, sewing, spinning, and various other domestic employments. We wish we could chronicle more such industrial displays, for we consider them an excellent feature in agricultural shows.

Bourbon County Society of Kentucky.—We learn from the Paris Citizen, that the Eighth Annual show of this Society took place near Paris, and continued three days, and is said to be the largest and most varied ever held in Kentucky. The first two days were devoted to the exhibition of domestic animals, agricultural products, and farming implements; the third day, to that of domestic manufactures. The show of horses present was considered very superior; they were of all varieties, from the mettlesome thorough-bred, to the enormous cart-horse. The Durhams and other horned stock were well represented, and gave evidence in their splendid proportions of the superiority of Kentucky pastures. The descendants are said to be an improvement over the original importations from England. Mr. Clay was present, and had a superb pair of blankets presented him by Mrs. James Hutchcraft. These were made from the wool of Leicester sheep, and were of uncommon size and thickness, weighing 23 lbs. the pair. On the presentation of these blankets, Mr. Clay was addressed by the Hon. Garrett Davis, M. C., and he replied in his usual elegant and happy manner.

Hampshire, Hampden, and Franklin Society, Massachusetts.—The united show for the three wealthy and populous counties above, came off at the beautiful town of Northampton, on the 18th and 19th October, and we much regret on more accounts than one, that we could not, be present. The Boston Cultivator furnishes a full report. A large number of working-oxen of course were present, and to these were added some superb fat oxen, exhibited by Mr. Sumner Chapin. The committee who reported upon this subject, attributes the superiority of the cattle to the large infusion of Short-Horn blood in their veins, and hence their fine symmetry, light offal, and increased weight of flesh on the more valuable parts, as compared with native stock when fattened for the shambles. Mr. Paoli Lathrop exhibited some choice Short-Horns. Of native cows the committee thus speak:—

Of the ten cows entered for the premium as native animals, nearly or all have an intermixture of Short-Horn or other foreign blood. We awarded to Mr. Minor Hitchcock the first premium in this class. In his written statement to us it appears that her average product in milk for the six months, ending 1st October, was 49 lbs. per day, and in the months of June and July, 58 lbs. per day. In butter, her average product in the same time was more than 11 lbs. per week, and in the month of July alone, nearly 14 lbs. per week; yet in the same time he used the necessary milk and cream for his family of four persons. Your committee have entire confidence in the statement of Mr. Hitchcock; yet it is proper here to remark, that from his account of her, and though awarded, a premium as a native animal, she partakes highly of the blood of the Short-Horns. In the two classes of animals entered as of native and foreign origin it is obvious that a proper discrimination was not made; for in some of the former there is evidently more of the blood of distinct imported races than the latter. Yet your committee deemed it their duty to award the premiums of the society to the two classes as they found them.

Now here it is, most everywhere that our native cows are found excelling as milkers, we can trace a portion of their blood, (usually the greatest share,) to the Durhams, and yet there are those who are constantly decrying the Short-Horns for not being milkers. Verily a few particular people are very hard to be convinced. It is our intention hereafter to make up a table of the milking qualities of the Short-Horns and their grades, and any one possessing information upon this subject, we shall be glad by their communicating the same to us. Mr. Paoli Lathrop of South Hadley took the first premiums on Durham bulls and heifers. Mr. Ira Fenton of Belchertown on Durham cows. Mr. Sumner Chapin of Springfield, the first premiums on Fat Cattle and Working-Oxen.