The Rensselaer County Agricultural Society began holding annual public fairs in 1842 (though it had fairs from its very beginning in 1819). In 1860 changed its name to the Rensselaer County Agricultural and Manufacturers Society. Another name change, to the Rensselaer County Agricultural and Horticultural Society came later, sometime between 1873 and 1882 during which time the organization had some difficulties.

The Rensselaer County Agricultural and Liberal Arts Society (possibly under another name?) began holding annual public fairs in 1865. In 1870 it began holding them in Nassau.

For decades the two organizations both continued to have their own fairs. At some point they more or less merged:

The Schaghticoke Fair of the Rensselaer County Agricultural and Horticultural Society will be from September 1 to 4, with night shows while it lasts. The Nassay Fair of the Agricultural and Liberal Arts Society of Rensselaer County will be from August 29 to September 1.
“Fair Dates Are Announced By Commissioner; Schaghticoke, Nassau and Cambridge Among Large Number Listed.” Troy Times. May 15, 1930: 11 cols 1-2.

The Schaghticoke Fair is operated under two charters, the Rensselaer County Agricultural and Horticultural Society and the Agricultural and Liberal Arts Society, the latter being the charter of the former Nassau Fair.
“State Lists Dates For Fairs In Area.” Times Record. April 7, 1964: 23 col 5.

The combined Agricultural and Liberal Arts Society of Rensselaer County and the Rensselaer County Agricultural and Horticultural Society Fair will run through Tuesday, Sept. 4.
Bukowiecki, Helen. “Schaghticoke Fair Crews Busy For Thursday Opening.” Times Record. August 25, 1973: 7 cols 1-8.

The older of the two organizations had its earliest fairs in Batestown (formerly the southern part of the Town of Lansingburgh) and in the southernmost part of Village of Lansingburgh.

RENSSELAER CO. CATTLE SHOW AND FAIR,

Farmers, Mechanics, Manufacturers, Artists, and others,

At Troy, [Batestown,] Wednesday and Thursday, Sept. 22d and 23d.

Plan of Grounds and Buildings.

"Rensselaer Co. Cattle Show and Fair For Farmers, Mechanics, Manufacturers, Artists, and others, at Troy, (Batestown<,) Wednesday and Thursday, Sept. 22d and 23d. Plan of Grounds and Buildings." Lansingburgh Gazette. 1847.

“Rensselaer Co. Cattle Show and Fair For Farmers, Mechanics, Manufacturers, Artists, and others, at Troy, (Batestown,) Wednesday and Thursday, Sept. 22d and 23d. Plan of Grounds and Buildings.” Lansingburgh Gazette. 1847.


EXPLANATION.

A.—Grand floral Hall, 120 by 40 feet, for flowers, fruits, paintings, embroidery, ladies’ worsted and needle work of all kinds, and shell work, and choice ornamental articles in the nonenumerated and mechanical departments.
B.—Mechanic’s Hall, 108 by 24 feet; for cabinet makers’ and trunk makers’ ware, hats and caps, and other articles in the mechanical, and non-enumerated departments.
C.—Manufacturers’ Hall, 108 by 24 feet; for broad cloths, fulled cloths, cassimeres, and other woolen fabrics, calicoes, Shirtings, and other cotton fabrics, and domestic manufactures.
D.—Farmers’ and Gardners’ Hall, 60 by 24 feet; for household products, including carpeting, fulled cloth, flannel, tow cloth, bagging, hearth rugs, blankets, stockings, &c., and for farm and garden products, including butter, cheese, vegetables, corn and wheat in the ear, &c.
E.—Hall, 60 by 24 feet; for machines and stoves in operation.
F.—Sheep and swine pens.
G.—Cattle posts and railing.
H.—Carriage track.
I.—Main entrance.
K. L.—Gates for visitors.
N. N.—Offices.
O.—Flag and bulletin.
P.—Agricultural implements.
R. R.—Trains and pairs of working oxen.
S. S.—For the trial of horses.
T.—Floral Decorations.
U.—Verandah for house plants.
V. W.—Gates.
PREMIUMS

To the amount of $1500 in Cash, besides Silver Plate, Medals, Diplomas, Books, &c., are offered upon Farms, Winter Crops, Garden Vegetables, Butter and Cheese, Fruits, Flowers, Bees and Hives, Farm Stock of all kinds, Farm Implements, Household Products, Domestic Manufactures of Cotton, Woolen and mixed fabrics, Embroidery on silk, Cloth and canvass, Worsted raised and chair werk, Ladies’ Needlework of all kinds, shell work, all descriptions of Mechanics’ Work, embracing 29 classes, new inventions and works of Art, and the fine Arts.

Rensselaer County Agricultural and Manufacturers Society Fair Grounds [Batestown]  Filed November 20, 1860.

Rensselaer County Agricultural and Manufacturers Society Fair Grounds [Batestown] Filed November 20, 1860.

THE COMING INDUSTRIAL EXHIBITION.

How the Grounds Look, and what is to be Done.


[…]
The grounds of the Society are most eligibly situated between this city and Lansingburgh. The entrance from the main road is directly on this side of the tollgate, and after driving a few yards, the visitor reaches the front of the grounds, which is on the east line of the proposed avenue between Troy and its neighboring village. The north gate is reserved for the entrance of stock; the south gate for carriages, while in the centre are the ticket-offices and gates for foot-passengers.
On the grounds one cannot but be struck with their picturesque character, and the judicious manner in which they have been prepared for the purposes of this exhibition. We have never seen any Fair arrangements that struke the beholder so favorably. The general design is that of three large buildings, each 100 feet long and two stories high, situated midway between the north and south ends of the grounds, and a short distance from the entrance. Along the southerly fence are an immense number of pens for cattle, and opposite them tight stalls for horses.
Of these main buildings, the first, near the entrance, is called No. 1. The lower story is arranged for the exhibition of agricultural products, and is called Agricultural Hall. Two stairways, one for entrance; the other for exit—lead to the second floor, which is appropriated for household products, and is designated as the Ladies’ Department. This hall is 75 feet long by 20 wife, and is appropriately shelved for the handiwork of the fair exhibitors.
The north-east large building is named No. 5.—The lower floor is called Mechanics’ Hall; the upper, Horicultural and Floral Hall. The latter is 100 feet long and 20 wife. It will undoubtedly be very attractive, and with the mechanical display below, draw multitudes of visitors.
The south-east large show building, No. 3, is designated Manufacturers’ Hall, and is arranged with shelves and fixtures for the reception of all articules in this department of industry. The second story of No. 3 is the Art Gallery. It is constructed with a large sky-light, and will afford a very fine spot for th eexhibition of pictures. There is every indication that there will be a large and select display of art treasures, and that this department, which is a novel one in such exhibitions, and yet a branch of industry that stands pre-eminent, will be well cared for. Mr. J. C. Markham, the accomplished Secretary, and an artist and genuine lover of art, has this province under his special keeping. We shall look to him for a creditable representation of American art and of our first masters. [Jared C. Markham was later to be the architect of the Saratoga Monument.]
[…]
The accommodations for animals are also very extensive. Pure spring water will be conducted from the hill to the centre of the grounds, where a fountain will be in perpetual motion. The grounds will thus be beautified, while thirsty humanity and stock cattle will find refreshment.
Near the centre of the grounds is a circular course for the trial of horses, and at the easterly end is the spacious reservoir where the steam fire-engines are to draw water on the day of the grand trial. Near this point is another gate and ticket office for the accommodation of persons coming by the railroad. […]
The exhibition opens on the 19th of September, and continues in operation for nine days. There is every indication of a perfect avalanche of articles for exhibition, and of a display that will afford solid satisfaction to the many thousands who will visit it. […]
Troy Daily Whig. September 7, 1860: 3 cols 2-3.

Detail showing Rensselaer County Agricultural Society Fair Grounds in Batestown from: Lake, D. J, and S. N Beers. Map of Rensselaer Co., New York. Philadelphia: Smith, Gallup & Co. Publishers, 1861. Map. Retrieved from the Library of Congress, .

Detail showing Rensselaer County Agricultural Society Fair Grounds in Batestown from: Lake, D. J, and S. N Beers. Map of Rensselaer Co., New York. Philadelphia: Smith, Gallup & Co. Publishers, 1861. Map. Retrieved from the Library of Congress, .


Lake, D. J, and S. N Beers. Map of Rensselaer Co., New York. Philadelphia: Smith, Gallup & Co. Publishers, 1861. Map. Retrieved from the Library of Congress, .