This establishment occupies rooms, expressly built for its accommodation, at 13 St. Charles street, and was opened in 1844, under the personal inspection of the proprietor, Mr. G. Cooke, who is himself an artist of taste, and well known among the profession. The principal object was, to form a rallying point for the exhibition of the works of celebrated artists, both of foreign and American origin, and to dispose of such as might please the fancy of the public, at a certain fixed price. Here, visitors will have an opportunity of selecting copies and originals from a quarter that may be relied upon, works both of the old masters, and of the best of the modern schools. The proprietor is under obligations to a number of the gentlemen of this city, connoisseurs of painting, for the exhibition of some of the most prominent pieces. From R. D. Shepherd, Esq., he has a picture by Rothmel, representing De Soto discovering the Mississippi. If this artist should leave no other work, his reputation, as a genius of no ordinary ability, will remain as durable as the canvas on which he has portrayed the Spaniard and the "Father of Waters." From James Robb, Esq., whose magnificent collection of modern paintings is better known in other cities than our own, the gallery has received its richest treasures, and most valuable contributions. The chef d'oeuvre is from the pencil of a native artist now at Rome, Leutze; and illustrates this sentence in our Lord's prayer--"deliver us from evil." To speak of this gem in terms equal to its merits, would place it immeasurably above the estimation of the age in which we live. Aware that it may be considered presumption to compare living genius with the justly venerated names of the immortal dead, whose works, on account of their antiquity and intrinsic worth, are doubly valued--yet, at the risk of losing our little reputation in such matters, we venture the assertion that this picture of Leutze's will compare with the most beautiful of the Italian school, and is excelled by none in America, not excepting those of our lamented and talented Alston. This picture alone would make any gallery in Europe attractive, and the public are greatly indebted to Mr. Robb for the opportunity he has afforded them of seeing not only this, but many other brilliant productions. Here, also, is a landscape of no ordinary excellence, by Boddington, an English artist, who has most successfully represented one of his native scenes, in a style of handling peculiarly true and free. Here may be seen four of Doughty's best landscapes, and several fine specimens from the pencils of Cole and Chapman. The portrait of Col. David Crocket, as large as life, in his forest costume, by Chapman, and two large altar pieces, copied from celebrated works in the Vatican--The Entombing of Christ, after Corregio--and The Crucifixion of St. Peter, after Guido--comprise a portion of the more recent additions to the gallery.