At the last regular meeting of the American Geographical and Statistical Society at its rooms in the Cooper Institute, Professor Newberry, of Columbia College, delivered an address on the subject of his explorations in Utah and Arizona Territories. The speaker commenced by giving a short history of the circumstances under which the two government expeditions to which he was attached were organized. He then confined his remarks to the subject of the latter expedition, no account of which has yet been published. Its aim was principally to explore the region embraced by what is known as the old Spanish trail from Santa Fe to California. After giving an interesting account of the topography of the region traversed, he proceeded to speak of the traces which were found on every hand of a former occupancy by a numerous population now extinct. These were most numerous near the course of the San Juan river. There were found ruins of immense structures, a view of one of which he exhibited, built regularly of bricks, a foot in thickness, and about eighteen inches in length, with the joints properly broken, and as regularly laid and as smooth as any in a Fifth Avenue mansion. This structure he said was as large as the Croton reservoir. Inside were rooms nicely plastered as the walls of a modern house. There were also traces of extensive canals, which had been constructed to bring water to these towns, which were received into large cisterns. The lecturer also exhibited pieces of pottery which he said abounded everywhere, showing that in a former age all this vast region had been inhabited. He gave it as his opinion that the depopulation of this region was attributable to the fact that both to the north and the south were warlike hordes, and from the incursions of one and the other of these, the peaceable Aztecs, who had been the former denizens of the country, had been gradually wiped out. The only people left here now were the Mokies, who lived in towns inclosed within high, thick walls, and who were almost inaccessible. These people were visited, and the explorers were received by them with great hospitality. The speaker concluded by giving a short account of the manners of the people and their customs, as far as an opportunity was had to observe them.