WASHINGTON IRVING--now sixty-seven years of age--had found a resting-place at _Wolfert's Roost_, close by the scenes which lie in the immortal beauty that radiates from his pages, and when he thought that in this Tusculum he was safe from all annoying, free to enjoy the quietness and ease he had earned from the world, the same vandals laid the track through his grounds, not only destroying all their beauty and attraction, but leaving fens from which these summer heats distilled contagion. He has therefore been ill for some weeks, and as he had never a strong constitution, and has preserved his equable but not vigorous health only by the most constant carefulness, his physicians and friends begin to be alarmed for the result. Heaven avert the end they so fearfully anticipate. He cannot go alone: The honest Knickerbocker, the gentle Crayon, and the faithful brother Agapida, with Washington Irving will forever leave the world, which cannot yet resign itself to the loss of either. * * * * * Mr. SEBA SMITH, so well known as the author of the "Letters of Major Jack Downing," and to a different sort of readers for his more serious contributions to our literature, has just completed the printing of an original and very remarkable work, upon which he has been engaged about two years, entitled "New Elements of Geometry," and it will soon be published in this city by Putnam, and in London by Bentley. It will probably produce a sensation in the world of science. Its design is the reconstruction of the entire methods of Geometry. All geometers, from the dawn of the science, have built their systems upon these definitions: _A line is length without breadth_, and _A surface is length and breadth, without thickness_. Mr. Smith asserts that these definitions are false, and sustains his position by numerous demonstrations in the pure Euclidean style. He declares that every mathematical line has a definite _breadth_, which is as measurable as its length, and that every mathematical surface has a _thickness_, as measurable as the contents of any solid. His demonstrations, on diagrams, seem to be eminently clear, simple, and conclusive. The effects of this discovery and these demonstrations are, to simplify very much the whole subject of Geometry and mathematics, and to clear it of many obscurities and difficulties. All geometers heretofore have claimed that there are _three kinds_ of quantity in Geometry, different in their _natures_, and requiring units of different natures to measure them. Mr. Smith shows that there is but _one_ kind of quantity in Geometry, and but one kind of unit; and that lines, surfaces, and solids are always measured by the same identical unit.