Their number as shown by the agricultural statistics collected in 1839, by order of our General Government, was 15,000,000 neat cattle; 4,335,000 horses and mules, (the number of each not being specified;) 19,311,000 sheep; and 26,300,000 swine. There is much reason to question the entire accuracy of these returns, yet there is doubtless an approximation to the truth. Sheep have greatly increased since that period, and would probably number, the present year, (1848,) not less than 30,000,000; and if our own manufactures continue to thrive, and we should moreover become wool exporters, of which there is now a reasonable prospect, an accurate return for 1850, will undoubtedly give us not less than 33,000,000 for the entire Union. There has been a great increase in the value of the other animals enumerated, but not in a ratio corresponding with that of sheep. This is not only manifest in their augmented numbers, but in the gradual and steady improvement of the species. It may be safely predicted, that this improvement will not only be sustained, but largely increased; for there are some intelligent and spirited breeders to be found in every section of the country, whose liberal exertions and successful examples are doing much for this object. Wherever intelligence and sound judgment are to be found, it will be impossible long to resist the effects of a comparison between animals, which, on an equal quantity of the same food, with the same attention and in the same time, will return 50, 20, or even 10 per cent. more in their intrinsic value or marketable product, than the ordinary class. This improvement has been, relatively, most conspicuous in the Western and Southern states; not that the present average of excellence in their animals surpasses, or even reaches that of the North and East; but the latter have long been pursuing this object, with more or less energy, and they have for many years had large numbers of excellent specimens of each variety; while with few exceptions, if we exclude the blood-horse or racing nag, the former have, till recently, paid comparatively little attention to the improvement of their domestic animals. The spirit for improvement through extensive sections, is now awakened, and the older settled portions of the country may hereafter expect competitors, whose success will be fully commensurate with their own. Before going into the management of the different varieties, we will give some general principles and remarks applicable to the treatment of all. _The purpose for which animals are required_, should be first determined, before selecting such as may be necessary either for breeding or use. Throughout the Northeastern states, cows for the dairy, oxen for the yoke, and both for the butcher, are wanted. In much of the West and South, beef alone is the principal object; while the dairy is neglected, and the work of the ox is seldom relied on, except for occasional drudgery.