WE present our readers this week with sketches taken by our correspondent in Nebraska.     The first drawing gives a scene where the frontiersmen is actually making improvements and acting up to the spirit, and not the letter of the pre-emption law.     There are in the Far West many such homes, tenanted only be hardworking families, with little refinement, but enjoying after their labor that peace and tranquility which the educated dweller in cities often longs for in vain.     All, however, do not work with the same appreciation of the law, as will be abundantly shown by the following incident, which came under the notice of our correspondent, and in which, indeed, he figured as one of the green 'un's.     He shall tell it in his own words:      "Come! Lay aside your paper, put away your pencils and let us have an old-fashioned ride, like those we often enjoyed through the mountains of the Old Dominion in days of yore; where we thought our equestrian feats rivaled those of the knights, in their tilts and tournaments, and we enjoyed the exciting pleasure with a better relish than ever did a prince or nobleman engage in the festivities at the Field of the Cloth of Gold. What say you?" exclaimed my enthusiastic friend, Colonel Rogers, with whom I had been spending a short time, at his pleasant Prairie Cottage, as he laid down an armful of melons, fresh from the patch. The suggestion required no repetition; and in a few minutes we were away upon the verdant prairies, mounted on a dashing pair of ponies, which, like their riders, seemed eager for their morning exercise. We followed no frequented road or beaten path, but took a dim "Indian Trail" that lead toward a broad fertile valley a few miles distant. One moment we were galloping through a grove of tall forest trees; the next, we went plunging down a steep hill-side into a narrow vale, where a gurgling stream, pure as the sparkling dew, made merry music, as its bright waters washed the pebbled banks, which were fringed with flowers and adorned with tufts of fern and luxuriant grass. Here we detained a few minutes to refresh ourselves and ponies, and again pursued our course down the glen, and soon reached the broad valley. Away across the prairie we saw an odd object, and turning our animals in that direction, soon discovered it to be a couple of regular Westernized down-easters, engaging in building what seemed to be large turkey traps. Approaching the parties, we accosted one of them.      "Many turkeys around here?"      "Turkeys indeed!" replied the frontiersman, "think there's turkeys out in the prary? Must be a stranger in these parts, or yeu'd [sic]be looking for turkeys in the timber?"      "Oh no, you are mistaken; we are not hunting, but asked the question, as you appear to be constructing a turkey trap."      "Turkey trap the d'l!" said the Yankee, somewhat nettled at our remark. "Call that premption improvement a turkey trap, du yeu ? Wal, I kinder reckon I wasn't far eout of the way when I tuck yer two coons fur green 'uns. Guess yer jest from the east'n country, and havent learnt the A B C's out here on the prarys yet? Why, stranger, everything is done different here from what it's down east, as daylight is from darkness; an. less a fellow understands heself right up to the handle, he don't stand no show at all with the cute fellows one finds out here on the frontier." [sic]      "You are right," we replied, wishing to court conversation and a development of 'frontier cuteness.' "We are not long in this country and are ignorant of many of the customs and ways of the people in this fast community, and always regard it as a kindness for a friend to post us."