Every tract of land of one thousand acres or less, lying in more than one county, may be entered for taxation on the land book of the county where the greater part thereof in value lies, but the entry thereof and payment of taxes thereon, in any county where any part thereof is situated, shall, for the time during which the same is so entered and paid, be a discharge of the whole of the taxes and levies charged and chargeable thereon. Every tract of land of more than one thousand acres, lying in two or more counties, shall, for the purpose of taxation, be entered and charged with all taxes in each tax district of the several counties in which any part of it is, to the extent, as near as may be, that the same lies in such district. When any such tract of more than one thousand acres is thus assessed, partly in one county and partly in another, the several officers of such counties whose duty it is to make out the landbooks of the respective counties shall value the part lying in his county without regard to the value of the whole tract, and he shall ascertain its value, as in other cases, according to the rule prescribed in this chapter.