The county seat of the said county of Lea shall be established at the town of Lovington, in said county; and the board of county commissioners of said county, to be appointed as hereinafter provided, shall select and designate the plat of ground known as the public square in said town, being described on the recorded plat of said town of Lovington as block ten (10) thereof, as the place in said town upon which shall be built the courthouse and public buildings of the said county of Lea.