All land mentioned in §§ 11, 12 and 15 of Article VII, of the Constitution of the State of Texas, now belonging to the University of Texas shall be subject to† taxation for county purposes to the same extent as lands privately owned; provided they shall be rendered for taxation upon values fixed by the State Tax Board; and providing that the State shall remit annually to each of the counties in which said lands are located an amount equal to the tax imposed upon said land for county purposes.