No appropriation of public funds shall be made to any school or institution of learning not owned or exclusively controlled by the State or some political subdivision thereof; provided, first, that the General Assembly may, and the governing bodies of the several counties, cities and towns may, subject to such limitations as may be imposed by the General Assembly, appropriate funds for educational purposes which may be expended in furtherance of elementary, secondary, collegiate or graduate education of Virginia students in public and nonsectarian private schools and institutions of learning, in addition to those owned or exclusively controlled by the State or any such county, city or town; second, that the General Assembly may appropriate funds to an agency, or to a school or institution of learning owned or controlled by an agency, created and established by two or more States under a joint agreement to which this State is a party for the purpose of providing educational facilities for the citizens of the several States joining in such agreement; third, that counties, cities, towns, and districts may make appropriations to nonsectarian schools of manual, industrial, or technical training, and also to any school or institution of learning owned or exclusively controlled by such county, city, town, or school district.