Solely for the purpose of applying the provisions of Chapter 135 of the N.C. Gen. Stat. of North Carolina, “Retirement System for Teachers and State Employees, Social Security,” the institutions of this Chapter are included within the definition of the term “public school,” and the institutional employees are included within the definition of the term “teacher,” as these terms are defined in N.C. Gen. Stat. § 135-1 (1963, c. 448, s. 23; 1979, c. 462, s. 2.)