PageHeader : Funkcialaj Ekvacioj, 28 (1985), 1?32 Title : Rational Solutions of the Second and Title : the Fourth Painleve Equations AuthorInfo : By AuthorInfo : Yoshihiro MURATA AuthorInfo : (Tokyo Metropolitan University, Japan) section : 0. Introduction section : 1. Painleve Systems subsection : 1o Equations $P_{2}$ and $S_{2}$ subsection : 2o Equations $P_{4}$ , $S_{4}$ and $E_{4}$ section : 2. Transformations for $P_{2}$ and $P_{4}$ subsection : 1o Transformations for $S_{2}$ and $P_{2}$ subsection : 2o Transformations for $S_{4}$ and $P_{4}$ section : 3. Proof of Theorem 1 subsection : 1o subsection : 2o subsection : 3o section : 4. Proof of Theorem 2 (Necessary Conditions) subsection : 1o subsection : 2o subsection : 3o subsection : 4o section : 5. Proof of Theorem 2 (Sufficient Conditions) subsection : 1o subsection : 2o subsection : 3o section : References section : Appendix subsection : 1o subsection : 2o