A careful analysis of the planar modes of vibration of ethylene and ethylene-d₄ is carried out in order (a) to determine finally the value of the C=C stretching force constant in these key molecules, (b) to find what interactions, particularly those between the two ends of the molecules, are real, and (c) to determine the vibrational forms and the potential energy distributions in the normal modes, and how they are affected by altering the potential function. Solutions are obtained both with and without correction for anharmonicity, and estimates are made of the effects of other corrections which may be necessary. The limits found for the C=C stretching constant are 9.336, 9.388 × 10⁵ dyne/cm., with a most probable value of 9.343, the carbon atoms being uncorrected for anharmonicity. The zero-order constant is unlikely to be greater than 9.57. There is detectable real interaction between the two ends of the molecule, for both stretching and bending coordinates. Interactions are discussed.