The present investigation is concerned with the fact that crankshaft-propeller torsional oscillations are coupled to the torsional oscillations of the engine as a whole. The basic phenomenon was discussed by Den Hartog and Butterfield in the elementary case of a single radial engine with a single resonant frequency on the suspension. A general method of calculation is presented for long crankshaft engines. I t is an extension of Biot's method, where, in addition to the usual dynamic moduli at both crankshaft ends, the solution contains the dynamic modulus of the engine suspension plus air frame with respect to the harmonic torque exerted by the crankcase. (1) INERTIA COUPLING BETWEEN CRANK ASSEMBLY AND CRANKCASE MOTION L 4>x BE the angular coordinate of the xth crankpin with respect to the crankcase and \p be the angular coordinate of the crankcase. The complete expression for the kinetic energy of the crank assembly is a quadratic, homogeneous expression in the angular velocities $x and \p Tx = (1/2)^/(0*) + UxM(4>x) + (1 /2)^7(0.) The coefficients are periodic functions, of which only the mean values I, M, and V will be considered. For instance, in the case of a single piston per crankpin, these coefficients are: M = Ie + 6K [1 (H/L)] Ic =M+\R* i + 4JJX , H J bH(L H)'