<div class="htmlview paragraph">This paper describes a method of attaching masses to a shaft in specified correction planes and eliminating resonant vibration amplitudes. It is shown that the presence of a single form of elastic deflection in the operating range requires only one correction plane and that two forms (that is, two modes of vibration) require two correction planes, and so on. A shaft that will not exhibit resonance in any mode of vibration is one in which every section of the shaft is running about its mass center, and this would require an infinite number of correction planes.</div>