The Theorem of Three Moments in a simple form, referring to bending moments at any three consecutive supports A, B, C, of a continuous beam uniform in each bay, AB = a, BG = c, takes the form

w and being constant load intensities over AB and CB respectively.

On p. 159, Vol. 42 (1938), of this journal, Capt. J. Morris discussed a modification in this case (and in the more general case when the beam is in thrust) when the load intensity varies according to a parabolic law.

In reference 1 Biot has given a simple and valuable formula for what he calls the “ dynamic modulus “ of a flywheel system or airscrew in terms of resonance and anti-resonance frequencies. The resonance frequencies are the natural frequencies when the systems are free, and the anti-resonance frequencies are the natural frequencies when the end of the flywheel shaft (or the airscrew boss) is fixed. The dynamic modulus is defined to be the ratio of the amplitude of the applied periodic couple to the amplitude of the angular movement produced at the point of application, and is a function of the frequency of the periodic couple. A very useful application of the dynamic modulus can be made to engine-propeller systems, for the natural frequencies of the combination are such that the dynamic moduli of the two components are equal and opposite.