In the Journal for October, 1923, I gave the following formulæ for the frequencies in torsional vibration of the crankshaft system (see Fig. 1) of a direct drive engine having equal throws and equal journals, viz.:—

1

and

2

where

3

c=torsional stiffness (the CI/L) of an “equivalent journal”;

p=polar moment of inertia of the “equivalent pulley” of a throw;

r=ratio of the torsional stiffness of the shaft between the airscrew and the first “ equivalent pulley,” to that of an “ equivalent journal “;

n=number of throws.