IT is often necessary to deduce the endurance of metals under a random succession of loads of varying magnitude from the behaviour of specimens tested with stress cycles of constant amplitude. One way of doing this is to use the cumulative damage law, whieh may be written: where N is the number of cycles of random loading required to produce fracture, pi is the fraction of these cycles with stress amplitude si, and Ni is the endurance of a specimen tested at a constant stress amplitude equal to si.