In 1869 Wilhelm Heinrich Waagen (1841-1900) entered the field with the study of Ammonites subradiatus.
Among the many who followed the method of attack first outlined by Hyatt, or who independently discovered his method, only a few can be mentioned here - namely, Waagen (1869), Neumayr (1871), Wiirttemberger (1880), Branco (1880), Mojsisovics (1882), Buckman (1887), Karpinsky (1889), Jackson (1890), Beecher (1890), Perrin-Smith (1897), Clarke (1898) and Grabau (1904).
Such gradations, termed " mutations " by Waagen, are distinguished, as observed, in single characters; they are the xx.
The minute gradations observed by Hyatt, Waagen and all invertebrate palaeontologists, in the hard parts (shells) of molluscs, &c., are analogous to the equally minute gradations observed by vertebrate palaeontologists in the hard parts of reptiles and mammals.
The mutations of Waagen may possibly, in fact, prove to be identical with the " definite variations " or " rectigradations " observed by Osborn in the teeth of mammals.
The essence of Waagen's law is orthogenesis, or evolution in a definite direction, and, if there does exist an internal hereditary principle controlling such orthogenetic evolution, there does not appear to be any essential contradiction between its gradual operation in the " mutations of Waagen " and its occasional hurried operation in the " mutations of de Vries," which are by their definition discontinuous or saltatory (Osborn, 1907).