A great deal has been published, especially during the last decade, on cross-field generators—both metadynes and amplidynes. Much of this work has been concerned with the application of these machines in servo mechanisms or control systems rather than with the theory of the machines themselves, and, as a result, most authors only describe applications of the type of machine in which they are specially interested, and neglect the general theory of the machine itself.The object of this short study is the development of a generalized quantitative steady-state theory of cross-field machines of the metadyne-amplidyne type, in order to show the essential unity in that theory. The term “amplidyne” is normally used for cross-field generators in which the compensating winding is of just sufficient strength to neutralize the armature m.m.f. It will be shown that metadyne generators (which have a constant output-current property) and amplidyne generators (which have a constant output-voltage property) are two special modes of working of the same class of machine, and that between these limits there exist many other modes which fall between the two extremes.In order to avoid any ambiguity it should be stated that the term “metadyne” has not always been used in the same sense: it has sometimes been used to cover both constant-current characteristics and constant-voltage (amplifier) characteristics. The term is here used consistently to mean a cross-field generator having any degree of compensation other than 100%, or nearly this value, and thus having constant-current characteristics.The quantitative theory, given in Section 2, has been checked experimentally on two machines initially designed for use as a metadyne and as an amplidyne, respectively. The former had a solid yoke and salient poles, as in a normal d.c. machine, but the latter was built from punched laminations as in an a.c. machine, the windings being placed in slots. In Section 3, methods of determining on noload the constants of any cross-field machine are given. In Section 4, experimental results on load are shown to confirm the theory of Section 2, using constants derived as in Section 3, and close agreement is found to occur between theory and practice.