The object in making the following investigation was to facilitate the obtaining of a more accurate determination of the reactance of the end turns of rotating alternating current machinery. Such formulae as are available at present are, as far as the author knows, based on incorrect assumptions, or fail to consider the various factors present. The accuracy of the results obtained when using such formulae is very small. Often the calculated reactance will not be within 400% of the correct value. Because of this, it was felt that a more accurate analysis of this problem would be of value, chiefly to the designing engineer. In this report, the "end turns" of the machine windings are considered to be the part of the turns of the coils on the armature of the machine not lying in armature slots. These turns, the connecting conductors between the armature bars, lie against each other in a belt extending around the circumference of the armature. In nearly all motor coils, the end turns consist of a short section extending straight out from the armature slot, a much longer section bent nearly parallel with the core, an abruptly curved end section, and two lengths similar to the first two. It is obvious that the accurate determination of the inductance of such coils must take into account the peculiar shape of the coils and the effect of the coils upon each other. It is this second effect which is usually neglected in determinations of the reactance. Actually this mutual inductance is of greater importance than the self inductance of the coils.