and practice are more closely linked. Enormous improvements have been made in the performance of gears during the last two hundred years or so, and this has been due principally to the careful attention given to the shape of the teeth. The theoretical shape of the tooth profile used in most modern gears is an involute. When precision gears are cut by modern gear-cutting machines, the accuracy with which the actual teeth conform to their theoretical shape is quite remarkable, and far exceeds the accuracy which is attained in the manufacture of most other types of machine elements. The first part of this book deals with spur gears, which are gears with teeth that are parallel to the gear axis. The second part describes helical gears, whose teeth form helices about the gear axis.