(f) The thickness of the feed or shaving
(g) The effect on cutting speed of using water or other cooling medium on the tool.
Third. The best methods of analyzing the driving and feeding power of machine tools and, after considering their limitations as to speeds and feeds, of deciding upon the proper counter-shaft or other general driving speeds.
Fourth. After the study of the first, second, and third problems had resulted in the discovery of certain clearly defined laws, which were expressed by mathematical formulæ, the last and most difficult task of all lay in finding a means for solving the entire problcLii which should be so practical and simple as to enable an ordinary mechanic to answer quickly and accurately for each machine in the shop the question, "What driving speed, feed, and depth of cut will in each particular case do the work in the quickest time?"
In 1881, in the machine shop of the Midvale Steel Company, the writer began a systematic study of the laws involved in the first and second problems above referred to by devoting the entire time of a large vertical boring mill to this work, with special arrangements for varying the drive so as to obtain any desired speed. The needed uniformity of the metal was obtained by using large locomotive tirea of known chemical composition, physical properties and hardness, weighing from 1,500 to 2,000 pounds.
For the greater part of the succeeding 22 years these experiments were carried on, first at Midvale and later in several other shops, under the general
