The paper is a contribution towards a rational quantitative theory of the tool-life problem. In the first part of the paper, the authors discuss an adiabatic theory of high-speed metal cutting, with no coolant. In machining medium-carbon steel with dry tungsten-carbide, cutting takes place under two widely different physical conditions, depending on the speed of cutting. Plastic deformation of the metal takes place as the chip crosses the tool face, and a higher temperature is developed most intensely at or near the surface of the cutting in contact with the tool face. Consequently the temperatures generated are higher—perhaps much higher—in the lower layers of the chip than elsewhere. If the speed of cutting is high, there is not sufficient time for effective diffusion of heat to take place into the colder parts of the cutting; the heat in fact stays where it is generated. The conditions are adiabatic. On the other hand, when cutting is slow enough, there is time for complete diffusion of heat to take place, whereby the temperature becomes uniform through the thickness of the chip. This is the isothermal case. It is found that these extremes occur when Reynolds thermal number (speed × thickness of chip ÷ thermal diffusivity) is large or small, respectively. In the second part of the paper, a series of experiments made by M. F. Judkins and W. E. Uecker in 1933 on tool life is examined, and a rule is given that embodies the results of these tests with unexpected accuracy. In the third and last part of the paper, a study is made of those properties of the metal cut and of the tool that affect the life of the tool. The method of dimensional analysis is applied to deduce a general form for the life-law. Judkins and Uecker's experimental result conforms to this law within the limits of the tests. But further experiment alone can confirm the general form—in its wider application.