In another measuring machine on the same principle the delicacy of the measurement has been carried still farther, by substituting for the large divided wheel one having 200 teeth, which engage an endless screw or worm. This will easily be understood by reference to Fig. 31, where a similar arrangement is applied to another purpose. Imagine that a wheel like P, Fig. 31, but with 200 teeth, has taken the place of E in Fig. 30, and that the wheel, T, on the axis of the endless screw is shaped like E, Fig. 30. One turn of the axis carrying the endless screw, therefore, turns the wheel through 1/200 of a revolution, and as this axis bears a graduated head, having 250 divisions, the screw having 20 threads to the inch, is, when one division passes the index, advanced through a space equal to 1/250 × 1/200 × 1/20, or 1/1000000 an inch; that is, the one-millionth part of an inch. This is an interval so small that ten times its length would hardly be appreciated with the highest powers of the microscope, and the machine is far too delicate for any practical requirements of the present day. It will indicate the expansion caused by heat in an iron bar which has merely been touched with the finger for an instant, and even the difference of length produced by the heat radiated from the person using it. A movement of 1/1000000 of an inch is shown by the gravity-piece remaining suspended instead of falling, and the piece falls again when the tangent-screw is turned back through 1/250 of a revolution, a difference of reading representing a possible movement of the measuring surface through only 2/1000000 an inch. This proves the marvellous perfection of the workmanship, for it shows that the amount of play in the bearings of the screws does not exceed one-millionth of an inch.