The direct fractional-reading micrometer shown in Fig. 39 is the result of talks with many mechanics in which all agreed that such a feature added to a micrometer would, by making it both a fractional and decimal gage, more than double its practical value. While approximate readings in 64ths, etc., may be obtained by the graduations on the barrel _B_ as on an ordinary inch scale, the exact readings of 64th, etc., may be obtained only by reference to graduations on the movable thimble _A_. There are but eight places on _A_ which coincide with the long graduation line on _B_ when any 64th, 32d, 16th, or 8th is being measured, and each of these eight places is marked with a line, and the 64th, 32d, 16th, or 8th for which that line should be used is marked thereon. (See _a_ and _b_, Fig. 40.) The line _a_ would be used for 3/32, 7/32, 11/32, etc., and the line _b_ for 1/64, 9/64, 17/64, etc. Now suppose we wish to accurately measure 15/32 inch. We first roughly read it off the inch scale on sleeve _B_ by turning out thimble _A_. Having secured it closely by drawing edge of _A_ over that graduation, we find that the line _a_ (Fig. 40) on the movable thimble very nearly or exactly coincides with the long graduation line on _B_. When these lines coincide, we have the exact measurement of 15/32 inch without reference to how many thousandths may be contained in the fraction. Thus all through the scale any fraction may be found instantly. There is no mental arithmetic, use of tables, or memory work in using the tool. The new graduations are independent of the old, and may be used equally well with or without them. [Illustration: Fig. 40. Graduations on the Fractional-reading Micrometer] Micrometers may also be graduated as in Fig. 41. Instead of using the zero line on _A_ as a base line, a point is taken one-fifth of a turn around _A_, and the graduated scale on _B_ is placed to correspond, as shown in the engraving; also, instead of making lines _a_, _b_, etc., on _A_, full length, they are made about half an inch long, and the numerators are entirely omitted and the denominators placed at the end instead of under the line. To the ordinary user of the tool, this is all that is necessary for a perfectly clear reading of the fractions.[20] [Illustration: Fig. 41. Another Method of Graduating for Fractional Reading] Sensitive Attachment for Measuring Instruments No matter how finely and accurately micrometers and verniers may be made, dependence must in all cases be placed on the sensitiveness of a man's hand to obtain the exact dimensions of the piece to be measured. In order to overcome this difficulty and eliminate the personal equation in the manufacture of duplicate and interchangeable parts, the sensitive attachment to the micrometer shown in Fig. 42 may be used, and will be found of much value. [Illustration: Fig. 42. Sensitive Micrometer Attachment]