The application of the foregoing principles to the slide rule can be shown most conveniently by describing the construction of a simple form of slide rule:—Take a strip of card about 11 in. long and 2 in. wide; draw a line down the centre of its width, and mark off two points, 10 in. apart. Draw cross lines at these points and figure them 1 and 10 on each side, as in Fig. 3. Next mark off lengths of 3·01, 4·77, 6·02, 6·99, 7·78, 8·45, 9·03 and 9·54 inches, from the line marked 1. Draw cross lines as before, and figure these lines, 2, 3, 4, 5, 6, 7, 8 and 9. To fill in the intermediate divisions of the scale, take the logs, of 1·1, 1·2, 1·3, etc. (from a table), multiply each by 10, and thus obtain the distances from 1, at which the several subdivisions are to be placed. Mark these 1·2, 1·3, 1·4, etc., and complete the scale, making the interpolated division marks shorter to facilitate reading, as with an ordinary measuring rule. Cutting the card cleanly down the centre line, we have the essentials of the slide rule. [Illustration: FIG. 3.] The fundamental principle of the slide rule is now evident:—Each scale is graduated in such a manner that the _distance of any number from 1 is proportional to the logarithm of that number_. [Illustration: FIG. 4.] “We know that to find the product of 2 × 3 by logarithms, we add 0·301, or log. 2, to 0·477, the log. of 3, obtaining 0·778, or log. 6. With our primitive slide rule we place 1 on the lower scale to 3·01 in. (which we have marked 2) on the upper scale (Fig. 4). Then over 4·77 in. on the lower scale (which we marked 3), we have 7·78 in. (which we marked 6) on the upper scale. Conversely, to divide 6 by 3, we place 3 on the lower scale in agreement with 6 on the upper, and over 1 on the lower scale read 2 on the upper scale. This method of adding and subtracting scale lengths will be seen to be identical with that used in the simple case shown in Fig. 1. THE MODERN SLIDE RULE. The modern form of slide rule, variously styled the Gravêt, the Tavernier-Gravêt, and the Mannheim rule, is frequently made of boxwood, but all the leading instrument makers now supply rules made of boxwood or mahogany, and faced with celluloid, the white surface of which brings out the graduations much more distinctly than lines engraved on a boxwood surface. The celluloid facings should not be polished, as a dull surface is much less fatiguing to the eyes. The most generally used, and on the whole the most convenient size of rule, is about 10½in. long, 1¼in. wide, and about ⅜in. thick; but 5 in., 8 in., 15 in., 20 in., 24 in. and 40 in. rules are also made. In the centre of the stock of the rule a movable slip is fitted, which constitutes the slide, and corresponds to the lower of the two rules of our rudimentary examples. [Illustration: FIG. 5.]