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FIG. 91.-Section of a 10-inch plain Mannheim Rule, showing face scales, A, B, C, and D.

FIG. 92.-Reverse of same rule, showing S, L, and T scales on back of slide.

therefore the squares of the aligned readings on the two lower scales when the indexes are in alignment.

On the reverse side of the slide are sine and tangent scales and a scale of logarithms, which can be read by the index marks on the end notches or transparent plate at the back of the rule, or by inserting the slide turned over, and using the runner.

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FIG. 93. Section of Linear scale on beveled edge of Mannheim rule.

On the beveled edge of the Mannheim rule is an English scale, and on the opposite edge a metric scale which, in some rules, is continued along the channel of the rule.

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FIG. 93A.-Section of Metric scale on lower edge of Mannheim rule.

Some of the modifications of this arrangement of scales are as follows:

(1) An inverted scale in place of the direct B scale.

(2) The sine scale instead of being on the back of the slide is placed in the middle of the face of the slide, between scales B and C. In place of the sine scale on the back of the slide, is an inverted B or C scale.

(3) Instead of the metric scale on the edge of the rule a scale of the cubes of readings on the D scale, the hair-line being carried down on a tongue on the runner, as in the POLYPHASE and the MULTIPLEX.

(4) The stock widened to carry the cube scale below the D scale, A and C scales on the upper part of the stock, and on the slide two C scales with inverted C or CI between, as in the TRIPLEX.

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(5) A two-faced rule with A, B, sine, C and D scales on one face; and A, BI, tangent, CI, and D scales on the reverse, with an L scale (scale of logarithms) on the lower edge or lower stock, as in the DUPLEX.

(6) Stock widened to carry in addition to the scales of (5) on the reverse, a continuous log log scale mounted in three sections on the upper stock, giving direct readings for exponentials, logarithms to base e or any other base, and any power or root, as in the LOG LOG DUPLEX.

This rule has a C scale in place of the BI scale, and the widened lower stock has the L scale on its face below the D scale.

283. Graduation of the A and B Scales. Examine the upper or A scale on your rule. Observe the graduation

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FIG. 95.-Section of a 10-inch Multiplex Rule. The first half of the B scale is inverted, but the scale is not marked BI because the second half is direct.

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FIG. 96.-Section of a 10-inch Triplex Rule. The scales reading from the top are A, C, CI, C, D, and K.

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FIG. 97.-Section of Duplex Rule showing face scales.

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FIG. 98. Section of Duplex Rule, showing scales on back.

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