_The Faber Log.-log. Rule._—In this instrument shown in Fig. 15, the two log.-log. scales are placed on the face of the rule. One section, extending from 1·1 to 2·9, is placed above the A scale, and the other section, extending from 2·9 to 100,000, is placed below the D scale. These scales are used in conjunction with the C scale of the slide in the manner previously described. The width of the rule is increased slightly, but the arrangement is more convenient than that formerly employed, wherein the log.-log. scales were placed on the bevelled edge of the rule and read by a tongue projecting from the cursor. [Illustration: FIG. 16.] Another novel feature of this rule is the provision of two special scales at the bottom of the groove, to which a bevelled metal index or marker on the left end of the slide can be set. The upper of these scales is for determining the efficiency of dynamos and electric motors; the lower for determining the loss of potential in an electric circuit. _The Perry Log.-log. Rule._—In this rule, introduced by Messrs. A. G. Thornton, Limited, Manchester, the log.-log. scales are arranged as in Fig. 16, the E scale, running from 1·1 to 10,000, being placed above the A scale of the rule, and the -E or E^{−1} scale running from 0·93 to 0·0001, below the D scale of the rule. These scales are read in conjunction with the B scales on the slide by the aid of the cursor. The following tabular statement embodies all the instructions required for using this form of log.-log. slide rule:— When _x_ is greater than 1. _x^n_ Set 1 on B to _x_ on E; over _n_ on B read _x^n_ on E _x_^{-_n_} Set 1 on B to _x_ on E; under _n_ on B read _x_^{-_n_} on E^{−1} _x_^{_ⁱ⁄ₙ_} Set _n_ on B to _x_ on E; over 1 on B read _x_^{_ⁱ⁄ₙ_} on E _x_^{_⁻ⁱ⁄ₙ_} Set _n_ on B to _x_ on E; under 1 on B read _x_^{_⁻ⁱ⁄ₙ_} on E^{−1} When _x_ is less than 1. _x^n_ Set 1 on B to _x_ on E^{−1}; under _n_ on B read _x^n_ on E^{−1} _x_^{-_n_} Set 1 on B to _x_ on E^{−1}; over _n_ on B read _x_^{-_n_} on E _x_^{_ⁱ⁄ₙ_} Set _n_ on B to _x_ on E^{−1}; under 1 on B read _x_^{_ⁱ⁄ₙ_} on E^{−1} _x_^{_⁻ⁱ⁄ₙ_} Set _n_ on B to _x_ on E^{−1}; over 1 on B read _x_^{_⁻ⁱ⁄ₙ_} on E If 10 on B is used in place of 1 on B, read _x_^{_ⁿ⁄₁₀_} in place of _x^n_ on E, and _x_^{-_ⁿ⁄₁₀_} in place of _x_^{-_n_} on E^{−1}. If 100 on B is used, these readings are to be taken as _x_^{_ⁿ⁄₁₀₀_} and _x_^{-_ⁿ⁄₁₀₀_} respectively. In rules with no -E scale the value of _x_^{-_n_} is obtained by the usual rules for reciprocals. We may either determine _x^n_ and find its reciprocal or, first find the reciprocal of _x_ and raise it to the _n_th power. The first method should be followed when the number _x_ is found on the E scale. EX.—3·45^{−1·82} = 0·105.