In using the log.-log. scales it is important to observe (1) that the values engraved on the scale are definite and unalterable (_e.g._, 1·2 can only be read as 1·2 and not as 120, 0·0012, etc., as with the ordinary scales); (2) that the upper portion of each scale should be regarded as forming a prolongation to the right of the lower portion; and (3) that immediately above any value on the lower portion of the scale is found the 10th power of that value on the upper portion of the scale. Keeping these points in view, if we set 1·1 on E to 1 on D we find over 2 on D the value of 1·1^2 = 1·21 on E. Similarly, over 3 we find 1·1^3 = 1·331, and so on. Then, reading across the slide, we have, over 2, the value of 1·1^{2 × 10} = 1·1^{20} = 6·73, and over 3 we have 1·1^{3 × 10} = 1·1^{30} = 17·4. Hence the rule:—_To find the value of x^n, set x on E to 1 on D, and over n on D read x^n on E._ With the slide set as above, the 8th, 9th, etc., powers of 1·1 cannot be read off; but it is seen that, according to (2) in the foregoing, the missing portion of the E scale is that part of the upper scale (2 to about 2·6) which is outside the rule to the left. Hence placing 1·1 to 10 on D, the 8th, 9th, etc., powers of 1·1 will be read off _on the upper part_ of the E scale. In general, then, If _x_ on the _lower_ line is set to 1 on D, then _x^n_ is read directly on that line and _x_^{10_n_} on the upper line. If _x_ on the _upper_ line is set to 1 on D, then _x^n_ is read directly on that line and _x_^{_ⁿ⁄₁₀_} on the lower line. If _x_ on the _lower_ line is set to 10 on D, then _x_^{_ⁿ⁄₁₀_} is read directly on that line and _x^n_ on the upper line. If _x_ on the _upper_ line is set to 10 on D, then _x_^{_ⁿ⁄₁₀_} is read directly on that line and _x_^{_ⁿ⁄₁₀₀_} on the lower line. These rules are conveniently exhibited in the accompanying diagram (Fig. 14). They are equally applicable to both the E and -E scales of the 10 in. rule, and include practically all the instruction required for determining the _n_th power or the _n_th root of a number. They do not apply directly to the 20 in. rule, however, for here the relation of the lower and upper scales will be _x^n_ and _x_^{100_n_}. EX.—Find 1·167^{2·56}. Set 1·167 on E to 1 on D, and over 2·56 on D read 1·485 on E. EX.—Find 4·6^{1·61}. Set 4·6 on upper E scale to 1 on D, and over 1·61 on D read 11·7 (11·67) on E. EX.—Find 1·4^{0·27} and 1·4^{2·7}. Set 1·4 on E to 10 on D, and over 2·7 on D read 1·095 = 1·4^{0·27} on lower E scale and 2·48 = 1·4^{2·7} on upper E scale. [Illustration: FIG. 14.] EX.—Find 46^{0·0184} and 46^{0·184}. Set 46 on upper E scale to 10 on D, and over 1·84 on D read 1·073 on lower E scale and 2·022 (2·0228) on upper E scale. EX.—Find 0·074^{1·15}. Using the -E scale, set 0·074 to 1 on D, and over 1·15 on D read 0·05 on -E. The method of determining the root of a number will be obvious from the preceding examples.