Set cursor to 2·86 on A and drawing the slide to the right find 1·42 under 1 on C, when 1·42 on B is under the cursor. Then reading under 1, ∛(10) and ∛(100,) we have ∛(2·86) = 1·42; ∛(28·6) = 3·06 and ∛(286) = 6·59. It will be seen that factorising with powers of 10, we multiply the initial root by ∛(10) and ∛(100). Obviously the three roots will always be found on D, in their natural order and at intervals of one-third the length of the rule. The number of digits in the roots of numbers which do not lie between 1 and 1000, is found as before explained. In any method of extracting cube roots in which the slide has to be adjusted to give equal readings on B and D, the author has found it of advantage to adopt the following plan:—The cursor being set to, say, 4·8 on A, bring a near _main_ division line on B, as 1·7, to the cursor; then 1 on C is at 1·68 on D. The difference in the readings is two small divisions on D, and moving the slide forward by _one-third the space representing this difference_, we obtain 1·687 as the root required. With a little practice it is possible to obtain more accurate results by this method than by comparing the reading on D with that on the less finely-graded B scale. MISCELLANEOUS POWERS AND ROOTS. In addition to squares and cubes, certain other powers and roots may be readily obtained with the slide rule. _Two-thirds Power._—The value of N^⅔ is found on A over ∛̅N on D. The number of digits is decided by the rule for squares, working from the number of digits in the cube root. It will often be found preferable to treat N^⅔ as N ÷ ∛̅N, as in this way the magnitude of the result is much more readily appreciated. _Three-two Power._—N^{³⁄₂} can be obtained by cubing the square root, deciding the number of digits in each process. For the reason just given, it is preferable to regard N^{³⁄₂} as N × √̅N. _Fourth Power._—For N^4 set the index of C to N on D and over N on C read N^4 on A; or find the square of the square of N, deciding the number of digits at each step. _Fourth Root._—Similarly for ∜̅N, take the square root of the square root. _Four-third Power._—N^{⁴⁄₃} = N^{1·33} (useful in gas-engine diagram calculations) is best treated as N × ∛̅N. Other powers can be found by repeated multiplication. Thus setting 1 on B to N on A, we have on A, N^2 over N; N^3 over N^2; N^4 over N^3; N^5 over N^4, etc. In the same way, setting N on B to N on D, we can read such values as N^¾, N^⅞, etc. POWERS AND ROOTS BY LOGARITHMS. For powers or roots other than those of the simple forms already discussed, it is necessary to employ the usual logarithmic process. Thus to find _a^n_ = _x_, we multiply the logarithm of _a_ by _n_, and find the number _x_ corresponding to the logarithm so obtained. Similarly, to find _ⁿ√̅a_ = _x_ we divide the logarithm of _a_ by _n_, and find the number _x_ corresponding to the resulting logarithm.