By keeping these points in view, the number of digits in the cube (N) of a given number (_n_) are readily deduced. Thus, if the units scale is used, N = 3_n_ − 2; if the tens scale, N = 3_n_ − 1; while if the hundreds scale be used, N = 3_n_. Placed in the form of rules:— N = 3_n_ − 2 when the product is read on the L.H. scale of A with the slide to the _right_ (units scale). N = 3_n_ − 1 when the product is read on the R.H. scale of A; slide to the _right_ (tens scale). N = 3_n_ when the product is read on the L.H. scale of A with the slide to the _left_ (hundreds scale). With decimals the same rule applies, but, as before, the number of digits must be read as −1, −2, etc., when one, two, etc., cyphers follow immediately after the decimal point. EX.—Find the value of 1·4^3. Placing the L.H. index of C to 1·4 on D, the reading on A opposite 1·4 on the L.H. scale of B is found to be about 2·745 [2·744]. EX.—Find the value of 26·4^3. Placing the L.H. index of C to 26·4 on D, the reading on A opposite 26·4 on the L.H. scale of B is found to be about 18,400 [18,399·744]. EX.—Find the value of 7·3^3. In this case it becomes necessary to use the R.H. index of C, which is set to 7·3 on D, when opposite 7·3 on the L.H. scale of B is read 389 [389·017] on A. EX.—Find the value of 0·073^3. From the setting as before it is seen that the number of digits in the number must be multiplied by 3. Hence, as there is −1 digit in 0·073, there will be −3 in the cube, which is therefore read 0·000389. The last two examples serve to illustrate the principle of factorising with powers of 10. Thus 0·073 = 7·3 × 10^{−2}; 0·073^3 = 7·3^3 × (10^{−2})^3 = 389 × 10^{−6} = 0·000389. _Cube Root_ (_Direct Method_).—One method of extracting the cube root of a number is by an inversion of the foregoing operation. Using the same scales, _the slide is moved either to the right or left until under the given number on A is found a number on the_ L.H. _B scale, identical with the number simultaneously found on D under the right or left index of C_. This number is the required cube root. From what has already been said regarding the combined use of these scales in cubing, it will be evident that in extracting the cube root of a number, it is necessary, in order to decide which scales are to be used, to know the number of figures to be dealt with. We therefore (as in the arithmetical method of extraction) point off the given number into sections of three figures each, commencing at the decimal point, and proceeding to the left for numbers greater than unity, and to the right for numbers less than unity. Then if the first section of figures on the left consists of— 1 figure, the number will evidently require to be taken on what we have called the “units” scale—_i.e._, on the L.H. scale of A, using the L.H. index of C.