[Illustration: FIG. 12.] The lines should be drawn in Indian ink with a very sharp pen and on the _under_ side of the celluloid so that the lines lie in close contact with the face of the rule. _The Radial Cursor_, another device for the same purpose, is always used in conjunction with the upper scales. As will be seen from Fig. 13, the body of the cursor P carries a graduated bar S which can be removed in a direction transverse to the rule, and adjusted to any desired position. Pivoted to the lower end of S is a radial arm R of transparent celluloid on which a centre line is engraved. A reference to the illustration will show that the principle involved is that of similar triangles, the width of the slide being used as one of the elements. Thus, to take a simple case, if 2 on S is set to the index on P, and 1 on B is brought to N on A, then by swinging the radial arm until its centre line agrees with 1 on C, we can read N^2 on A. Evidently, since in the two similar triangles A O N^2 and N _t_ N^2 the length of A O is twice that of N _t_, it results that A N^2 = 2 A N. In general, then, to find the _n_th power of a number, we set the cursor to 1 or 10 on A, bring _n_ on the cross bar S to the index on the cursor, and 1 on B to N on A. Then to 1 on C we set the line on the radial arm, and under the latter read N^{_n_} on A. The inverse proceeding for finding the _n_th root will be obvious. [Illustration: FIG. 13.] An advantage offered by this and analogous methods of obtaining powers and roots is that the result is obtained on the ordinary scale of the rule, and hence it can be taken directly into any further calculation which may be necessary. COMBINED OPERATIONS.