Some rules will be found figured as shown in Fig. 5; in others, the right-hand upper scales are marked 10, 20, 30, etc. Again, others are marked decimally, the lower scales and the left-hand upper scales being figured 1, 1·1, 1·2, 1·3 ... 2·5, etc. The latter form has advantages from the point of view of the beginner. The method of reading the A and B scales, just given, applies only when these scales are regarded as altogether independent of the lower pair of scales C and D. Some operators prefer to use the A and B scales, and some the C and D scales, for the ordinary operations of proportion, multiplication, and division. Each method has its advantages, as will be shown, but in the more complex calculations, as involution and evolution, etc., the relation of the upper scales to the lower scales becomes a very important factor. The distance 1–10 on the upper scales is one-half of the distance 1–10 on the lower scales. Hence any distance from 1, taken on the upper scales, represents _twice the logarithm_ which the same distance represents on the lower scales. In other words, the length which represents log. N on D, would represent 2 log. N on A; and, conversely, the length which represents log. N on A, would represent (log. N)/(2) on D. Now we have seen (page 8) that multiplying the log. of a number by 2 gives the log. of the square of the number. Hence, above any number on D we find its _square_ on A, or, conversely, below any number on A, we find its _square root_ on D. Thus, above 2 we find 4; under 49, we find 7 and so on. Obviously the same relation exists between the B and C scales. THE CURSOR OR RUNNER. All modern slide rules are now fitted with a _cursor_ or _runner_, which usually consists of a light metal frame moving under spring control in grooves in the edges of the stock of the rule. This frame carries a piece of glass, mica or transparent celluloid, about 1 in. square, across the centre of which a fine reference line is drawn exactly at right angles to the line of scales. To “set the cursor” to any value on the scales of the rule, the frame is taken between the thumb and forefinger and adjusted in position until the line falls exactly upon the graduation, or upon an estimated value, between a pair of graduations, as the case may be. Having fixed one number in this way, another value on either of the scales on the slide may be similarly adjusted in reference to the cursor line. The cursor will be found very convenient in making such settings, especially when either or both of the numbers are located by eye estimation. It also finds a very important use in referring the readings of the upper scale to those of the lower, or _vice versa_, while as an aid in continued multiplication and division and complex calculations generally, its value is inestimable.