Any uncertainty in reading the result can be avoided by observing the following rule: _If in setting the index_ (1 _or_ 10) _in multiplication, or in setting the numerator to the denominator in division, it is necessary to cross the slide, then it will also be necessary to cross the slide to read the product or quotient._ THE UNIVERSAL SLIDE RULE.—In this instrument the stock carries two similar scales running from 1 to 10, to which the slide can be set. Above the upper one is the logarithm scale and under the lower one the scale of squares 1 to 100. On the edge of the stock of the rule, under the cursor groove, is a scale running from 1 to 1000. An index projecting from the cursor enables this scale to be used with the scales on the face of the rule, giving cubes, cube roots, etc. On the slide, the lower scale is an ordinary scale, 1 to 10. The centre scale is the first part of a scale giving the values of sin _n_ cos _n_, this scale being continued along the upper edge of the slide (marked “sin-cos”) up to the graduation 50. On the remainder of this line is a scale running from right to left (0 to 50) and giving the value of cos^2_n_. In surveying, these scales greatly facilitate the calculations for the horizontal distance between the observer’s station and any point, and the difference in height of these two points. On the back of the slide are scales for the sines and tangents of angles. The values of the sines and tangents of angles from 34′ to 5° 44′ differ little from one another, and the one centre scale suffices for both functions of these small angles. THE FIX SLIDE RULE.—This is a standard rule in all respects, except that the A scale is displaced by a distance (π)/(4) so that over 1 on D is found 0·7854 on A. This enables calculations relating to the area and cubic contents of cylinders to be determined very readily. THE BEGHIN SLIDE RULE.—We have seen that a disadvantage attending the use of the ordinary C and D scales, is that it is occasionally necessary to traverse the slide through its own length in order to change the indices or to bring other parts of the slide into a readable position with regard to the stock. To obviate this disadvantage, Tserepachinsky devised an ingenious arrangement which has since been used in various rules, notably in the Beghin slide rule made by Messrs. Tavernier-Gravêt of Paris. In this rule the C and D scales are used as in the standard rule, but in place of the A and B scales, we have another pair of C and D scales, displaced by one-half the length of the rule. The lower pair of scales may therefore be regarded as running from 10^{_n_} to 10^{_n_ + 1}, and the upper pair as running from √(10) × 10^{_n_} to √(10) × 10^{_n_ + 1}. With this arrangement, _without moving the slide more than half its length_, to the left or right, it is always possible to compare _all values between_ 1 _and_ 10 _on the two scales_. This is a great advantage especially in continuous working.