What's up with this scale? Isn't it just a scale over-range extension? Nope. It's pretty clever actually, and totally, completely unique. Here's what Relay themselves had to say about it! The following is all excerpted from the 1959 RELAY DUPLEX SLIDE RULES instruction manual. In the front of the manual, going through the available scales on their rules, they say the LL'1 scale is "...used with C and D scales. This LL'1 scale is deviced by us to substitute LL1 and LL0 scales." (sic). I will here point out that 1. their spelling isn't reel good, and 2. in the manual, they refer to the scale as LL'1, but on the rule itself it looks more like LL1'. Oh well. On page 15 we begin the usage of this unique scale. " As a extension of the C scale there is a very short scale at the right end of the C scale marked from 1 to 1.1 in red. This minute scale called LL'1 is invented in our laboratory to substitute the several lower LL scales in calculation of ln x, x to the y power, and e to the x power, etc. " I won't give all the instructions, but from what I'll give users will see that this thing really works. In fact, it's a pretty darn good way to save some space to use for other scales, and I'll point out that that is exactly what they did on the 157. "Natural logarithms: ( ln x ) when x is nearly equal to 1, its natural logarithm is approximately equal to x-1. But using LL'1 scale we can obtain its value more precisely. The procedure is: A. opposite (x-1) on D, set the hairline. B. Opposite the hairline, set x on LL'1. C. Opposite right index of C, read answer on D. Example: ln 1.05 = 0.0488. In ordinary slide rule we use the LL1 and D scales, and read the result on the LL1 scale. A. Opposite .05 on D, set 1.05 on LL'1. B. Opposite right index of C, read 0.0488 on D." "Computation of x to the y power. Using the LL'1 scale, we can compute the form x^y without LL1 and LL0 scales. Example 1. 1.06^2.68 = 1.169. In ordinary slide rule we use the LL1 and CI scales, and read the answer on the LL2 scale. A. Opposite .06 on D, set 1.06 on LL'1. B. Opposite 2.68 on C, read 1.169 on LL2. Example 2. 1.008^14.8 = 1.125. Without the ordinary LL0 scale this computation can be done. A. Opposite .008 on D, set 1.008 on LL'1. B. Opposite 14.8 on C, read 1.125 on LL2."
Additional examples are given for fractional powers, and powers of e using this little scale. The 157 already has an impressive scale layout, as it was intended for electronic engineers. About the 157, Relay said it was designed for the Expert Electrical Engineer, and was made to handle all normal computations, and all vectorial and hyperbolic computations/functions too. And, without this tiny little LL'1 scale, there wouldn't have been room for all the specialized scales in addition to a good selection of "normal" scales. An impressive and capable rule, and partly due to one tiny little overlooked scale! |