The following short table gives the scale layouts of a number of 10 inch (actually, 25cm) log-log duplex slide rules from a few of the major manufacturers.

The first column indicates the materials from which the rule was constructed:

P Solid plastic B Bamboo, with plastic (usually celluloid) on the face Y Mahogany, with plastic (usually celluloid) on the face W Other wood, with plastic (usually celluloid) on the face M Metal, an aluminum or magnesium alloy, with scales printed or silkscreened on paint T Wood, with DuPont Teflon used for one side of the sliding rails

Specialized rules, or rules with specialized scales, have not been included in this table, so that it could be short and provide ease of comparison between the scale layouts of the rules listed.

In this table scales are identified by a uniform nomenclature to indicate what the scale did, rather than by the name appearing on the rule (this latter is the usual practice when rules are offered for sale as antiques, as is unavoidable given the wide variety of slide rule scales and their names). Also, a uniform rule has been used to designate the front and back of the rules, regardless of which side was designated the front of the rule by the manufacturer for the same reason, because this table is intended for the purpose of facilitating quick comparisons rather than for historical purposes.

Even avoiding specialized rules, some complication in nomenclature was unavoidable since it was desired to list here some older rules which used scales slightly different from those which later became standardized on later rules. Thus, S(m), used in one case, indicates an S scale like that on the Mannheim slide rule, which corresponds to the A and B scales instead of the C and D scales.

As well, the notation LL1(d), for example, indicates a log-log scale to the base 10 that spans a range intermediate between that of the LL0 and LL1 scales. A lowercase g indicates a scale composed of gauge points on two rules. The two scales labelled LL00/1 and LL02/3 on several slide rules were keyed to the A and B scales and covered the same range as the pairs of conventional inverse log-log scales noted in the names I have given them; the two scales were labelled LL0 and LL00 on the actual rules. The scale labelled LL0* on three Keuffel and Esser slide rules is an even more complicated case; this is also an inverse log-log scale keyed to the A and B scales, but its extent begins midway through LL01 and ends midway through LL03. Thus, it reaches from .97 to .05, and, as it still uses 1/e as its base, it is wrapped around the rule.

The three tangent scales on the Flying Fish 1003, although labelled tg0, tg1, and tg2 on the rule, are indeed T1, T2, and T3 scales in the notation I am using, as they cover the ranges from 5.5 degrees to 45 degrees, 45 degrees to 84.5 degrees, and 84 degrees to 89.45 degrees respectively.

Keuffel and Esser Y 4090-3 (dms) Log-Log Duplex Trig LL0* A|B K CI|T S1 S0 L LL1 DF|CF CIF C|D LL3 LL2 Y 4091-3 Log-Log Duplex Trig LL0* A|B K CI|T S1 S0 L LL1 DF|CF CIF CI C|D LL3 LL2 Y 4092 (dms) Log-Log Duplex A|B S(m) C|D LL1 LL2 LL3|C T CI|D L Y 4092-3 (dms) Log-Log Duplex LL0* A|B S(m) T C|LL3 LL2 LL1 K DF|CF CIF CI C|D L Y 4093-3 Log-Log Duplex Vector Sh1 Sh2 Th|SI1 SI2 TI|D S T L LL03 DF|CF B CI C|D LL3 LL2 Y 4080-3 68-1325 (dms) Log-Log Duplex Trig LL01 L K A|B T ST S|D DI LL1 LL02 LL03 DF|CF CIF CI C|D LL3 LL2 Y 4081-3 68-1215 Log-Log Duplex Decitrig (prior to 1947) LL00/1 LL02/3 A|B T ST S|D DI K L LL1 DF|CF CIF CI C|D LL3 LL2 Y 4081-3 68-1220 Log-Log Duplex Decitrig LL01 L K A|B T ST S|D DI LL1 LL02 LL03 DF|CF CIF CI C|D LL3 LL2 Y E4081 68-1210 Log-Log Duplex Decitrig LL01 L K A|B T ST S|D DI LL1 LL02 LL03 DF|CF CIF CI C|D LL3 LL2 Y 4082-3 (dms) Log-Log Duplex (prior to 1947) LL00/1 LL02/3 A|B T ST S|D DI F L LL1 DF|CF CIF CI C|D LL3 LL2 Y 4082-3 (dms) Log-Log Duplex LL01 L K A|B T ST S|D DI LL1 LL02 LL03 DF|CF CIF CI C|D LL3 LL2 Y 4083-3 68-1439 Log-Log Duplex Vector LL00/1 LL02/3 A|B T ST S|D Th Sh2 Sh1 L LL1 DF|CF CIF CI C|D LL3 LL2 P 4181-3 68-1287 Log-Log Duplex Decitrig LL01 L K A|B T ST S|D DI LL1 LL02 LL03 DF|CF CIF CI C|D LL3 LL2 P E4181 68-1251 Log-Log Duplex Decitrig LL01 L K A|B T ST S|D DI LL1 LL02 LL03 DF|CF CIF CI C|D LL3 LL2 P 68-1100 Deci-Lon LL03 LL02 LL01 LL00 A|B T ST S C|D DI K R1 R2 DF|CF CIF L CI C|D LL0 LL1 LL2 LL3 P (prototype) KE-Lon g Sh1 Sh2 Th A|B T ST S C|D DI K R1 R2 LL03 LL02 LL01 LL00 DF|DF CIF L CI C|D LL0 LL1 LL2 LL3 Pickett B B-1 LL00 L K A|B S ST T C|D R1 R2 LL0 LL01 LL02 LL03 DF|CF CIF CI C|D LL3 LL2 LL1 M N3 Power Log Exponential Log Log Dual Base R1 R2 K A|B ST S T1 T2 CI C|D DI Q1 Q2 Q3 LL0 LL00 LL1 LL01 DF|CF CIF Ln L CI C|D LL2 LL02 LL3 LL03 M 4 Vector Hyperbolic Log Log Q1 Q2 Q3 DF|CF T ST S CI C|D DI R1 R2 LL01(d) LL02(d) LL03(d) LL04(d) DF/M|CF/M Th Sh1 Sh2 CI C|D LL1(d) LL2(d) LL3(d) LL4(d) M N4 Vector Type Log Log Dual Base Speed Rule Q1 Q2 Q3 DF|CF CIF T1 T2 ST S CI C|D DI R1 R2 LL1(d) LL01(d) LL2(d) LL02(d) DF/M|CF/M TH Sh1 Sh2 Ln L CI C|D LL3(d) LL03(d) LL4(d) LL04(d) M 500 Ortho-Phase Log Log LL00/1 LL02/3 A|B T ST S|D K L LL1 DF|CF CIF CI C|D LL3 LL2 M N500 Hi Log/Log LL1 LL01 A|B T ST S C|D DI K LL2 LL02 DF|CF CIF L CI C|D LL3 LL03 M N803 Log Log Speed Rule Dual Base R1 R2 K A|B S ST T CI C|D DI DFM LL0 LL00 LL1 LL01 DF|CF CIF L CI C|D LL2 LL02 LL3 LL03 P Microline 140 LL01 K A|B S ST T C|D DI LL1 LL02 LL03 DF|CF CIF L CI C|D LL2 LL3 Dietzgen W 1725 Th Sh2 Sh1 A|B T1 T2 ST S|D DI K LL01 LL02 LL03 DF|CF CIF L CI C|D LL3 LL2 LL1 W 1732 Maniphase Multiplex Decimal Trig Type Log Log (same as 4081-3) LL00/1 LL02/3 A|B T ST S|D DI K L LL1 DF|CF CIF CI C|D LL3 LL2 Y 1733 Polymath Decimal Trig Type Log Log Rule LL01 L K A|B T ST S|D DI LL1 LL02 LL03 DF|CF CIF CI C|D LL3 LL2 T 1734 Decimal Trig Type Log Log LL01 K A|B T1 T2 ST S|D DI LL1 LL02 LL03 DF|CF CIF L CI C|D LL3 LL2 W 1735 Maniphase Multiplex Vector Type Log Log Rule (same as 4083-3) LL00/1 LL02/3 A|B T ST S|D Th Sh2 Sh1 L LL1 DF|CF CIF CI C|D LL3 LL2 M 1738 Multiphase Improved Decimal Trig Type Log Log Rule LL01 K A|B T1 T2 ST S|D DI LL1 LL02 LL03 DF|CF CIF L CI C|D LL3 LL2 Hemmi B 251 K A|B T S ST C|D DI L DF|CF CIF CI C|D LL3 LL2 LL1 B 259 L K A|B T S ST C|D DI LL0 LL00 LL01 LL02 LL03 DF|CF CIF CI C|D LL3 LL2 LL1 B 259D-S LL0 LL00 K A|B T S ST C|D R1 R2 L LL01 LL02 LL03 DF|CF CIF CI C|D LL3 LL2 LL1 B 260 LL00 LL0 K A|B T S ST C|D DI P L LL01 LL02 LL03 DF|CF CIF CI C|D LL3 LL2 LL1 P 254W K A|B TI SI C|D DI L LL01 LL02 LL03 DF|CF CIF CI C|D LL3 LL2 LL1 P 261 T ST K A|B BI CI C|D L P S LL01 LL02 LL03 DF|CF CIF CI C|D LL3 LL2 LL1 Post B 1460 Versalog LL01 LL02 LL03|T ST S C|D LL3 LL2 LL1 LL0 LL00 K DF|CF CIF CI C|D R1 R2 L B 44CA-600 Versalog II L LL01 LL02 LL03|T ST S C|D LL3 LL2 LL1 LL00 K A DF|CF CIF CI C|D R1 R2 LL0 W 1462 LL00/1 LL02/3 A|B K L C|LL3 LL2 LL1 T DF|CF CIF CI C|D S ST Hughes-Owens B 1773 K A|B T S ST C|D DI L DF|CF CIF CI C|D LL3 LL2 LL1 B 1777 Versalog LL01 LL02 LL03|T ST S C|D LL3 LL2 LL1 LL0 LL00 K DF|CF CIF CI C|D R1 R2 L B 341 3012 Versalog II L LL01 LL02 LL03|T ST S C|D LL3 LL2 LL1 LL00 K A DF|CF CIF CI C|D R1 R2 LL0 Ricoh/Relay B 150 LL00/1 LL02/3 A|B K CI C|D S ST T L LL1 DF|CF CIF CI C|D LL3 LL2 LL1 B 151 LL00 L K A|B S ST T C|D DI P LL0 LL01 LL02 LL03 DF|CF CIF CI C|D LL3 LL2 LL1 B 153 K A|B S ST T C|D DI L LL1 DF|DF CIF CI C|D LL3 LL2 Lafayette Radio B 99-7055 LL0 L K A|B S ST T C|D DI P LL0 LL01 LL02 LL03 DF|CF CIF CI C|D LL3 LL2 LL1 Aristo P 0908 TriLog T1 T2 A|B BI CI C|D P S ST LL1 LL2 LL3 DF|CF CIF CI C|D L K P 0968 Studio LL01 LL02 LL03 A|B L K C|D LL3 LL2 LL1 T ST DF|CF CIF CI C|D P S P 0969 StudioLog LL00 LL01 LL02 LL03 A|B BI K L CI C|D LL3 LL2 LL1 LL0 ST T1 T2 DF|CF CIF S CI C|D DI P S P 0970 MultiLog LL00 K A|B T ST S C|D DI LL0 LL01 LL02 LL03 DF|CF CIF L CI C|D LL3 LL2 LL1 P 0972 HyperLog H2 Sh2 Th K A|B T ST S P C|D DI Ch Sh1 H1 LL00 LL01 LL02 LL03 DF|CF CIF L CI C|D LL3 LL2 LL1 LL0 Faber-Castell P 52/82 L K A|B CI C|D LL1 LL2 LL3 T1 T2 DF|CF CIF CI C|D S ST P P 2/82 T1 T2 A|B BI CI C|D P S LL01 LL02 LL03 K|K L ST CF|DF LL1 LL2 LL3 P 2/82 (revised version) L T1 T2 A|B BI CI C|D ST S P LL03 LL02 LL01 K|K' C CIF CF|DF LL1 LL2 LL3 P 2/83 K T1 T2 DF|CF CIF CI C|D S ST P LL03 LL02 LL01 R2|R2 L C R1|R1 LL1 LL2 LL3 P 2/83N Novo-Duplex [Novo-Biplex] T1 T2 K A DF|CF B CIF CI C|D DI S ST P LL03 LL02 LL01 LL00 R2|R2 CI L C R1|R1 LL0 LL1 LL2 LL3 Nestler P Elemath L K A|B BI CI C|D LL1 LL2 LL3 T1 T2 DF|CF CIF CI C|D P S ST P Polymath LL01 LL02 LL03 A|B L K C|D LL3 LL2 LL1 T ST DF|CF CIF CI C|D P S P 0292 Multimath P S T1 T2 A|B K CI C|D R1 R2 L ST LL00 LL01 LL02 LL03 DF|CF CIF CI C|D LL3 LL2 LL1 LL0 Staedtler-Mars P 944-28 L K A|B ST T S C|D DI LL0 LL00 LL01 LL02 LL03 DF|CF CIF CI C|D LL3 LL2 LL1 Wolters-Noordhoff P 1200 Darmstadt-Special T1 T2 A|B BI CI C|D P S ST LL1 LL2 LL3 DF|CF CIF CI C|D K L LL0 Graphoplex P 694a Tecnilog P T2 A|B T1 ST S C|D DI K L LL3 DF|CF CIF CI C|D LL2 LL1 P 690a Neperlog LL00 L T2 A|B T1 ST S C|D P DI LL0 LL01 LL02 LL03 DF|CF CIF K CI C|D LL3 LL2 LL1 P 691a Neperlog Hyperbolic L P Ch A|B T ST S C|D Th Sh2 Sh1 LL01 LL02 LL03 DF|CF CIF K CI C|D LL3 LL2 LL1 Koh-I-Noor P 10010 Techno-Log LL01 L A|B T ST S C|D DI LL1 LL02 LL03 DF|CF CIF K CI C|D LL3 LL2 Blundell P Academy Duplex g S(m) A|B T1 T2 ST S C|D K L P DF|CF CIF CI C|D LL3 LL2 B T.50 (same as 4081-3) LL00/1 LL02/3 A|B T ST S|D DI K L LL1 DF|CF CIF CI C|D LL3 LL2 Blundell Harling P A506 Super Duplex Sh1 Sh2 Th A|B T ST S|D DI K L LL01 LL02 LL03 DF|CF CIF CI C|D LL3 LL2 LL1 Sterling Plastics P 594 Decimal Trig Log-Log LL01 K A|B T1 T2 ST S|D DI LL1 LL02 LL03 DF|CF CIF L CI C|D LL3 LL2 Leningrad W 5161-57 K A|B S ST T C|D DI L LL1 DF|CF CIF CI C|D LL3 LL2 Flying Fish P 1002 Sh1 Sh2 K A|B S P T1 T2 C|D DI L Th LL01 LL02 LL03 DF|CF CIF H1 H2 CI C|D LL3 LL2 LL1 P 1003 Sh1 Sh2 Q1 Q2 Q3|L T1 T2 T3 S ST C|D R2 R1 Th Ch LL00 LL01 LL02 LL03 DF|CF CIF H1 H2 P CI C|D LL3 LL2 LL1 LL0 P 1004 Th Ch K A|B T ST S C|D DI Sh2 Sh1 LL01 LL02 LL03 DF|CF CIF L CI C|D LL3 LL2 LL1 P 1009 Sh1 Sh2 K A|B T ST S C|D DI P Th LL01 LL02 LL03 DF|CF CIF L CI C|D LL3 LL2 LL1 P 1013 LL00 K A|S T ST C|D L LL0 LL01 LL02 LL03 DF|CF CIF CI C|D LL3 LL2 LL1

In many cases, where two slide rules from different manufacturers have the same scale arrangement, as with the Ricoh 151 and the Lafayette 99-7055, or the Hemmi 251 and the Hughes-Owens 1773, the slide rule involved is simply the same slide rule, sold under a different model number by another firm. The many different scale arrangements do indicate that for ordinary duplex log-log slide rules, whose number of scales was limited, no one arrangement of scales was clearly ideal; only when the number of scales available became larger, as on such rules as the Deci-Lon, the 2/83 N, the Aristo 0972, or the Nestler 0292, was there a greater degree of comfort in placing the scales on the rule.

The Ricoh 151 and 153 were also sold as the S.I.C. 151 and 153, and some early Versalog slide rules also bore the Hemmi 258 designation.

As far as I know, however, Hemmi never actually made any Hemmi 258 slide rules that it sold itself in Japan or anywhere else, although one web site suggests that the Versalog was modified from the Hemmi 258, which implies that the Hemmi 258 not only was sold, but had a different scale arrangement from the Versalog.

Of the arrangements above, some are archaic, specifically those where the inverse log-log scales are an afterthought, and work with the A and B scales instead of the C and D scales. While Keuffel and Esser may be the main culprit in this respect, having made such rules up until 1947, some other makers independently made slide rules of this kind; even Pickett, which specifically criticized this design as obsolete in one of its catalogs, went this way with the 500.

Other arrangements are notable. Pickett slide rules were unique in having a triple-length scale split into three parts for cube roots, instead of the K scale. A double-length scale for square roots was more common on those rules as well. I have just included one of the Pickett metal rules, the N3, for comparison here.

One of the most popular slide rules with such a double-length scale was the Versalog, made for the Frederick Post company by Hemmi, and also sold in Canada by Hughes-Owens. Because it had this double-length scale, it didn't have the A and B scales. The Versalog II did add an A scale.

The Pickett B-1 (made by Ricoh) and the Hemmi 269D-S both combined a double-length scale for square roots with the complete set of both the A scale and the B scale. The two slide rules had the same complement of scales, but arranged differently:

Pickett B B-1 LL00 L K A|B S ST T C|D R1 R2 LL0 LL01 LL02 LL03 DF|CF CIF CI C|D LL3 LL2 LL1 M N3 Power Log Exponential Log Log Dual Base R1 R2 K A|B ST S T1 T2 CI C|D DI Q1 Q2 Q3 LL0 LL00 LL1 LL01 DF|CF CIF Ln L CI C|D LL2 LL02 LL3 LL03 Hemmi B 259D-S LL0 LL00 K A|B T S ST C|D R1 R2 L LL01 LL02 LL03 DF|CF CIF CI C|D LL3 LL2 LL1 Keuffel and Esser P 68-1100 Deci-Lon LL03 LL02 LL01 LL00 A|B T ST S C|D DI K R1 R2 DF|CF CIF L CI C|D LL0 LL1 LL2 LL3 Faber-Castell P 2/83N Novo-Duplex [Novo-Biplex] T1 T2 K A DF|CF B CIF CI C|D DI S ST P LL03 LL02 LL01 LL00 R2|R2 CI L C R1|R1 LL0 LL1 LL2 LL3

The Keuffel and Esser Deci-Lon and the Faber-Castell 2/83N also have a double-length square root scale and A and B scales. However, the Faber-Castell 2/83N is different in two respects: the A and B scales aren't adjacent, but need to be used with the cursor, and the square root scales appear twice, on the slider and on the stator. Those two slide rules are listed in another category below as well, for how their log-log scales are laid out. Given that the Faber-Castell slide rule is unconventional - and if we ignore Pickett metal slide rules, which go even further in having excellent scale layouts, one can see why, in at least some senses, the Keuffel and Esser Deci-Lon could arguably be said to qualify as the "best slide rule ever", which explains why it is very popular with slide rule collectors.

The P scale is found on many European rules, but hardly ever on American rules. It was part of the Darmstadt pattern, and slide rules of that type were also made by both Hemmi and Ricoh. But they also included it on a very few duplex slide rules. One of these, the Hemmi 260, is noted for having a very good scale arrangement for an ordinary log-log slide rule, and some other slide rules were made with very similar scale arrangements:

Hemmi B 260 LL00 LL0 K A|B T S ST C|D DI P L LL01 LL02 LL03 DF|CF CIF CI C|D LL3 LL2 LL1 Ricoh/Relay B 151 LL00 L K A|B S ST T C|D DI P LL0 LL01 LL02 LL03 DF|CF CIF CI C|D LL3 LL2 LL1

When a duplex slide rule has both log-log and inverse log-log scales, typically they are arranged so that most of the log-log scales, and most of the inverse log-log scales, are on one side of the rule, but one of each group of scales is on the other side of the rule. This was true even when those sets of scales each consisted of three scales instead of four, because the slide rules involved had room for fewer scales in total.

A few slide rules, however, kept all the log-log scales of each group together, and were noted for this. One of the most notable slide rules of this type was the Keuffel & Esser Deci-Lon slide rule, which made room for this by having one of the stator arms of the rule visibly wider than the other, giving the slide rule a unique appearance.

But there were others. Many Pickett rules achieved this, since these rules often made the scales more compact by having pairs of scales face towards a single line. Slide rules by Aristo are also notable for having achieved this; being made of plastic, perhaps it was thought the expense of making them a bit wider would no longer be inordinate.

Keuffel and Esser P 68-1100 Deci-Lon LL03 LL02 LL01 LL00 A|B T ST S C|D DI K R1 R2 DF|CF CIF L CI C|D LL0 LL1 LL2 LL3 Aristo P 0969 StudioLog LL00 LL01 LL02 LL03 A|B BI K L CI C|D LL3 LL2 LL1 LL0 ST T1 T2 DF|CF CIF S CI C|D DI P S Faber-Castell P 2/83N Novo-Duplex [Novo-Biplex] T1 T2 K A DF|CF B CIF CI C|D DI S ST P LL03 LL02 LL01 LL00 R2|R2 CI L C R1|R1 LL0 LL1 LL2 LL3 Pickett M N3 Power Log Exponential Log Log Dual Base R1 R2 K A|B ST S T1 T2 CI C|D DI Q1 Q2 Q3 LL0 LL00 LL1 LL01 DF|CF CIF Ln L CI C|D LL2 LL02 LL3 LL03

Of course, the Faber-Castell also was unique in having two pairs of R1 and R2 scales (labelled W1 and W2) that slid against each other for ease in multiplication with higher precision.

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