Peripheral Hairlines in FaberCastell Cursors Layout and uses

Peripheral Hairlines in Faber-Castell Cursors Layout and uses 2009 -04 -30 By J. G. Fernández

Peripheral Hairlines in Faber-Castell Cursors What are “peripheral hairlines”? Central Main hairline Left peripheral hairline Right peripheral hairline Standard (or not) cursor marks In Faber Castell manuals these are also referred as “side -lines”

Peripheral Hairlines in Faber-Castell Cursors What is their main use? To enable hairline “access” to extended scales that central hairline cannot reach To transfer data in a “peripheral” hairline from one side to the other Pictures Origin: www. reglasdecalculo. com

Peripheral Hairlines in Faber-Castell Cursors Predecessors to peripheral hairlines In some former slide rules there were also two other complete hairlines q & d marks k. W & d marks However, these were only “long” cursor marks. There might be no extended scales (see annex at the end) Pictures Origin: www. sliderulemuseum. com

Peripheral Hairlines in Faber-Castell Cursors What slide rules have “peripheral hairlines”? (1) 2/82 front 2/82 back 2/82 N front 2/82 N back Pictures Origin: www. reglasdecalculo. com

Peripheral Hairlines in Faber-Castell Cursors What slide rules have “peripheral hairlines”? (2) 2/83 front 2/83 back 2/83 N front 2/83 N back Pictures Origin: www. reglasdecalculo. com

Peripheral Hairlines in Faber-Castell Cursors What slide rules have “peripheral hairlines”? (3) 62/82 62/83 front back 62/82 N 62/83 N front back Pictures Origin: www. reglasdecalculo. com

Peripheral Hairlines in Faber-Castell Cursors What slide rules have “peripheral hairlines”? (4) 63/82 63/83 front back 152/82 front 152/82 back Pictures Origin: www. reglasdecalculo. com

Peripheral Hairlines in Faber-Castell Cursors What slide rules have “peripheral hairlines”? (&5) 180/82 front 180/82 back 310/8 x series TR 1 -TR 3 series front …and more… Pictures Origin: www. reglasdecalculo. com

Peripheral Hairlines in Faber-Castell Cursors What could be their “basic” design? With only the use as secondary hairlines, -These should be near to the cursor left & right edges - If main hairline is at cursor centre, peripheral hairlines would be located symmetrically for aesthetics But, given that we have these two other lines, could we use them for another purpose? - In this example, distance from left to right is 1, 36 to convert PS in k. W Graphoplex 692 b More complex relations between peripheral hairlines and other marks may be interesting. Of course, this additional use could lead to different distances from right and left hairlines to centre one, (thus breaking symmetry)

Peripheral Hairlines in Faber-Castell Cursors But, is there such “additional” use? (1) 2/82 N front PS mark is also used as d mark, thus fixing its distance to main hairline Distance from left hairline to PS mark is to provide conversion from PS into k. W (1, 36) No “apparent” reason for Right hairline position (just to repeat back one? )

Peripheral Hairlines in Faber-Castell Cursors But, is there such “additional” use? (2) 2/82 N back Position of right hairline kept to match with other side hairline Distance from right to left hairlines is set to be the distance between 2 and e in LL 2. By doing this, conversion from Ln to Log 2 may be easily obtained Thus, This is the distance in D between peripheral hairlines! (and also applies to “red” LL’s)

Peripheral Hairlines in Faber-Castell Cursors But, is there such “additional” use? (3) 2/82 N back Example: Find log 2(8) 1. Set 8 in LL 3 with left hairline 2. Then in right hairline at D you see 3, the answer Example: Find log 2(0, 25) 1. Set 0, 25 in LL 03 with left hairline 2. Then in right hairline at D you see 2. Then the answer is -2. See other examples in the respective slide rule instruction manuals

Peripheral Hairlines in Faber-Castell Cursors But, is there such “additional” use? (&4) 2/82 N back Also, and, This means that the distance between left and right cursors also equals to the cube root of 3! (1 to 3 in K scale) Is it of any use?

Peripheral Hairlines in Faber-Castell Cursors Other examples with conversion to log 2(x) (1 a) 2/83 N front PS mark is also used as d mark, thus fixing its distance to main hairline Distance from left hairline to PS mark is to provide conversion from PS into k. W (1, 36) As K scale is in this side, cube root of 3 in D may be verified here

Peripheral Hairlines in Faber-Castell Cursors Other examples with conversion to log 2(x) (1 b) 2/83 N back Distance between left and right hairlines as between 2 and e in LL 2 Right hairline combined with A mark in C, D & CI to act also as d mark in W’s

Peripheral Hairlines in Faber-Castell Cursors Other examples with conversion to log 2(x) (2 a) 2/83 N front (English Version) HP mark is also used as d mark, thus fixing its distance to main hairline Distance from left hairline to HP mark is to provide conversion from HP into k. W (1, 34) This is different from PS to k. W and, thus, left hairline is changed! As K scale is in this side, cube root of 3 in D may be verified here

Peripheral Hairlines in Faber-Castell Cursors Other examples with conversion to log 2(x) (2 b) 2/83 N back (English Version) Distance between left and right hairlines as between 2 and e in LL 2 Right hairline combined with s mark in C, D & CI to act also as d mark in W’s

Peripheral Hairlines in Faber-Castell Cursors Other examples with conversion to log 2(x) (3) 62/82 N (English) HP mark also used as d mark Distance from left hairline to HP mark to provide conversion into k. W (1, 34) Distance between left and right hairlines as between 2 and e in LL 2 Front Back

Peripheral Hairlines in Faber-Castell Cursors Other examples with conversion to log 2(x) (&4) 62/83 N PS mark also used as d mark Distance from left hairline to PS mark to provide conversion into k. W (1, 36) Distance between left and right hairlines as between 2 and e in LL 2 Front Back

Peripheral Hairlines in Faber-Castell Cursors And two cases without such conversion (1 a) 63/82 front PS mark also used as d Right hairline is to provide PS to k. W distance from main hairline (1, 36) in A & B Distance from left hairline to PS mark to provide conversion into k. W (1, 36) The position of left and right hairlines is already fixed with distances described Pictures Origin: www. reglasdecalculo. com

Peripheral Hairlines in Faber-Castell Cursors And some cases without such conversion (1 b) 63/82 back Right and Left hairlines distances kept to match with other side hairlines Other models with such hairline distribution are 2/82, 2/83, 62/82 and 62/83 Pictures Origin: www. reglasdecalculo. com

Peripheral Hairlines in Faber-Castell Cursors And some cases without such conversion (2 a) 152/82 front Right hairline is PS mark to centre hairline (k. W) in A, B Left hairline acts as q (A) mark to centre hairline In this example peripheral hairlines are used only for common marks

Peripheral Hairlines in Faber-Castell Cursors And some cases without such conversion (2 b) 152/82 back No peripheral hairlines are used in this side No need to repeat the other side hairlines? Scales extend too little to need them? Maybe this is so because this is a “learning” model

Peripheral Hairlines in Faber-Castell Cursors Finally, one “confusing” case! (a) 63/83 front PS mark placed as c mark (1. 128) It would act as d mark if A & B existed! Distance from left hairline to PS mark to provide conversion into k. W (1, 36) q to d distances are taken from back side (no A, B!) Distance from right hairline to center (main) hairline: ~ 1, 165 If A & B existed it would be used as PS to k. W conversion! Position “copied” from 63/82 hairlines? WHY?

Peripheral Hairlines in Faber-Castell Cursors Finally, one “confusing” case! (b) 63/83 back Right and Left hairlines distances kept to match with other side hairlines Right hairline combined with q mark in C (and C, D & CI in front) to act also as d mark in W’s Although right and left hairlines “match” with 63/82 ones, there are other marks in each cursor different enough to disable interchangeability. Was this due to an intermediate manufacturing process?

Acknowledgements: Thank you for such good advice and support: - Dieter Von Jezierski - Panogiotis Venetsianos - Peter Holland - Jorge Fábregas …although any mistake is only my fault! Bibliography: Refer to slide rule manuals (2/83 N has the most complete), for explanations of said marks and hairlines

Peripheral Hairlines in Faber-Castell Cursors Annex: Historical Notes from Mr. Venetsianos (1) Most of the early one-sided slide rules had quite simple cursors counting one to three hairlines. The cursor with one single hairline As stated in the Pocketbook of the gauge marks, the metallic cursor with knife edges, as well as the cursor with a real hair-line, was not fitted to bear gauge marks. One had to wait for the framed glass cursor at the end of the 19 th century to find the first gauge marks applied to it. Many glass cursors, though, had only one central hairline which was usually scribed as one single stroke covering all the scales. To better guide the view, some hairlines where interrupted near the scales where the result had to be read. This was also applied to multiple-hairlines cursors. Later on, only the small portion of the hairline above the appropriate scale was retained. Nestler cursor for model No. 14 with interrupted hairline

Peripheral Hairlines in Faber-Castell Cursors Annex: Historical Notes from Mr. Venetsianos (2) The cursor with two hairlines Some of the early cursors for the one-sided slide rules had only one extra line, the distance between both marks, measured on the C & D lines, being equal to Their purpose was to replace the gauge mark 1, 128 of the scales and facilitate the calculation of areas of circles. The diameter was set on the D scale and the area was read off on the A scale. As there was no central hairline, the use of this cursor may have induced many errors: one had to carefully remember which hairline had been used when reporting results. Nestler cursor for model No. 14

Peripheral Hairlines in Faber-Castell Cursors Annex: Historical Notes from Mr. Venetsianos (&3) The cursor with three hairlines evenly spaced When the free-view cursors first appeared, there was more space available on them to apply sidelines. The latter had two purposes: 1. enable readings on the extended logarithmic lines; 2. replace the 1, 128 gauge mark in the calculation of areas of circles. The cursor with three hairlines unequally spaced The Electro models needed a cursor adapted to conversions from k. W to HP. This could of course be achieved by using the gauge marks 736 (for the metric HP) or 746 (for the British HP) but a supplementary hairline on the cursor was faster and easier to use. The three hairlines cursor was altered: one gap distance was set for conversions from k. W to HP, on the A & B scales, and the other gap was kept for calculations of areas of circles. The symmetry was broken. This layout had the drawback that, when the calculation was near the ends of the rule, a part of the cursor was extended out of the slide rule. Pictures Origin: www. sliderulemuseum. com

Thank You! 2009 -04 -30 By J. G. Fernández