### Original Odhner LUSID

A recent find, and one of the most whimsical, counterintuitive and plain ridiculous pinwheel calculators ever to be manufactured. I have been dying to get my hands on one, and now that it is in the collection, I was happy to be able to document how the machine actually functions, since it had to be disassembled anyway due to a number of problems.

This, N° 68369, is the early version with the butterfly clearing screws. I though I was on to something when I got LuSiD N° 68382, which had clearing cranks intead of butterflies. However, on rechenmaschinen-illustrated, there is a N° 78129 with butterflies, and I have also seen N° 89831, which also has butterflies. Other Odhner models carry butterflies until at least in the 90000 range of serial numbers, so either they were not very consistent in the Odhner factory, or the carriage of LuSiD 68382 was replaced or repaired later. A repair is not as simple as taking off the butterfly and putting a crank in its place, so someone invested a bit of time and parts. This machine was not functional when it came to me, which turned out to be down to incorrect reassembly after an attempted repair of some sort. Not being able to see how it ought to function prior to taking it apart was not conducive to a relaxed and stress-free repair though. After shifting back the coupling wheel for the Mult/Div lever one tooth, suddenly everything freed up as it should with the crank in the rest position, and the rest was a question of some light cleaning and reassembly. Here is the complete and reassembled machine:

The Odhner LUSID is a machine intended for the English currency as it was prior to 1971. The short explanation is that 1 pound sterling (LU) equalled 20 shillings (SI) which in turn each equalled 12 pennies (D). In other words, 240 pennies equalled one pound. Calculation and conversion of currency always was a big problem in the UK, as the currency system, not being in base 10, could easily make your head spin when trying e.g. to count how much 3123 items at 1s 7 and 3/4 pennies each would set you back. (The answer, in case you're wondering, is £256, 19 s, 11 1/4 d) Or worse, if the total cost would be £576 8s 6d, for 96356 articles - what is the price per article ? Or even worse still- how much would 115 and 11/12th of a yard of fabric cost at 1s 7 1/2 d per yard ? The only solution was to convert everything to decimal fractions of pounds (or yards) and count with those. That is long and laborious work, and bright minds at the Odhner factory thought it would make a good business model to construct a machine especially for these kinds of currency calculations. I guess the amount of machines that remain today are a good indication of how much of a success it really was ... not so much, then.

I am sure you already have a sinking feeling about it too, even with only a vague concept of the required features - and those are the following: it should be able to count in decimal fractions (easy, any Odhner can do that), but it should also be able to correctly add and carry decimal fractions of pennies, whole pennies (base 12), shillings (base 20) and pounds. In addition, it would be desireable to get the result not just in decimal fractions of pounds, but also in the equivalent in shillings, pennies and fractions of pennies (not decimal fractions of pennies, but e.g. 3/4 penny).

So far then for conversion in the result register - but what about the multiplication register ?

The answer of the Odhner engineers to that particular conundrum was as simple as it was insane. Essentially, shillings and pennies could only be added in a particular spot in the multiplication register, thus making the Odhner LUSID into a machine with a fixed carriage/comma. It is not entirely fixed, there is some freedom of movement possible but not over all that many positions. In order to also accommodate simple base 10 calculations, and some variation in the sizes of numbers, the register has two settings. Here is a picture of the carriage. The three red numbers are shillings (leftmost 2 positions) and pennies (right numeral wheel, which counts up to 11 instead of 9). The section to the right of the red wheels reads decimal fractions of pennies.

There is a fixed comma in the 8th position of the setting register (indicated by a round dot), and if the machine is adapted to that with two levers, one on the machine itself, and one on the carriage (only moveable when the carriage is completely to the right), the multiplication register simply counts in base 10, using the 6 £ positions, and the shillings and pennies digits. Sadly, the pennies digit still counts up to 11 before carrying, and there isn't much to be done about that. It of course also means that you cannot put more than £99 in the setting register, but since the multiplication register counts decimally in this case anyway, it is possible to use a floating comma.

There is another fixed comma in the setting register, at position 5 (indicated by a reversed triangle). If the machine is adapted to its use, now a different set of counting fingers is in operation, one of which provides for correct counting and carrying of decimal fractions of pennies, whole pennies, and shillings. As you can imagine, this is a fairly complicated system. The carriage shift also operates the *horizontal* position of the counter wheel which has, from right to left, sets of 4,2 and 1 teeth, as is visible on the following pictures.

1/2/4 teeth on the counting wheel:

From the carriage end, the inside of the switch looks like this:

The switch on the carriage shifts the steel part up and down, converting the stepped path into a straight path for the feeler fingers, thus changing from decimal operation to operation in s and d.

The direction switch on the carriage and the selector for which counter wheel to use (the other then doesn't move) look like this from above and from the front:

In the decimal fractions of pennies part of the carriage, ever turn of the crank counts 24 decimal fractions of pennies. Shift one place to the left, into the full pennies section, and it counts 2.4 pennies. Into the shillings section, it counts 2s per turn. Shift one more place to the left, and suddenly now it skips a digit and counts 1£ per turn into the pounds section. Which teeth engage with the carriage is determined by the feeling finger in the groove in the carriage, as can be seen from the following pictures.

Carriage to left:

Carriage in shilling position:

Carriage in decimal penny position:

You can see the counting gear shift horizontally during this process. The shillings section does not correctly carry to the pounds section (the maximum number of shillings per pound is 20, but if you keep counting up in the pennies section, it continues over 20 without carrying).

The next big pickle is the conversion of decimal fractions of pounds to shillings, pennies and fractions of pennies in the result register. This happens automatically, with rounding. The way how it is done is quite ingenious. There are three decimals of pounds in the result register, which can be covered by a shroud that simultaneously uncovers the SID section of the LUSID. The shillings, pennies and fractions are displayed on a numeral roll, with 10 fractions on a single revolution. For example, the rightmost part of the roll would contain the fractions 1/4, 1/2, 3/4, 1, 1 1/4, 1 1/2, 1 3/4, 2, and 2 1/4. Then the decimal counting register would carry over to the next digit, and this digit is in direct correspondence with a moveable shroud around the numeral roll. For every positive revolution of the 2nd decimal, the shroud rotates, and the hole shifts one place to the left. There are ten possible positions of the shroud, but only five for the holes in it. On moving over to 5, the shroud rotates on, but the hole shifts back to its rightmost position, and a second hole shifts over the second numeral roll which has the shillings on it. It consists of the odd numbers on the right (1,3,5,7,9,11,13,15,17 and 19) and the even numbers on the left (0-18). Every rotation of the first decimal thus increments the number of shillings with 2.

Starting position, 0s 0d:

adding £0.003

Then adding £0.010 shifts the shroud to the left, revealing the 3.

Adding another £0.010 shifts the shroud one more position:

Then adding £0.200 rolls the even numeral wheel in the shilling section over to 4. You can see from the three rightmost digits in the result register what exactly has happened - they are now at 223

(What the function is of the two separate numeral wheels with the larger numbers that are visible between the s,d section and the result register is a complete mystery to me. They are normally not actuated, and are completely covered by the carriage. Simply spacers ?)

But try to fit 1/1000 into 1/240 and you'll understand it is not really as simple as adding 1/4 d for every £0.001. Hence the results are "automatically rounded" - according to the Odhner LUSID, 1/1000 equals 1/4 penny most of the time, but not always. This was easily implemented: the pennies cyclinder has 50 available places, but only 48 fractions, so two numbers are duplicate : 3d and 9d occur twice. Hence, e.g. £0.037 and £0.038 both equal 9d.With all that information in mind, it should now be feasible to read the examples for the Odhner LUSID on rechenmaschinen-illustrated.com. They are quite clear, but do suppose a better understanding of the intricacies of old English currency and its decimal equivalents than most people today possess.

In general, I don't think the approach is quite foolproof. It is impossible to put shillings and pennies in the setting register, which means you have to resort to decimal equivalents when they need to go there. Since the capacity of the machine is only 2x6x10, or 5x3x10 depending on the position of the fixed comma, it wasn't particularly suitable for working with large numbers either.

My machine often screws up by rotating an extra digit somewhere in the multiplication register after shortened multiplication or correction of an overflow has been used. I haven't been able to track whether this is a design error or a fault in this particular machine. The errors produced appear to be reproducible. Large carry operations in the decimals of pennies section also often lead to blocking the machine. The first problem can probably be avoided by paying more attention when adding the numbers, so that corrections aren't necessary. It doesn't solve the large carry problem though.

In conclusion, I'm not quite sure what to think about this machine, and would love to hear from someone who actually worked with it in the 60s. Was it handy ? Did it effectively save time when doing currency calculations ? I'd love to hear about it!

In the mean time, I have unearthed another example, N° 65694, which is even earlier than the one discussed above, N°68369. There are some interesting differences between the two. They are not far apart in serial number, which leads me to belive that this kind of machine is the very earliest type of Lusid made by Odhner. The main differences are in the base, the switch on the carriage for shifting from decimal to £sd operation, and the comma sliders.

Some pictures:

Serial N°:

End view of the carriage of the early (top) and later (bottom) machine

And finally, the two machines together for a direct comparison, the later machine is on top: