Strange table calculator

A calculator issued by a pharmaceutical company...

Recently I acquired a small table “calculator” (Figure 1). The plastic machine measures 8.5 by 5 by 4.5 cm and contains a roller with a table that can be rotated with a ribbed wheel. On the front, the word “Min” and two rows of numbers are embossed. On the back is an additional table, which unfortunately is partially faded (Figure 2). 

The machine is marked with a logo “Cosaldon (Albert)”. Further markings are missing.

Cosaldon is a vasodilator drug with pentiphenylline, or 1-hexyltheophylline, as active ingredient. The drug was produced from the late 1950s[1] by Chemische Werke Albert of Wiesbaden-Biebrich, which became part of Hoechst in 1972. Cosaldon appeared in several variants, including a combination with nicotinic acid. A large number of variants were withdrawn from the market in 1990.[2] The drug was touted for the treatment of all kinds of vascular disorders and in particular cerebral ischemia (stroke). Later, Cosaldon was also used for the treatment of macular degeneration, although evidence of efficacy was weak.[3] 

The big question is: what is the calculator used for?

The tables

The tables are shown below. The first table begins with two rows that contain the numbers on the casing. Let's call them “x” (red and black). They correspond to red and black numbers on the rotating table, which in pairs belong to a certain value of “Min”. Values of x range from 8.6 to 90 while  “Min” ranges from ½  to 10. 

Riddles

It was a mystery to me what “Zone” means, why there is an inverse relationship between “Zeiteinheit” and “Entfernung”, and why two kinds of “Zeiteinheit” are given. What medical application calculates with times of less than 2 minutes on a scale of hundreds of kilometers?

All numbers in the rotating table are multiples of 0.16. For a given combination of “Min” and “x”, the red and black numbers are equal. But even different combinations of “Min” and “x” can sometimes produce the same value. If we put everything in a graph, with one curve per “Min” value, this is even more obvious: the curves are not smooth. Note: to better separate the curves, the y-axis of the graph has been made logarithmic.

Error?

The thick red line gives the curve for Min=7. This is the only curve that is not monotonic-non-rising. This is caused by a y-value of 1.28 for x=67.5 (made bold italic by me in the first table). This value corresponds to the y-values for Min=8 and Min=9 at x=67.5.
If we assume that the value for x=67.5 is equal to that of x=60, as is also the case for Min=½ to 6 and Min=8, then we would expect y=1.12 instead of 1.28.

Solution

“Zone K” gave me the solution to the riddle: in the 1960s in West Germany, the name “Zone K” was used for local telephone traffic. Within “Zone K” (the Nahzone), a call of less than 1.5 minutes costs 16 Pfennig (Ortsgesprächsgebühr).[4,5]  For long distance telephone traffic, 8 zones (Fernzone) were distinguished. The call cost per minute was derived from the local rate for 1.5 minutes, thus a multiple of 16 Pfennig. After 19:00 that amount was usually also charged for a Fernzone each1.5 minutes. 

The Fernsprechordnung März 1956 gives a table for a 3 minute call through a manual telephone exchange. The black figures apply between 18:30 and 21:30. No such table is given for a call through an automatic telephone exchange, but a table similar to the back of the Cosaldon calculator is given. This also shows that x=8.6 stands for 8+4/7. The black numbers now apply to 19:00–7:00. It was quite a puzzle back then to calculate your call charges!

For longer distances via an automatic telephone exchange in the evening, the Fernsprechordnung gives two numbers because not all telephone exchanges had yet been converted to the flat rate. In the copy of the Fernsprechordnung that I have seen, the numbers in brackets are crossed out in pencil, so during the validity period of this Fernsprechordnung, this conversion was probably completed. The bottom two rows of the table below contain the cost for a 3 minute call calculated with this data according to the formula 16×(3×60)/Zeiteinheit. These costs, according to the rule, are rounded up to a multiple of 16 Pfennig.

The costs correspond to those on the rotating table of the Cosaldon calculator. Thus, the calculator applies only to calls made through fully converted automatic telephone exchanges.

The mistake noted earlier for Min=7 and x=67.5 remains a mistake with this calculation: 16×(7×60)/67.5=100 Pfennig, which rounded up to a multiple of 16 Pfennig gives 112 Pfennig, not 128 Pfennig . 

The Ortsgesprächsgebühr had been raised from 15 Pfennig to 16 Pfennig in July 1954,[6]  and this rate was in effect until August 1964, when it rose to 20 Pfennig at a stroke. In December 1964 it was lowered to 18 Pfennig.[7]  The calculator must therefore have been made between about 1957 (start of Cosaldon production) and mid-1964 (change in telephone tariff). The machine could have been adapted to the rate change by replacing the sticker with the table on the roll. 

In 1971, the Fernsprechordnung was modified[8]  by introducing, among other things, three time periods: 6:00–18:00, 18:00–1:00 and 1:00–6:00. This would require three rows of numbers to be embossed on the body of the calculator. Therefore the machine became completely worthless except for calculator collectors.

Acknowledgements

Thanks to Hans Bloemen for finding the machine and photographing it.

References

[1] Staatsanzeiger für das Land Hessen, Nr. 10 (March 9, 1957)  page 234.

[2] Dt. Ärztebl. 88:25/26 (June 24, 1991)  page A-2314.

[3] Arznei-Telegramm 1 (1990)  page 5–6.

[4] Deutscher Bundestag — 3. Wahlperiode — 47. Sitzung. Bonn (October 29, 1958) page 2609.

[5] “Der Fünfminuten-Takt”, Der Spiegel (July 19, 1960)  page 16–17.

[6] Das Ostpreußenblatt, Hamburg, 5:23 (June 5, 1954) page 4.

[7] Dieter Schmidtchen, Hans Lukas, “Politische Ökonomie staatlicher Preisinterventionen”, Duncker & Humblot (1973)  page 135.

[8] Fernmeldeordnung May 5, 1971, Bundesgesetzblatt, 1971, Teil 1 (May 14, 1971)  page 604.