## Adapting segment machine of Anton Braun

In 1727 Anton Braun (1686-1728), mathematician and optician at the Imperial court in Vienna, built a large magnificent cylindrical mechanical calculating machine for Emperor Charles VI. It had a pinwheel mechanism like the Poleni machine and was mechanically very similar to it, except for the weights which Braun replaced with a crank. Poleni is reported to have burnt his machine when he heard of Braun’s wonderful achievement. It is not known when Braun began to build his second much smaller cylindrical machine. The question as to how much Philippe Vayringe (1684-1746), a mechanic and watchmaker from Lorraine who is also named on the top of the machine, was involved with its invention and construction, has not been conclusively answered. It is interesting to note, however, that this machine, whose top clearly seems to indicate an earlier construction date, closely resembles a design published by Jacob Leupold in 1727 in his book “Theatrum Arithmeticum“, where he declared it to be his own work. In spite of these open questions, one can say that this smaller machine of Braun, the original of which is exhibited in the Deutsches Museum in Munich to this day, is mechanically really fascinating.

Instead of having a set of pinwheels or stepped drums, it features a single central so-called adapting segment. This cardinal idea meant that the number of special, complicated parts could be drastically reduced. Below the setting mechanism one finds a set of vertical cylinders, each with nine rods of different lengths rising from its top. If, for example, the digit 9 is entered, the shortest rod is rotated to the outside. One full turn of the crank then turns the central adapting segment once around the central axle. It consists of a disc with various steps as well as a segment with nine cogs. When it is turned once round, it passes the setting cylinders, on each of which a certain rod pushes the corresponding step outwards, whereupon the cog-segment of the adapting segment engages a cogwheel of the result mechanism and thus rotates the numbered disc to the correct digit in the corresponding window. Thus, the smaller the entered digit, the later the adapting segment engages and fewer cogs are moved. Repeated revolutions of the crank just repeat this operation, leading to multiplication. A place-shift mechanism enables multiplying with multi-digit multipliers. Subtraction and division are done using the 9-complements of digits. Even though the tens-carry steps did not function properly in every place, the idea of a central adapting segment was a great innovation which found extensive use in 20th century machines like the famous Curta, even though here the central element was a stepped drum.

The authentic replica in the Arithmeum is one of three machines built between 1986 and 1996 by the precision mechanics school in Villingen-Schwenningen. The other two are in the museum of local history in Möhringen near Tuttlingen and in the Deutsches Museum in Munich.