483,906. Calculating-machines. TENNANT, W. J. (Soc. Industrielle d'Instruments de PrÚcision) July 25, 1936, No. 7538. [A Specification was laid open to inspection under Sect. 91 of the Acts. Sept. 14, 1936.] [Class 106 (i)] In an electric multiplying-machine, the multiplication of two factors is carried out stage by stage, first in the normal (base 10) notation and then in a special (e.g. base 11) notation to give at each stage a single digit of the result in two notations and at each stage the difference between the two single digits so obtained in the two notations is used to obtain the tens transfer to be added into the next stage of the multiplication. The machine evaluates the expression D-AB. For example, for digits 7 and 8 in the multiplier and multiplicand the result on the decadal system is 56 and on the hendecadal 51. The difference between the single-digits results 6 and 1, which the present apparatus gives (at each stage), is 5 and this is the necessary transfer in the decadal notation at the next stage. The difference so obtained is constant for the decade on the base 10 to which it relates and in the case of bases 10 and 11 gives the actual transfer. For other bases, e.g. 9 or 13, used instead of 11 the difference is constant for each decade but is not the actual number required. There are four switches SD0, SD1, SD2, SD3, Fig. 1, for the units, tens &c. respectively of the factor D; three switches SAO, SA1, SA2 for the units, tens and hundreds of the factor A, and two switches SB0 and SB1 for the units and tens of the factor B. The switches SA0 and SB0 &c. are each shown in halves marked T (tens) and U (units). The switches SA0 &c. and SB0 &c. are connected through an adjustable commutator 29. Fig. 1, however, only shows a few typical circuits. The numerous remaining circuits are obtainable from connection tables, Figs. 4, 5, 6, 15, 16<1>, 162 (all not shown), the use of which is explained in the Specification. The internal connections of the switches SA0 &c. and SB0 &c. are drawn in full in Figs. 7, 7A, 8, 8A (all not shown). The switches are of a rotary type, for example switches of the Yaxley type described in Specification 454,735, [Group XXXVII], and the factors A and B are set up by manually adjusting the switches. At the first stage, Figs. 1 and 12, if the numbers set up on switches SA0 and SB0 are, say, 7 and 8 the circuit is from switch SAO through commutator 29 to switch SB0, switch SD0 (adjusted to the unit of factor D), commutator 27, and line 5R0 to the units decadal indicator UD. A typical circuit (though not for 7 x 8) is shown in heavy lines in Fig. 1. The ten result lines OR0, 1R0, 2R0 ... leading to indicator UD are tapped on to a resistance W so that windings 23 and 24 at right-angles receive differential currents according to the result wire OR0, 1R0, .... which is live. A polarized rotor 25 carrying an indicator needle is thus positioned according to the units digit of the result (6). There is no return spring to needle 25 so that the result remains showing at the indicating window. The commutator 27 is then moved one step to the right from the position shown in Fig. 1, e.g. by hand. The connections are now appropriate to hendecadal multiplication and the latter part of the original typical circuit shown in heavy lines is diverted over the heavy dotted line to the units hendecadal indicator UH which has eleven result wires OR<1>0 &c. but is otherwise similar to the indicator UD. Indicator UH thus shows the units digit result 1 of the hendecadal multiplication 7 x 8. The indicators UD, TD, HD, TD, TTD are associated with the rising denominations of the product according to the decadal multiplication and the indicators UH, TH, HH, TH to the hendecadal multiplication. Differential switches DS0, DS1, DS2, DS3 are provided for the four tens-transfer stages required. In switch DS0 the contact arm 20 is adjusted by the needle 25 of the hendecadal indicator UH and a member carrying eleven contact studs 21 is adjusted by the decadal indicator UD. Since indicators UD and UH indicate the numbers 6 and 1 the arm 20 will rest on contact stud No. 5 to give a tens transfer of 5 at the next stage, Figs. 2 and 13. For this second stage of the multiplication, commutator 29 is advanced to make the next set of connections, Fig. 2, and the various switches are now connected as shown diagrammatically in Fig. 13. The units results of this stage on the decadal and hendecadal notation now appear at indicators TD and TH but the circuit starts through switch DS0 to take in the tens transfer determined by the previous stage. The heavy line in Fig. 2 shows a typical circuit leading into the tens hendecadal indicator TH. A further transfer is calculated and after further movement of commutator 29 the switches are connected as in Fig. 14 for the third stage of the operations; and so on for succeeding stages. The final result is then read off the indicating needles 25. The commutator 26 is moved downwards, Fig. 1 or 2, at each stage to connect the appropriate differential switch DS0 &c. in circuit at the successive stages of the multiplication. By reversing the digits on the index by which each switch SD0 &c. is set, addition may be performed to evaluate the expression D + AB. In the apparatus as shown for D-AB division may be performed. The dividend is set up on switches SD0 &c., the divisor is set up on switches SA0 &c. and the required quotient is found by trial and error on the switches SB0 &c. ; the remainder being indicated on the elements UD &c. The decadal and hendecadal results could be obtained simultaneously by duplicating all the circuits and arranging one set for decadal and the other for hendecadal operation.