The combination of multiplying mechanism, either direct or by repeated stroke, with the multiple keyboard has been made, but without the typewriting feature they do not serve as a real bookkeeping and billing machine.

The combination of the typewriter and the adding attachment lacks automatic means to print totals. The operator must read the totals and print them with the typewriter. Multiplication on such a combination is, of course, out of the question.

First Practical Combination

The culmination of the quest for a practical bookkeeping machine is a peculiar one, as it was dependent upon the ten-key recorder, which has never become as popular as the multiple-order keyboard on account of its limited capacity. The simplicity of its keyboard, however, lent to its combination with the typewriter, and the application of direct multiplication removed a large per cent of the limitation which formerly stood as an objection to this class of machine when multiplication becomes necessary.

For the combination, which finally produced the desired result, we must thank Mr. Hubert Hopkins, who is not only the patentee of such a combination, but also the inventor of the first practical ten-key recording-adder which has become commercially known as the “Dalton” machine.

Moon-Hopkins Billing Machine

His bookkeeping machine is commercially known as the “Moon-Hopkins Billing Machine.” [See illustration on opposite page].

The term “Bookkeeping Machine” has been misused by applying it to machines which only perform some of the functions of bookkeeping.

The principle of “Napier’s Bones” may be easily explained by imagining ten rectangular slips of cardboard, each divided into nine squares. In the top squares of the slips the ten digits are written, and each slip contains in its nine squares the first nine multiples of the digit which appears in the top square. With the exception of the top square, every square is divided into parts by a diagonal, the units being written on one side and the tens on the other, so that when a multiple consists of two figures they are separated by the diagonal. [Fig. 1] shows the slips corresponding to the numbers 2, 0, 8, 5, placed side by side in contact with one another, and next to them is placed another slip containing, in squares without diagonals, the first nine digits. The slips thus placed in contact give the multiples of the number 2085, the digits in each parallelogram being added together; for example, corresponding to the number 6 on the right-hand slip we have 0, 8 + 3, 0 + 4, 2, 1, whence we find 0, 1, 5, 2, 1 as the digits, written backwards, of 6 x 2085. The use of the slips for the purpose of multiplication is now evident, thus, to multiply 2085 by 736 we take out in this manner the multiples corresponding to 6, 3, 7 and set down the digits as they are obtained, from right to left, shifting them back one place and adding up the columns as in ordinary multiplication, viz., the figures as written down are