Part 20

The Bookkeeping and Billing Machine

An outgrowth of the recording-machine Art is represented in a new type of recording machine especially adapted to bookkeeping and the making out of invoices or reports where typewriting combined with arithmetical recording is necessary. This class of work demands a combination of the typewriter with adding and multiplying mechanism, having a capacity for printing the totals of either addition or multiplication.

Several attempts have been made to combine the typewriter and adding-recorder; and there have been combinations of multiplying and recording. Another combination that has been used to some extent for bookkeeping and billing is an adding attachment for typewriters, but all these combinations were lacking in one feature or another of what may be called a real bookkeeping machine and billing machine.

The combination of the typewriter and multiple-order keyboard recording-adders was too cumbersome, and the means employed for multiplication on such machines required too many manipulative motions from the operator. In simple cases of multiplication as high as fifty manipulative motions would be required to perform an example on such a machine.

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.

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.

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

12510 6255 14595 -------- 1534560

From Napier Tercentenary Celebration Handbook]

Napier’s rods or bones consist of ten oblong pieces of wood or other material with square ends. Each of the four faces of each rod contains multiples of one of the nine digits, and is similar to one of the slips just described, the first rod containing the multiples of 0, 1, 9, 8, the second of 0, 2, 9, 7, the third of 0, 3, 9, 6, the fourth of 0, 4, 9, 5, the fifth of 1, 2, 8, 7, the sixth of 1, 3, 8, 6, the seventh of 1, 4, 8, 5, the eighth of 2, 3, 7, 6, the ninth of 2, 4, 7, 5, and the tenth of 3, 4, 6, 5. Each rod, therefore, contains on two of its faces multiples of digits which are complementary to those on the other two faces; and the multiples of a digit and its complement are reversed in position. The arrangements of the numbers on the rods will be evident from fig. 2, which represents the four faces of the fifth bar. The set of ten rods is thus equivalent to four sets of slips as described above.

It is unnecessary to go into the history of the Hopkins Bookkeeping Machine to show the evolution of the Art relative to this class of machines, as the features that have made such a machine practical were developed by Hopkins himself, and at the present date there is none to dispute the title since his is the only machine having the required combination referred to. The scheme used by Hopkins for multiplication in his billing machine is, as stated, direct multiplication or that of adding the multiples of digits directly to the accumulator numeral wheels instead of pumping it into the accumulator wheels by repeated addition of the digits as is more commonly used.

The direct method of multiplying is old, as a matter of fact, the first mechanical means employed for multiplying worked by the direct method. But its combination with recording and typewriter mechanism invented by Hopkins was new.

Napier, in 1620, laid the foundation of the mechanical method of direct multiplication when he invented his multiplying bones. The scheme of overlapping the ordinal places is shown in the diagonal lines used to separate units from the tens in each multiple of the nine digits (see illustration, page 179), thus providing a convenient means by which the ordinal values may be added together.

The first attempt to set Napier’s scheme to mechanism that would add and register the overlapping ordinal values was patented by E. D. Barbour in 1872. See reproduction of patent drawings on opposite page.

THE BARBOUR MULTIPLIER

The accumulator mechanism of the Barbour machine, including the numeral wheels and their devices for transferring the tens, is mounted in a sliding carriage at the top of the machine (see Fig. 1), which may be operated by the hand-knob.

Extending through the bottom of the carriage are a series of pinions, one for each ordinal numeral wheel, and connected thereto by a ratchet and pawl action. The pinions are each so arranged as to be operative with a gear rack beneath the carriage when the carriage is slid back and forth.

Thus the wheels received action from one direction of the motion of the carriage and remain idle during the movement in the other direction. The degree of motion so received would, of course, depend upon the number of teeth in the racks below encountered by the pinions.

The gear racks employed by Barbour were numerous, one being provided for each multiple of the nine digits, arranged in groups constituting nine sets mounted on the drums marked B (see Fig. 4). Each of these sets contain nine mutilated gear racks, the arrangement of the teeth of which serve as the multiples of the digit they represent.

The teeth of the racks representing the multiples of the digits were arranged in groups of units and tens. For instance: 4 × 6 = 24, the rack representing the multiple of 4 × 6 would have two gear teeth in the tens place and four gear teeth in the units place, and likewise for the eighty other combinations.

Adding the multiples of the digits by overlapping the orders was accomplished by a very simple means, the arrangement of the racks being such that as the carriage was moved from left to right the numeral wheel pinions would move over the units rack teeth of a multiplying rack of one order and the tens rack teeth of a multiplying rack in the next lower order.

By close examination the reader will note from the drawings that the lower one of the sets of multiplying gear racks shown on the drum B, to the left in Fig. 4, is the series of one times the nine digits, the next set or series of racks above are the multiplying racks for the multiples of two, the lowest rack in that series having but two teeth, the next higher rack four teeth, the next rack six and the next eight.

So far no multiple of two has amounted to more than a units ordinal place, therefore these racks operate on a lower-order numeral wheel, and are all placed to the right of the center on the drum B, but the next rack above for adding the multiple of two times five requires that one shall be added to a higher order, and is therefore placed on the left side of the center of the drum.

Thus it will be noted that by reading the number of teeth on the right of each rack as units and those on the left as tens, that running anti-clockwise around the drum, each series of multiplying racks show multiples of the digits from one to four, it being obvious that the racks for adding the multiples of the higher digits are on the opposite side of the drums.