Calculating machine

“ To those not familiar with the technical features of the key-driven calculating machine Art, it would seem that if a machine could be made to add one column of digits, it would require no great invention or ingenuity to arrange such mechanisms in a plurality of orders. But the impossibility of effecting such a combination without exercising a high degree of invention will become evident as the reader becomes familiar with the requirements, which are best illustrated through the errors made by those who tried to produce such a machine. ”

“ Let us summarize on the Art, prior to Felt’s invention. A calculating machine that would calculate, if we eliminate the key-driven feature, was old. The key-driven feature applied to adding mechanism was old as adapted to a single-order machine with a capacity for adding only a single column of digits. ”

“ Difference Engine No. 1—First Idea at Cambridge, 1812—Plan for Dividing Astronomical Instruments—Idea of a Machine to calculate Tables by Differences—Illustrations by Piles of Cannon-balls. Calculating Machines comprise various pieces of mechanism for assisting the human mind in executing the operations of arithmetic. Some few of these perform the whole operation without any mental attention when once the given numbers have been put into the machine. ”

“ Let them remember that—not to mention the invention of that machine—the improvements alone introduced into the steam-engine by the celebrated Watt, occupied a period of not less than twenty years of the life of that distinguished person, and involved an expenditure of capital amounting to L.50,000. [1] The calculating machinery is a contrivance new even in its details. Its inventor did not take it up already imperfectly formed, after having received the contributions of human ingenuity exercised upon it for a century or more. ”

“ The High-Speed Calculator As previously stated, the calculating machine was old when Felt improved the Art by combining the key-drive with a plurality of co-operative orders of adding mechanism. The advantage in the machine he produced existed in the great increase in rapid manipulation which it offered over the older Art, especially in addition. To improve upon Felt’s contribution to the Art of calculating machines from a commercial standpoint demanded a combination that would give still greater possibilities in rapid manipulation. ”

“ The year after, we moved to Philadelphia where I rented a small shop and started to make ten of the calculating machines. While thus engaged, I saw the expediency of a small machine to supplement the larger one, and designed an adding machine which I named the ‘Arithmometer,’ and this patent, dated July 28, 1874, was the first one of the kind granted me by the United States Patent Office. It was also one of the first adding machines sold in the United States. ”

“ We decide that Simon will know just 4 numbers, 0, 1, 2, 3, in order to keep our model mechanical brain very simple. Then, for any register, we need only 2 relays; for any answer, we need only 2 lights.
Any calculating machine has a mentality, consisting of the whole collection of different ideas that the machine can ever actually express in one way or another. For example, a 10-place desk calculating machine can handle numbers up to 10 decimal digits without additional capacity. It cannot handle bigger numbers. ”

“ Nothing of the sort exists in the Difference Engine. We may say most aptly that the Analytical Engine weaves algebraical patterns just as the Jacquard-loom weaves flowers and leaves. Here, it seems to us, resides much more of originality than the Difference Engine can be fairly entitled to claim. We do not wish to deny to this latter all such claims. We believe that it is the only proposal or attempt ever made to construct a calculating machine founded on the principle of successive orders of differences, and capable of printing off its own results ”

“ Such adjustment, however, will only be necessary at very distant intervals, and after a considerable extent of printing and calculation has taken place; and when it is necessary, a provision is made in the machinery by which notice will be given by the sounding of a bell, so that the machine may not run beyond the extent of its powers of calculation.
Immediately behind the seven axes on which the figure wheels revolve, are seven other axes ”

“ The introduction of keys as a driving feature in the calculating machine Art demanded design and construction suitable to control the new idiosyncrasies of force and motion injected into the Art by their use, of which the elements of inertia and momentum were the most troublesome. ”

“ But the earliest piece of mechanism to which the name of a 'calculating machine' can fairly be given, appears to have been a machine invented by the celebrated Pascal. This philosopher and mathematician, at a very early age, being engaged with his father, who held an official situation in Upper Normandy, the duties of which required frequent numerical calculations, contrived a piece of mechanism to facilitate the performance of them. ”

“ The Art of either the calculating machine or the adding-recording machine is not new; it is, as a matter of fact, very old. As before stated, the Art of “accounting machine” dates back to the tenth century, but the first authentic evidence of a working machine is extant in models made by Pascal in 1642 (see illustration) . ”

“ From these a sufficient number of differences being derived, they are set upon the machine. The machine being then put in motion, the table axis will exhibit the successive values of the formula, corresponding to the substitutions of the successive whole numbers for the unknown quantity: at length the number exhibited on the table axis will be 0, which will evidently correspond to a root of the equation. By previous adjustment, the bell of the table axis will in this case ring and give notice of the exhibition of the value of the root in another part of the machinery. ”

“ Imagine the sudden whirl his numeral wheel would receive on a quick depression of a key and then consider that he provided no means for stopping these wheels; it is obvious that a correct result could not be obtained by the use of such mechanism. Some idea of what would take place in the Hill machine under manipulation by [Pg 26] an operator may be conceived from the speed attained in the operation of the keys of the up-to-date modern key-driven machine. ”

“ The recording-adding machine being designed to print the items and answers of addition, requires power for the printing which cannot be supplied by key depression. Thus an extra means for supplying that power must be provided in the form of a crank lever, or in the latest machines by a motor. The keys in such machines serve only as digital control to gauge the setting of mechanism which prints the items and adds them together. The secondary motion operates the mechanism to print and add and finally to clear the machine for the setting up of the next item. ”

“ It is to be expected, of course, that the manufacturer of such machines will not hold the same opinion as the [Pg 164] writer on this subject. But the fact that the generic principles of recording the items and totals were worked out before they even thought of constructing such a machine leaves little chance for anything but specific features of construction for them to make that may be considered new. ”

“ One of the consequences which has arisen in the prosecution of the invention of the calculating machinery, has been the discovery of a multitude of mechanical contrivances, which have been elicited by the exigencies of the undertaking, and which are as novel in their nature as the purposes were novel which they were designed to attain. ”

“ It may be found only in the time [Pg 150] allowed for the mechanical movements to take place, which shows that theoretical reasoning was the foundation for the distribution of the functions in the machine of these patents into increments of time, and that the arrangement of mechanism was especially designed to carry out this primary theoretical reasoning. While it is obvious that such procedure must accompany successful invention of mechanism, it is seldom that we find such fineness displayed as may be found in the timing of the mechanical functions of the later Comptometer. ”

“ Think of it; a machine built with the idea of offering the possibility of such key manipulation and supplying nothing to overcome the tremendous momentum set up in the numeral wheels and their driving mechanism, unless perchance Hill thought the operator of his machine could, mentally, control the wheels against over-rotation. [Pg 27]
[Pg 28]
Chapin Patent Drawings
[Pg 29] Lack of a proper descriptive term used to refer to an object, machine, etc., oftentimes leads to the use of an erroneous term. To call the Hill invention an adding machine is erroneous since it would not add correctly. ”

“ I showed him my machine. At once he saw it possibilities. We joined hands and set about designing the machine to make it as nearly perfect as possible in its adaptation to the needs of modern business.
The result of that work and our later association is the Monroe High Speed Adding-Calculator which is filling no small part in faithful, economic service in the realm of business. ”

“ Of the named improvements, of course, all are designed to fit the requirements of the machines they are shown as a part of in the drawings of the patent. They are also claimed as adaptable to other machines of the type, but some are so specific to the machine they form an improvement on that they are not adaptable to other makes. ”

“ Another volume, of the same size, which is announced by the same author, will render these by far the most valuable of their kind, provided their accuracy can be relied on. The quantity of mental labour saved, in the construction of such tables, by the help of the machine, is literally infinite: for, in fact, no previous calculation is at all requisite; and it will be necessary merely to put into the machine, at the end of every two pages, the number whose multiples are required. ”

“ In Fig. 2 of the illustration of Pascal’s machine, the machine has been reversed, and the bottom of the casing, which is hinged, thrown back, showing the numeral wheels and gearing of the different orders and the transfer levers for the carry of the tens.
Increased capacity of modern calculator
The Art of the modern machines is far removed from the older Art by its greatly increased capacity for rapid calculation which is found emanating from the provision of keys as the means of manipulation. ”

“ Likewise, without means for controlling the numeral wheels, the Hill invention was not an adding machine. The only term that may be correctly applied to the Hill invention is “adding mechanism,” which is broad enough to cover its incompleteness. And yet many thousands of people who have seen the Hill invention at the National Museum have probably carried away the idea that the Hill invention was a perfectly good key-driven adding machine. ”

“ In the new machine, we find that to overcome this unevenness of action, Felt reversed the ratchet action of the denomination actuators, so that no wheel action occurred on their down-stroke under the action of the keys, but on the upstroke of the actuators the numeral wheels were turned by the power of the actuator springs stored by the key depression, thus giving an even set rotating action that could not be forced and that could be controlled by a stop detent. ”

“ In many respects, this machine is efficient and well-balanced. Its reading and writing speed is close to its calculating speed. We can punch or print a result on the average for every 10 additions or 11⁄2 multiplications. The memory of 72 numbers in the machine is extremely useful; a smaller memory is a serious limitation on the achievements of a computing machine. The machine can do many kinds of arithmetic and logic. It is well educated and can compute automatically some rather complicated mathematical functions, like logarithm or sine. ”

“ To the unsophisticated, such a simple thing as applying keys to the ancient type of calculating machines that have been made and used for centuries, would seem but a simple mechanical application that the ordinary mechanic could accomplish. ”

“ Intricate calculations, moreover, can very often be dispensed with by the aid of mechanical devices, such as the ingenious calculating machines which perform additions and subtractions and very elaborate multiplications and divisions with surprising speed and accuracy, or apparatus for solving the higher equations, for determining the volume or area of geometrical figures, for carrying out integrations, and for developing a function in a Fourier’s series by mechanical means. ”

“ Once the human brake is removed the increase in speed is enormous. For example, it is intended that multiplication of two ten figure numbers shall be carried out in 500 μs. This is probably about 20,000 times faster than the normal speed with calculating machines.
It is evident that if the machine is to do all that is done by the normal human operator it must be provided with the analogues of three things, viz. ”

“ Colleges with scholars who write textbooks usually have not had a variety of expensive and versatile computing machinery. As a result, the main environment for stimulating possible authors has until recently been missing. The list of references is accordingly brief.
Aiken, Howard H., and others, Proceedings of a Symposium on Large-Scale Digital Calculating Machinery, Cambridge, Mass.: Harvard University Press, 1948, 302 pp.
Comrie, John Leslie, The Application of Commercial Calculating Machines to Scientific Computing, Mathematical Tables and Other Aids to Computation, vol. 2, no. ”