JF Ptak Science Books *Quick Post*

Here's a very interesting report from an 1878 issue of* Nature (*volume 18 pp 460) considering the construction and its consequences of the yet-built Babbage computer (analytical machine). Charles Babbage died in Marylebone in 1871 and bequeathed his working archive to his youngest son Henry (1824-1918) who expected to carry his father's work into the future. This is one attempt to construct a working machine from the Babbage plans. I've reproduced most of the Nature article below, with a few inconsequential edits. Enjoy.

*REPORTS Report of the Committee, consisting of Prof. Cayley, Dr. Farr, Mr. J. W. L. Glaisher, Dr. Pole, Prof. Fuller, Prof. A. B. W. Kennedy, Prof. Clifford, and Mr. C. W. Merrifield, appointed to consider the Advisability and to estimate the Expense of constructing Mr. Babbage's Analytical Machine, and of printing Tables by its means.* Drawn up by Mr. Merrifield. We desire in the first place to record our obligations to General Henry Babbage for the frank and liberal manner in which he has assisted the Committee, not only by placing at their disposal all the information within his reach, but by exhibiting and explaining to them, at no small loss of time and sacrifice of personal convenience, the machinery and papers left by his father, the late Mr. Babbage. Without the valuable aid thus kindly rendered to them by General Babbage it would have been simply impossible for the Committee to have come to any definite conclusions, or to present any useful report.

We refer to the chapter in Mr. Babbage's "Passages from the Life of a Philosopher,"and to General Menabrea's paper, translated and annotated by Lady Lovelace, in the third volume of "Taylor's Scientific Memoirs,"for a general description of the analytical engine.

The Report then, in Section I., contains an account of the general principles of calculating engines, and proceeds:

Section II. *Special Characteristics of Mr. Babbage's Analytical Engine.*

1. The Mill. The fundamental operation of Mr. Babbage's analytical engine is simple addition. This and the other elementary rules of subtraction, multiplication, and division, and all combinations of these, are performed in what is called "the mill."All the shifts which have to take place such as changing addition into subtraction by throwing a reversing train into gear, or the shift of the decimal place, carrying and borrowing, and so forth, are effected by a system of rotating cams acting upon or actuated by bell-cranks, tangs, and other similar devices commonly used in shifting machinery, sometimes under the name of clutches or escapements. These clutches and bell-cranks control the purely additive and carrying processes effected in the additive trains described in the note to Section I., and, being themselves suitably directed, secure that the proper processes shall be performed upon the proper subject-matter of operation, and duly recorded, or used, as may be required.

2. The Store. A series of columns, each containing a series of wheels, constitutes the store. This store, which may be im three or more dimensions, both receives the results of operations performed in the mill, and serves as a store for the numbers which are to be used in the mill, whether as original or as fresh subjects of operation in it. Each column in the store corresponds to a definite number, to which it is set either automatically or by hand, and the number of digits in this number is limited by the number of wheels carried on the shaft of the column. The wheels gear into a series of racks, which can be thrown into or out of gear by means of the card?

3. Variable Cards. All the numbers which are the subject of operation in the mill, whether they are the result of previous operations therein, or new numbers to be operated upon for the first time, are introduced to it in the form of Jacquard cards such as are used in weaving. One set of wires or axes transfers the numbers on these cards to the subject of operation in the mill, exactly as similar cards direct which of the warp threads are to be pushed up, and which down, in the Jacquard loom. The mill itself punches such cards when required.

4. Operation Cards. A different set of cards selects and prescribes the sequence of operations. These act, not upon the number wheels of the mill or store, but upon the earns and clutches which direct the gearing of these wheels and trains. Thus, in such an operation as (a b + c) d, we should require:-

1st, four variable cards with the numbers a, b, c, d.

2nd, an operation card directing the machine to multiply a and b together.

3rd, a record of the result, namely, the product a b p, as a fifth variable card

4th, an operation card directing the addition of p and c.

5th, a record of the result, namely, the sum/ + c q, as a sixth variable card.

6th, an operation card directing the machine to multiply (/ and d together.

7th, a record of the result, namely, the product q d pv either printed as a final result or punched in a seventh variable card

* Capability of the Engine.* It has already been remarked that the direct work of the engine is a combination and repetition of the processes of addition and subtraction. But in leading up to any given datum by these combinations, there is no difficulty in ascertaining tentatively when this datum is reached or about to be reached. This is strictly a tentative process, and it appears probable that each such tentamen requires to be specially provided for, so as to be duly noted in the subsequent operations of the machine. There is, however, no necessary restriction to any particular process, such as division; but any direct combination of arithmetic, such as the formation of a polynomial, can be made to lead up to a given value in such a manner as to yield the solution of the corresponding equation. In any such process, however, it is evident that there can be only (to choose a simile from mechanism) one degree of freedom; otherwise the problem would yield a locus, indeterminate alike in common arithmetic, and as regards the capabilities of the machine. The possibility of several roots would be a difficulty of exactly the same character as that which presents itself in Horner's solution of equations, and the same may be said of imaginary roots differing but little from equality. These, however, are extreme cases, with which it is usually possible to deal specially as they arise, and they need not be considered as detracting materially from the value of the engine. Theoretically, the grasp of the engine appears to include the whole synthesis of arithmetic, together with one degree of freedom tentatively. Its capability thus extends to any system of operations or equations which leads to a single numerical result. It appears to have been primarily designed with the following general object in view: to be coextensive with numerical synthesis and solution, without any special adaptation to a particular class of work, such as we see in the difference engine. It includes that, 2 majori, and it can either calculate any single result or tabulate any consecutive series of results just as well. But the absence of any specialty of adaptation is one of the leading features of the design. Mr. Babbage has also considered the indication of the passage through infinity as well as through zero, and also the approach to imaginary roots. For details upon these points we must refer to his "Passages from the Life of a Philosopher."

* Section III. Present Slate of the Design*. The only part of the analytical engine which. has yet been put together is a small portion of "the mill,"sufficient to show the methods of addition and subtraction, and of what Mr. Babbage calls his "anticipating carriage."It is understood that Gen. Babbage will (independently of this report) publish a full account of this method. No further mention of it will therefore be made here. V.Probable Cost. Without attempting any exact estimate, we may say that it would surprise us very much if it were found possible to obtain tenders for less than lojooo/., while it would pretty certainly cost a considerable sum to put the design in a fit state for obtaining tenders. On the other hand it would not surprise us if the cost were to reach three or four times the amount above suggested.

Section V. * Probable Cost. *Without attempting any exact estimate, we may say that it would surprise us very much if it were found possible to obtain tenders for less than 10,000 pounds., while it would pretty certainly cost a considerable sum to put the design in a fit state for obtaining tenders. On the other hand it would not surprise us if the cost were to reach three or four times the amount above suggested.

Section VI. refers to * Strength and Durability*, and VII. to

**Probable Utilisation of the Analytical Engine.**Section VIII, * Possible Modification of the Engine*. Without prejudging the general question referred to us as to the advisability of completing Mr. Babbage's engine in the exact shape in which it exists in the machinery and designs left by its inventor, it is open to consideration whether some modification of it, to the sacrifice o'f some portion of its generality, would not reduce the cost and simplify the machinery so as to bring it within the range of both commercial and mechanical certainty. The "mill."for example, is an exceedingly good mechanical arrangement for the operations of addition and subtraction, and with a slight modification, with or without store-columns, for multiplication. We have already called attention to the imperfection of the existing machines, which show weakness and occasional uncertainty. It is at least worth consideration whether a portion of the analytical engine might not thus be advantageously specialised so as to furnish a better multiplying machine than we at present possess. This, we have reason to believe, is a great' desideratum both in public and private office?, as well as in aid of mathematical calculators. Another important desideratum to which the machine might be adapted without the introduction of any tentative processes (out of which the complications of the machinery chiefly arise) is the solution of simultaneous equations containing many variables. This would include a large part of the calculations involved in the practical application of the method of least squares. The solution of such equations can always be expressed as the quotient of two determinants, and the obtaining this quotient is a final operation, which may be left to the operator to perform by ordinary arithmetic, or which may be the subject of a separate piece of machinery, so that the more direct work of forming the determinant, which is a mere combination of the three direct operations of addition, subtraction, and multiplication, may be entirely fieed from the tentative process of division, which may thus be prevented from complicating the direct machinery. In the absence of a special engine for the purpose, the solution of large sets of simultaneous equations is a most laborious task, and a very expensive process indeed, when it has to be paid for, in the cases in which the result is impeiatively needed. An engine that would do this work at moderate cost would place a new and most valuable computing power at the disposal of analysts and physicists. Other special modifications of the engine might also find a fair field for reproductive employment. We do not think it necessary to go into these questions at any great length, because they involve a departure, in the way of restriction and specialisation, from Mr. Babbage's idea, of which generality was the leading feature. Nevertheless, we think that we should be guilty of an omission if we were to fail to suggest them for consideration

IX. **General Conclusions, and Recommendation.**

I. We are of opinion that the labours of Mr. Babbage, firstly on his Difference Engine, and secondly on his Analytical Engine, are a marvel of mechanical ingenuity and resource.

2.We entertain no doubt as to the utility of such an engine as was in his contemplation when he undertook the invention of his analytical engine, supposing it to be successfully constructed and maintained in efficiency.

3.We do not consider that the possibilities of its misuse are any serious drawback to its use or value.

4.Apart from the question of its saving labour in operations now possible, we think the existence of such an instrument would place within reach much which, if not actually impossible, has been too close to the limits of human skill and endurance to bfl practically available.

5.We have come to the conclusion that in the present state of the design of the engine it is not possible for us to form any reasonable estimate of its cost, or of its strength and durability.

6.We are also of opinion that, in the present state of the design, it is not more than a theoretical possibility; that is to say, we do not consider it a certainty that it could be constructed and put together so as to run smoothly and correctly, and to do the work expected of it.

7.We think that there remains much detail to be worked out, and possibly some further invention needed, before the design can be rought into a state in which it would be possible to judge whether it would really so work.

8.We think that a further cost would have to be incurred in order to bring the design to this stage, and that it is just possible that a mechanical failure might cause this expenditure to be lost.

9.While we are unable to frame any exact estimates, we have reason to think that the cost of the engine, after the draw ings are completed, would be expressed in tens of thousands of pounds at least.

10.We think there is even less possibility of forming an opinion as to its strength and durability than as to its feasibility or cost.

11.Having regard to all these considerations, we have come, not without reluctance, to the conclusion that we cannot advise the British Association to take any steps, either by way of re commendation or otherwise, to procure the construction of Mr. Babbage's analytical engine and the printing tables by its means.

12.We think it, however, a question for further consideration whether some specialised modification of the engine might not be worth construction, to serve as a simple multiplying machine, and another modification of it arranged for the calculation of determinants, so as to serve for the solution of simultaneous equations. This, however, inasmuch as it involves a departure from the general idea of the inventor, we regard as lying outside the terms of reference, and therefore perhaps rather for the consideration of Mr. Babbage's representatives than ours. We accordingly confine ourselves to the mere mention of it by way of suggestion

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