August 2 2, 1878] 



NATURE 



439 



6th, an operation card directing the machine to multiply q and 

 d together. 



7th, a record of the result, namely, the product q d — p^, 

 either pruited as a final result or punched in a seventh variable 

 card. 



III. Capability of the Engine. — It has already been remarked 

 that the direct work of the engine is a combination and repe- 

 tition of the processes of addition and subtraction. But in 

 leading up to any given datum by these combinations, there is 

 no difhculty in ascertaining tentatively when this datum is 

 reached or about to be reached. This is strictly a tentative pro- 

 cess, and it appears probable that each such tentamen requires 

 to be specially provided for, so as to be duly noted in the sub- 

 sequent 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, indeter- 

 minate alike in common arithmetic, and as regards the capabili- 

 ties 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 equation-, 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. Theoreti- 

 cally, 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 opera- 

 tions or equations which leads to a single numerical result. 



It appears to have been primarily designed with the following 

 generaJ object in view : to h^ 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, 

 h majon, 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." 



IV. Present State of the Design. — The only part of the ana- 

 lytical engine which has yet been put together is a small portion 

 of "themill," 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 (indepen- 

 dently 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 10,000/., 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. 



VIII. Possible Modification of the Engine. —Wi'Co.omX pre- 

 judging 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 of 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 arrange- 

 ment for the operations of addition and subtraction, and with a 

 slight modification, with or without store-columns, for multipli- 

 cation. We have already called attention to the imperfection of 

 the existing machines, which show weakne.s 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 offices, as well as in aid 

 of mathematical calculators. 



! Another important desideratum to which the machine might 



j 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 



I variables. This would include a large part of the calculations 



involved in the practical application of the method of least 



I 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 multiplica- 



, tion, may be entirely fieedfrom 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 in- 

 volve a departure, in the way of restrict! on 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 Dif- 

 ference Engine, and secondly on his Analytical Engine, are a 

 marvel of mechanical ingenuity and resoiu'ce. 



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 be 

 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 brought 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 le.^ possibility of forming an 

 opinion as to its strength and durability than as to its feasibility 

 or cost, 



1 1 . 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 considera- 

 tion 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 calcu- 

 lation of determinants, so as to serve for the solution of simul- 

 taneous equations. Thi-, 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 



I for the consideration of Mr. Babbage's representatives than om-s. 



