on babbage's analytical machine. 101 



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 deter- 

 minant, which is a mere combination of the three direct operations of 

 addition, subtraction, and multiplication, may be entirely freed from the 

 tentative process of division, which would thus be prevented from compli- 

 cating the direct machinery. In the absence of a special engine for the 

 purpose, the solution of large sets of simultaneous equations is a most 

 laboi'ious task, and a very expensive pi-ocess indeed, when it has to be 

 paid for, in the cases in which the result is imperatively 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 specialization, 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. 



1. 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. 



S. 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, hefore 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 



