on babbage's analytical machine. 97 



III. 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, how- 

 ever, no necessary restriction to any particular process, such as division ; 

 but any direct combination of arithmetic, such as the formation of a poly- 

 nomial, 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, how- 

 ever, 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, inde- 

 terminate 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 solu- 

 tion 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. Theo- 

 retically, the grasp of the engine appears to include the whole synthesis 

 of arithmetic, together with one degree of freedom tentatively. Its capa- 

 bility 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 a majori, and it can either 

 calculate any single result, or tabulate any consecutive series of results 

 just as well. But the absence of any speciality of adaptation is one of the 

 leading features of the design. 



Mr. Babbage had 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 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 called his " anticipating car- 

 riage." It is understood that General Babbage will (independently of 

 this report) publish a full account of this method. No further mention 

 of it will therefore be made here, 



A small portion of the work is in gun-metal wheels and cranks, 

 mounted for the most part on steel shafts. But the greater part of the 

 wheels are in a sort of pewter hardened with zinc. This was adopted from 

 motives of economy. They are for the most part not cast, but moulded 

 by pressure, and the moulds of most of them are in existence. 



A large number of drawings of the machinery are also in existence. It 

 is supposed that these are complete to the extent of giving an account of 

 1878. h 



