ON CABBAGE'S ANALYTICAL MACniNE. 95 



the number of separate steps is reduced from that expressed by the number 

 itself to eleven times the number of its digits ; that is to say, for example, 

 the addition of the number 73592 to any otber number is reduced from 

 73592 to 55 steps, and although of this latter some are slipped, there is 

 no gain of time thereby, except in so far as several of the steps may be 

 made simultaneously. The ordinary engines beat the human calculator 

 in respect of adding all the figures simultaneously ; but Mr. Babbage was 

 the first to devise a method of performing all the carrying simultaneously 

 too. 



Mechanical invention has not yet gone bejond the reduction of the 

 distinct steps involved in the addition of a number consisting of n digits 

 to less than Wn ; practically, from the necessity of accompanying the 

 carrying with a warning step, rather more are required. 



In all the calculating machines at present known, including Mr. 

 Babbage's analytical engine, multiplication is really effected by repeated 

 addition. It is true that, by a multiplication of parts, more than one addi- 

 tion may be going on simultaneously ; but it yet remains true, as a matter 

 of mechanism, that the process is purely one of iterated addition. 



By means of reversing wheels or trains, subtraction is as easily and 

 directly performed as addition, and that without becoming in any degree 

 a tentative process. But it is important to observe that the process can 

 be made tentative, so as to give notice when a minuend is, or is about to 

 become, exhausted. This is the necessary preparation for division, which is 

 thus essentially a tentative process. That does not take it out of the power 

 of the machine, because the machine may be, and is, so devised as to accept 

 and act upon the notice. Nevertheless it is a step alieni generis from the 

 direct processes of addition, multiplication, and subtraction. It need hardly 

 be stated that the process of obtaining a quotient consists in counting the 

 number of subtractions employed, up to the machine giving notice of the 

 minuend being exhausted. 



Another essentially distinct train is involved in the decimal shift of the 

 unit, in all the four elementary rules. This is most simply and most 

 commonly effected by the sliding of an axis or frame longitudinally, after 

 the manner of a common sliding- scale or rule, so as to bring either the 

 figures, or the teeth which represent them, against those to which their 

 decimal places correspond, and to no others. In multiplication and divi- 

 sion, this means a shift for each step of the multiplication and division. 



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



1. The mill. — The fundamental operation of Mr. Babbage's analytical 

 engine is simple additition. This and the other elementary rules of sub- 

 traction, 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 



the reducing bar. In practice the arrangement is usually circular, the bar PQ 

 revolving about an axis parallel to itself instead of sliding. If the numbers on the 

 wheels pq are placed one way we get addition ; if reversed, subtraction. Otherwise 

 we may reverse by introducing an additional set of wheels between the wheels^ 

 and the racks. 



This is the bare principle, admitting of many transformations, and making, like 

 the other, no provision for carrying. 



