ox 



babbage's 



ANALYTICAL MACHINE. 



93 



The primary movement of calculating engines is the discontinuous 

 train, of which one form is sketched in the accompanying diagram (fig. 1) : 

 — B is the follower, an ordinary spur wheel with (say) 10 teeth ; A is its 

 driver, and this has only a single tooth. With a suitable proportion of parts, 

 the single tooth of A only moves B one interval for a whole revolution of 

 A; for it only gears with B by means of this single tooth. "When that is 

 not in gear, A simply slips past the teeth of B without moving the latter. 



All the other machinery of calculating engines leads up to and makes 

 use of this, or of some transformation of it, as its means of dealing with 

 units of whatever decimal rank, instead of allowing indefinite fractions of 

 units to appear in the result which has to be printed from. 



Fig. 1. 



The primary operation of calculation is counting : the secondary opera- 

 tion is addition, with its counterpart, subtraction. The addition and sub- 

 traction are in reality effected by means of counting, which still remains 

 the primary operation ; but the necessity for economising labour and time 

 forces upon us devices for performing the counting processes in a summary 

 manner, and for allowing several of them to go on simultaneously in the 

 calculating engine. For, if we use simple counting as our only operation, 

 and suppose our engine set to 2312 (say), then, in order to add 3245 to it 

 by mere repetition, we have 3245 unit operations to perform, and this is 

 practically intolerable. If, however, we can separate the counting, so as 

 to count on units to units only, tens to tens only, hundreds to hundreds 

 only, and so forth, we shall only have 



3 + 2 + 4 + 5 = 14 



turns of the handle, as against 3245 turns. In general terms the number 

 of operations will be measured by the sum of the digits of the number, 

 instead of by the actual number itself. This is exactly analogous to what 

 we should do ourselves in ordinary arithmetic in working an addition 

 sum, if we had not learnt the addition table, but had to count on our 

 fingers in order to add. This statement of the work is, however, incom- 

 plete. In the first place the convenience of machinery obliges us to pro- 

 vide 10 steps for each figure, whatever it may be, and there must be an 

 arrangement by which the setting of the figure to be added shall cause a 

 wheel to gain ground by so many steps as the number indicates, and to 

 mark time without gaining ground for the other steps up to 10. Thus, in 

 adding 7 our driver must make a complete turn or 10 steps, equivalent to 

 1 step of the follower ; but only 7 of these steps of the driver must be 

 effective steps, the others being skipped steps. There are various devices 

 for this. One of the simplest and most direct is that used in Thomas's 



