405 



MACHINES, CALCULATING. 



MACHINES, CALCULATING. 



406 



and so on. The numbers in front of the whole machine will now 

 stand thug : 



K A 1 - A- A" 1 - A"- A 7 - 



By the addition (in the proceeding table) of 5 in the third column to 

 8 in the fourth, there should be produced 13, whereas 3 only appears 

 under the index of the cylinder (in the third column of the present 

 table I, therefore 1 must be carried. The operation of carrying is per- 

 formed by the action of the moving power in the second quadrant of 

 ita revolution ; and, in the present example, this does nothing more 

 than turn the cylinder marked 3 (in the first line, third column) 

 though one-tenth of a revolution, which brings 4 to the front of that 

 cylinder. The reader may now imagine the 3 to be effaced, and the 

 number 4 introduced in its place. Now the moving power turning 

 through the third quarter of a revolution, the cylinders on the second 

 and fourth axles are made to turn through as many tenths of a revolu- 

 tion as are expressed by the figures on the cylinders immediately on 

 their right hand. Thus, the cylinder marked 4 in the column oi the 

 last table will turn through four-tenths, and this movement will bring 

 to its front the number 8 ; the cylinder marked 6 will be turned 

 through three-tenths of a revolution, which will bring to its front the 

 figure 9 ; and so on. The numbers in front of the machine will now 

 stand thus : 



The moving power turning through the fourth quadrant will pre- 

 form the operations of carrying; and, in the present example, the 

 cylinder marked 9 will turn one-tenth, which brings (for 10) to its 

 front ; this causes another carrying, and the cylinder marked 8, in the 

 name column, will turn one-tenth ; which brings 9 to its front. The 

 cylinder marked 1 in the fourth column will turn one-tenth on account 

 of the carrying from the cylinder 5 below it, which brings 2 to its 

 front ; and the machine will stand thus : 



The operation is now completed : the number succeeding 3125 in the 

 series u 7776 ; and the like operations being performed with the instru- 

 ment in the present state, the next number will be obtained in the first 

 column. It haa been supposed that the instrument has only six axle 

 carrying cylinders ; but it U evident that, if a number consisting of 

 more than four places of figures were given, or were to be produced, a 

 greater number of axles would be necessary. 



In a limited space, we can do no more than give the following 

 general notion of the mechanism by which these remarkable move- 

 ments are produced. Immediately behind each column of the cylinders 



carrying the figures and In a vertical plane perpendicular to the 

 front of the machine, is a vertical axle X which carries, opposite to 

 *oh cylinder, two horizontal wheels A and B, and between them a 

 moTMbla bolt C, also in horizontal position. These two wheels are 



capable of being connected with or disconnected from the axle, so that 

 they may or may not turn with the latter. The upper wheel A is 

 furnished with teeth, standing out horizontally from the rim, and these 

 work in the like teeth formed about the cylinder D carrying the figures 

 so that the wheel A, when it turns with its axle, may be said to drive 

 the cylinder. It is also furnished with teeth which are perpendicular 

 to its lower surface, in the manner of an inverted crown wheel. The 

 bolt c, which is under this wheel, and passes through the axle, is 

 capable of being moved a short distance horizontally ; it is provided, 

 near its extremity, with a pin or tooth a standing perpendicularly 

 above its upper surface, and with a pin 6 perpendicularly below its 

 inferior surface. And the lower wheel B carries a wedge or inclined 

 plane c. Behind the wheels on the axle X is another axle Y, which is 

 also in a vertical position ; this carries a projecting bar or finger m 

 which revolves horizonally when the axle is made to turn by the action 

 of the moving power. During its revolution it meets, at a proper place, 

 one extremity of a lever n which is capable of turning on a pivot at p ; 

 that extremity being displaced, the extremity of the opposite arm 

 presses against the end of the bolt c in the axis x and causes the upper 

 pin a to enter between two teeth of the crown-wheel A. This wheel is 

 thus fixed to its axle so as to be compelled to turn with the bolt ; and 

 the horizont il teeth of the wheel, consequently, cause the cylinder D 

 carrying the figures to turn on its proper axis z. Such is the nature 

 of the mechanism that, while the moving power describes the first 

 and third quadrants of its revolution, the cylinder D might make a 

 complete revolution ; but, in general, the cylinder is to make only as 

 many tenths of a revolution as are expressed by the figure in front of 

 the next cylinder on its right hand ; and therefore the bolt is to be 

 withdrawn from the crown-wheel when such part of a revolution has 

 been performed. This is accomplished by the pin b, which, moving 

 along the wedge or inclined plane c, draws the bolt back so that the 

 pin a above is removed from between the teeth of the crown-wheel ; 

 the latter is thus disengaged from its axle and ceases to revolve : at the 

 same time the cylinder D, with which it is connected by the horizontal 

 teeth, ceases also to revolve. The cylinder remains then at rest till it 

 is moved at a subsequent step in the process. If the cylinder is not to 

 turn while the. moving power describes the first and third quadrants, 

 an apparatus provided for the purpose removes out of its place the 

 lever which should press against the end of the bolt. For every 

 vertical axis carrying cylinders in front of the machine, there is an 

 axle carrying wheels and bolts, and an axle carrying the fingers which 

 lock the bolts : and behind every cylinder is its proper apparatus, 

 consisting of wheels, bolt, and finger. 



The process of currying, which takes place when the moving power 

 is describing the second and fourth quadrants of its revolution, is 

 accomplished thus: A bar or finger revolves on the axle of the 

 lowest cylinder D, for example, in the first vertical column on the left ; 

 and, at a proper time comes against the extremity of a claw which then 

 engages itself between the teeth of a ratchet-wheel connected with the 

 next cylinder above it : both the wheel and cylinder are thus made tc 

 turn, but the length and position of the claw are such that the cylindei 

 can only make one-tenth of a revolution, and thus bring to the front a 

 figure greater by unity than that which was there before. When a 

 cylinder has made the movement just indicated, a projecting pin, 

 called a thumb, on the axle of the lower cylinder, touches a trigger 

 which raises, out of a notch in the claw, a hook which retained the 

 latter : a spiral spring then draws back the claw and allows it to fall 

 between the next teeth of the ratchet-wheel without creating any 

 movement in the cylinder ; and the apparatus is thus prepared for the 

 next carrying operation which is to take place. 



It was proposed by the inventor to apply to the machine an apparatus 

 by which the numbers obtained from the cylinders in the left-hand 

 column might be immediately transferred, by the operation of punch- 

 ing, to plates of copper, in order that the results given by the machine 

 might be printed without a possibility of error. To effect this, a 

 curvilinear bar of metal was to act on an arm of a lever so as to raise it 

 to ten different heights corresponding to the ten figures on the surface 

 of a cylinder ; and the opposite arm of the lever was to move an arch 

 carrying ten punches having on them the characters 1, 2, 3, &c. in 

 relief. The plate of copper being below, a bent lever was to press the 

 punch upon the plate, and produce the impression of the figure. The 

 different figures in front of the first column of cylinders would thus be 

 successively transferred to the copper-plate ; and the arch and plate 

 being shifted, the set of figures brought in front of the cylinders in the 

 same column, at the next operation with the machine, would be trans- 

 ferred in like manner. 



If Mr. Babbage's plan had ever been fully carried out, the machine 

 would perform the several operations of simple arithmetic on any 

 numbers whatever. It would combine the quantities algebraically 

 or arithmetically in an unlimited variety of relations. It would use 

 algebraic signs according to their proper laws, and develope the con- 

 sequences of those laws. It would arbitrarily substitute any formula 

 for any other, effacing the first from the columns on which it is repre- 

 sented and making the second appear in its stead. It would effect 

 processes of differentiation and integration on functions in which the 

 operations take place by successive steps. The inventor further asserts 

 that the engine would be particularly fitted for the operations of the 

 combinatory analysis, for computing the numbers of Bernoulli, &c. 



