Babbage's Difference Engine accomplishes these additions by the movements of a number of cylinders having on the convex surface of each the series of numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, 0. The opera tions are thus distributed : by the first, the additions are made ; and by the second, there is introduced the 1 which should be carried to the ten's place every time that the sum of two numbers is greater than 10. Let it be imagined that there are several vertical axles, on each of which are several cylinders one above another ; and that these axles with their cylinders are capable of being turned by wheelwork, so that any one of the ten figures may be made to stand on the face of the machine, and immediately under a fixed index. Let it be further imagined that, when tho moving power (the hand of the operator applied to a winch) has made one quarter of a revolution, the first, third, fifth, &c., axles may turn, causing the cylinders on them to make parts of a revolution or allowing them to remain at rest as the case may he, while all the cylinders on the second, fourth, &o., axles remain at rest. Again, when the moving power has made the second quarter of a revolution, let it be imagined that certain, only, of the cylinders on the first, third, fifth, fic. axles make one-tenth of a revolution, so that, whatever figure be under the index of each of these moving cylinders, the next figure, in increasing order, may be brought under that index ; the cylinders on the second, fourth, &c., axles still remain ing at rest. Let it next be imagined that, when the moving power describes the third quarter of a revolution, the cylinders on tho second, fourth, &c., axles describe parts of a revolution or remain at rest, the cylinders on the other axles being unmoved : and lastly, when the moving power has described the fourth quarter of a revo lution, let certain cylinders only on the second, fourth, fic., axles make one-tenth of a revolution, the other cylinders remaining at rest. Then it may bo understood that by the first and third of these motions, numbers are added together: while, by the second and fourth, 1 ie carried to each figure which ought to be increased in consequence of a sum of two figures being greater than 10.
As an example, let it be required to obtain the numbers of the series in the first column above, beginning with 3125. The figures composing the numbers aro brought under the indices in front of the cylinders on the first vertical axis, towards the left hand ; and the figures composing the several orders of differences in front of the cylinders on the other axis, towards the right, as in this second table. Then the moving power being turned one quarter of a revo lution, each cylinder ip the first, third, and fifth vertical columns will be turned through as many tenths of a revolution as aro expressed by the number in front of the cylinder immediately on Its right hand : thus, the cylinder having 3 in flout (at the top of the first vertical column) will move through four-tenths of a revolution, and the number 7 will be brought under its index in front. The cylinder hav ing 1 in front (in the first vertical column) will be turned through six-tenths a a revolution, which will bring 7 under its index in front ; and so on. The numbers in front of the whole machine will now stand thus :— By the addition (in the preceeding 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), therefore 1 must be carried. The operation of carrying is per formed by the action of the moving power in the second quadrant of its 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 band. Thus, the cylinder marked 4 in the column of 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 0 (for 10) to its front ; this causes another carrying, and the cylinder marked 8, in the Caine 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 aeries is 7776 ; and th'e like operations being performed with the instru ment in the present state, the next number will be obtained in the first column. It has been supposed that the instrument has only six axles carrying cylinders ; but it is 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 than give the following general notion of the mechanism by which these remarkable move ments are produced. Immediately behind each column of the oylindere carrying the figures and In a vertical plane perpendicular to the front of the machine, ie a vertical axle x which carries, opposite to each cylinder, two horizontal wheels A and B, and between them a moveable bolt 0, also In a horizontal position. These two wheels are capable of being connected with or disconnebted 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 n 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 a, 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 b perpendicularly below its inferior surface. And the lower wheel n carries a wedge or inclined plane c. Behind the wheels on the axle x is another axle v, 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 e 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 I 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 n 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 ou 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.