are respectively 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9 teeth, and a considerable blank space; the section with 9 teeth being the farthest from the centre of the machine. The 8 teeth of the next section are a prolongation of an equal number of the teeth of the preceding; and so on for each section. So that to the eye the reckoner presents a series of successively decreasing teeth, and from its stepped appearance it may be termed a "stepped reckoner." The stopping or locking half of the cylinder is also stepped to correspond with the stepped reckoner. On the upper axis is a tube, free to slide longitudinally, and having a key fitting into a groove in the axis. The tube carries at its outer end a pinion of 10 teeth gearing with the stepped reckoner, and at its other end a star wheel of 10 rays fitting the stepped stop. A fork projecting below the number slide, fits into a groove round the tube, so that the motion of the number slide is communicated to the tube, whose pinion is thus placed in position to gear with that section of the reckoner, the teeth of which correspond in number with the figure in front of the curved rule. The pinion and star wheel are at such a distance apart, that the latter is always upon the section of the stepped stop, corresponding to the section of the reckoner, with which the former is placed to gear. On the lower axis, and nearer to the centre of the machine, is a piece movable longitudinally, but carried round with the axis by a pin fitting into a hole at the end of the stepped stop. It is composed of the "secondary carrying tooth," and its corresponding stop, there being an incline on the inner edge of the latter, the use of which will be presently explained. Just above this movable piece, there are, fixed on the upper axis, a second pinion of 10 teeth and a star wheel. The pinion is so set, that when the piece below it is close up to the stepped stop, the secondary carrying tooth passes it by; but when the piece is moved inwards, this carrying tooth gears with the pinion and when revolving, moves it one tooth forward. As soon as this has taken place, the incline comes in contact with a pin in the frame of the machine, which pushes the piece into its former position. Under the discs on the circle, the before-mentioned upper axis carries two reversed bevil wheels of 10 teeth each, on a tube free to move longitudinally, but carried round by a key fitting into a groove on the axis. These wheels are moved longitudinally by the regulator, as may be seen by taking off the circle. Between them. (and in gear with one or other of them, according to the position of the regulator) is a similar bevil wheel on the spindle of the corresponding number disc, and above the wheel is the "primary carrying tooth." As the pinions and the bevil wheels have each 10 teeth, and the number disc has 10 figures, every tooth when the pinions are moved counts one, either forward or backward on the disc. When the figure in the aperture over the disc passes from 9 to 0 in addition, or from 0 to 9 in subtraction, the primary carrying tooth passes the wedge-shaped end of the upper arm of the carrying lever, which it pushes back. This carrying lever moves on a perpendicular axis. Its lower arm clutches a pin in the shaft of a fork under and parallel with the lower axis beneath the next higher number slide. This fork fits into a groove round the movable picce of the secondary carrying tooth, which it shoots inwards into position for adding or carrying 1 as above described. Each lower axis is timed to operate on the pinions above it, at least one tooth later than its neighbour to the right, to allow time for the latter to shoot the carrying tooth. This is not the case, however, with the axis under the lowest Number Slide but one, and the Index Slides B and C, which are all timed to act simultaneously with the lowest Number Slide. It will be seen that each revolution of the motive-handle and consequently of the reckoners, causes the latter to move the pinions above them as many teeth as there are on the sections of the reckoners over which the pinions are respectively set by the number slides. This motion of the pinions is communicated to the number discs, and therefore adds or subtracts accordingly. Thomas de Colmar's straight machine is very similar in mechanism and is a little cheaper than the circular. I have tried both and personally prefer the straight machine; my reason is mainly because it is lighter and more portable, the straight arithmometer is contained in a box 33 x 7 x 35 inches, whereas Edmonson's circular is very much larger and heavier. Either of these machines will add, subtract, multiply, divide and extract the Square Root. As a sample of the speed of operation, it may be stated that the following multiple is worked in less than half a minute: 93,857,926 x 987,416,381,792-92,676,853,693,421,283,392. It multiplies and adds, or multiplies and subtracts, in one operation, which takes no more time than multiplying alone. It will multiply 12 figures by 12 figures (giving a product of 24 figures); or, with a multiplicand of 8 figures it will work a multiplier of any number of figures, however great. It will divide a dividend of any number of figures by a divisor of 8 figures, and will carry a quotient to any number of places of decimals. The method of working either machine is learnt in a very short time, and will be found invaluable to those who desire to get out FIG. 4.-THE STRAIGHT ARITHMOMETER. A, Small brass studs gliding in slits. B, Button by means of which the machine is adjusted for subtraction (or division) and multiplication (or addition). c, Holes at the bottom of which are seen the results of the operations. D, Holes in which are seen figures indicating the multiplier and the quotient. M, M, M, M is a movable plate. N, The handle which is to work the machine. o, Right button, by means of which all the figures in D. D. can be adjusted to zero. button, by means of which all the figures c, c, c, can be placed at zero. P, Left elaborate life tables, or other tabular matter involving the close application of the mind for many hours to figures. In the Journal of the Institute of Actuaries will be found papers by General Hannyngton (vol. xvi.), and by Mr. Peter Gray, giving directions in considerable detail for performing the most elaborate calculations in the formation of life contingency tables by aid of the Arithmometer; to these papers the reader is referred for farther information. 1 Messrs. Stanley, Great Turnstile, Holborn, are the agents for Edmonson's circular machine, 251. Mr. Redfern is the agent for De Colmar's Arithmometre, price 201. |