Part 20

To come to the point:--the small figure 4, in Plate 41, relates to this subject. My geering is there seen in three forms or applications--each one intended to bring the above property into play. The part _n o_, represents the manner in which two wheels with singly-inclined teeth, work together when one of them is furnished with a cheek, as directed in fig. 3 of Plate 14. But here, in addition to that, the teeth of both wheels are sloped _more_ on one side than on the other, so as to assume _a wedge-like form_: insomuch, that in beginning to work, (if not _perfectly_ formed) the wheels would not occupy the same plane. For, in fact, the _cheek screws_ press home the cheek _o_ against a number of thin washers all round the wheel, and thus only draw the wedge-formed teeth into each other as they become _bedded_, and successive washers are taken away. Hence, a good degree of precision is obtained--accompanied with little friction, and thus with great durability.

But we stop not here. The part _p q_ of this figure, shews a pair of wheels doubly inclined--one of them only, being made in two halves, which are connected together by screws and washers, like that just described. Here then, _another_ degree of friction is got rid of--namely, that of the cheek _o_: but still, a small degree remains, (dependent on the double versed sine of the angle formed on the wheel’s circumference, by the _thickness_ of a tooth). This quantity, is indeed, very minute; and brings, perhaps, the whole near enough to perfection. To do, however, completely away with all _friction_, (see my preceding statement)--as well in the wheel acting _backward_, as in that acting _forward_, we must do what is shewn in the parts _r_ or _s_ of fig. 4: we must have a _pair_ of V wheels on the same shaft, with the power of turning one of them in reference to the other; and then connecting them by proper screws, &c. to preserve the position thus given: by which means, in a word, all shake or _backlash_ will be completely annulled.

PART FIFTH. A NEW CENTURY OF Inventions.

OF AN ADDING MACHINE, _Or Machine to Cast up large Columns of Figures_.

This Machine is not, generally, an _arithmetical Machine_. It points _lower_: and therefore promises more general utility. Though less comprehensive than machines which perform all the _rules_ of arithmetic, it is thought capable of taking a prominent place in the counting-house, and there of effecting two useful purposes--to secure correctness; and thus, in many cases, to banish contention. It is represented in figs. 1, 2, 3, and 4 of Plate 42, and in figs. 3 and 4 of Plate 43.

There are two distinct classes of operations which may be noticed in this Machine: the one that does the _addition_, properly speaking; and the other that records it by figures, in the very terms of common arithmetic. The first operation is the adding: which is performed by means of an endless geering chain, stretched round the wheels _A B C D_, (fig. 1) and _over_ the two rows of smaller pulleys _a b c d e f g h i_; where, observe, that the chain is bent round the pulley _A_, merely to shorten the Machine, as otherwise the keys 1 2 3, &c. to 9, might have been placed in a straight line, and thus the bending of the chain have been avoided.

The chain, as before observed, _geers_ in the wheels _B_ and _D_, which both have ratchets to make them turn one way only. Now, the keys 1 2, &c. have pulleys at their lower ends, which press on the aforesaid chain more or less according to the _number it is to produce_, and the depth to which it is suffered to go by the bed on which the keys rest, when pressed down with the fingers. Thus, if the _key_ 1 be pressed, as low as it can go, it will bend the chain enough to draw the wheel _B_ round _one tooth_--which the catch _E_ will _secure_, and which the wheel _C_ will permit it to do by the spring _F_ giving way. But when the key 1 is suffered to rise again, this spring _F_ will tighten the chain by drawing it round the pulleys _A_ and _D_, thus giving it a circulating motion, more or less rapid, according to the number of the _key_ pressed. Thus, the key 5 would carry _five_ teeth of the wheel _B_ to the left; and the catch _E_ would fix the wheel _B_ in this new position: after which the spring _T_ would tighten the chain in the same direction and manner as before. It is thus evident, that which-ever key is pressed down, a given number of teeth in the wheel _B_, will be _taken_ and secured by the catch _E_; and, afterwards, the chain be again stretched by the spring _F_. It may be remarked, that, in the figure, _all_ the keys are supposed _pressed down_: so as to turn the wheel _B_, a number of teeth equal to the sum of the digits 1, 2, 3--to 9. But this is merely supposed to shew the increasing deflexion of the chain, as the digits increase: for the fact can hardly ever occur. We draw from it, however, one piece of knowledge--which is, that should the eye, in computing, catch several numbers at once on the page, the fingers may impress them at once on the keys and chain; when the result will be the same as though performed in due succession.

Thus then, the process of _adding_, is reduced to that of touching (and pressing as low as possible) a series of keys, which are _marked_ with the names of the several digits, and each of which is sure to affect the result according to it’s real value: And this seems all that need be observed in the description of this process. It remains, however, to describe the 5th. figure, which is an elevation of the _edge_ of the keyboard, intended to shew the manner in which the two rows of keys are combined and brought to a convenient distance, for the purpose of being easily _fingered_.

We now come to the other part of the subject--that of recording the several effects before-mentioned. The principle feature in this part, is the System of _carrying_, or transferring to a new _place of figures_, the results obtained at any given one. This operation depends on the effect we can produce by one wheel on another, placed near it, on the same pin; and on the possibility of affecting the second, _much_ less than the first is affected: Thus, in fig. 3 and 4, (Plate 42,) if _A_ be any tooth of one such wheel, placed _out_ of the plane of the pinion _B_, it will, in turning, produce no effect upon that pinion: but if we drive a pin (_a_) into the tooth _A_, that pin will move the pinion _B_ one tooth (and no more) every time this pin passes from _a_ to _b_. And if we now place a second wheel (_F_) similar to _A_, at a small distance from it, so as to _geer_ in _all_ the teeth of the pinion _B_, this latter wheel will be turned a space equal to _one_ tooth, every time the pin _a_ passes the line of the centres of the wheel and pinion _A B_, (say from _a_ to _b_.) It may be added, likewise, that this motion, _of one tooth_, is assured by the instrument shewn at _E D_, which is called in French _a tout ou rien_, (signifying all or nothing) and which, as soon as the given motion is _half_ performed, is sure to effect the rest: and thus does this part of the process acquire, likewise, a great degree of certainty--if indeed, certainty admits of comparison.

It is then, easy to perceive, how this effect on the different _places_ of figures is produced: and it is clear, that with the chain motion just described, it forms the basis of the whole Machine. There is, however, one other process to be mentioned, and as the 2d. figure is before us, we shall now advert to it. In adding up large sums, we have sometimes to _work_ on the _tens_, sometimes on the _hundreds_; which mutations are thus performed: The wheel _B_, (fig. 2) is the same as that _B_, fig. 1; and it turns the square shaft _B G_, on which the wheels _k l_ slide. The wheel _l_ is to our present purpose. It is _now_ opposite the place of shillings; but by the slide _m_, it can be successively placed opposite _pounds_, tens, hundreds, &c. at pleasure: on either of which columns, therefore, we can operate by the chain first described--the wheel _B_ being the common mover.

We shall now turn to figs. 3 and 4 of Plate 43, which give another representation of the carrying-mechanism, adapted especially to the anomalous _carriages_ of 4, 12, and 20, in reference to farthings, pence, shillings, and pounds, and _then_ following the decuple ratio.

In fig. 3, _k l_ represent the two acting wheels of the shaft _B G_, fig. 2; the latter _dotted_, as being placed _behind_ the former; these wheels, however, are not our present object, but rather the carrying system before alluded to; and described separately, in fig. 3 of Plate 42. _A_, in figures 3 and 4 (of Plate 43) is the first wheel of this series. It has 12 teeth with _three_ carriage-pins (or plates) _a_, which jog the carrying-pinion _B_, at every passage of 4 teeth; thus shewing every _penny_ that is accumulated by the _farthings_. This is so, because the farthings are marked on the teeth of this first wheel in this order--1, 2, 3, 0; 1, 2, 3, &c. and it is in passing from 3 to 0, that this wheel, by the carriage-pinion _B_, jogs forward the _pence wheel_ _C_ one tooth: But this pence wheel is divided into 12 numbers, from 0 to 11; and has on it only _one_ carrying-pin (or plate) _b_; so that, here, there is no effect produced on the third wheel _D_, until 12 pence have been brought to this second wheel _C_, by the first, or farthing wheel _A_. Now, this third wheel _D_, is marked, on it’s _twenty_ teeth, with the figures 0 to 19, and makes, therefore, one revolution, then only, when there have been twenty shillings impressed upon it by twenty jogs of the carriage-pin _b_, in the second wheel _C_. But when this wheel _D_ has made one whole revolution, it’s single _carriage-pin_ _c_, acting on the small _carriage-pinion_, like that _c d_, (but not shewn) jogs forward, by one tooth, the wheel _E_, which expresses _pounds_; and having _two_ carriage-pins _e f_, turns the wheel called _tens of pounds_, one tooth for every half turn of this wheel _E_: and as, on all the succeeding wheels, to the left from _E_--(see fig. 2, Plate 42) there are two sets of digits up to 10, and two carriage-pins; the decuple ratio now continues without any change: and thus can we cast up sums consisting of pounds, shillings, pence, and farthings, expressing the results, in a row of figures, exactly as they would be written by an accountant. The opening, through which they would appear, being shewn in fig. 1, at the point _w_, corresponding with the line _x y_ of fig. 2 in the same Plate.

I shall only remark, further, that the figures 3 and 4 in Plate 43, are of the natural size, founded, indeed, on the use of a chain that I think _too large_; being, in a word, the real chain _de Vaucanson_, mentioned in a former article: and that the figures of Plate 42 are made to half these dimensions, in order to bring them into a convenient compass on the Plate.

I would just repeat, that I have not attempted here an arithmetical machine in general; but a Machine fit for the daily operations of the counting-house; by which to favour the thinking faculty, by easing it of this ungrateful and uncertain labour. Had I been thus minded, I could have gone further, in a road which has been already _travelled_ by my noble friend the late Earl Stanhope, (then Lord Mahon) but I took a lower aim; intending in the words of Bacon--“to come home to men’s business and bosoms.”

OF A ROTATORY PUNCH MACHINE _Adapted to my own Engraving Machine_.

It is highly desirable, (not to say indispensable) in the use of my engraving Machine, to have punches not only of the true cylindrical form, but exactly of the proper length. (See the remarks on this subject, in the description of that Machine). It is, therefore, a matter of consequence, to be assured that both these circumstances unite; and to unite them _without_ depending on personal skill, whenever the work can be accomplished without such dependence: and this is the object of the present rotatory Punch Machine. Adverting first to the length of the punch: _that_ is insured by having a kind of slide on the Punch Machine, formed like the _frog_ spoken of in the above article--Engraving Machine. In the 5th. figure of Plate 43, this slide is shewn at _a_, and it is at exactly the same distance from the centre of motion _A_, as the bottom of the frog-plate fig. 3 Plate 39 is from _it’s_ centre of motion. Thus, the bottom of the punch is filed straight, once for all, and being fixed in proper clams, as in the figures, the shaft _A_ is set a-turning, by power--from which motion two uses are derived: first, the cylindrical form is given to the punch by presenting to it, in it’s revolution, a _file_ duly wedged on the (now fixed) slide of the Machine _B B_; against which it is kept turning, till, by a due depression of the centre _A_, the radius is brought to the length required, and the surface perfectly formed and smoothed. This being achieved, the cams _c d_, are fixed to the slide _B B_, and to the turning body _A d_, so that when the die _f_ is moved toward the left hand by the said cams, the prepared punch gently presses on it, and begins to receive it’s impressions; which are gradually deepened by the set screws _g h_, fig. 6; till, at once, the proper radius is given, and the engraving sufficiently transferred from the die to the punch--an operation which this process is calculated to perform, rather by means of frequent and gentle contacts, than by slow and heavy pressure. It need not be added, that the motion of the slide _B B_ is reciprocated by the spring _C_, against that _D_, after each forward motion given to it--as _begun_ by the _cams_ _c d_, and continued by the contact of the die and punch, all which a mere inspection of the figures will sufficiently explain. It is likewise evident, that the figs. 5 and 6, shew, both, the same objects, namely:--the regulating wedges _i k_, the upper set screws _g h_, and the rollers _E_, on which the slide vibrates during the operation of the Machine.

OF A PORTABLE PUMP, _To be worked by the Feet_.

It is not solely because, to work with the feet is a good method of employing the strength of men, that this device is presented to the mechanical public; but it is with the view of _so_ employing the feet and hands, that they may occasion a constant and _equable_ flow of water. The means, (see Plate 44, fig. 1) are, to provide the man with two supports _a b_ for his hands, and two pedals _c d_ for his feet, by which the two rods _e f_ are worked; and by them, through the cords or chains _g h_, the piston rods _i_ and _k_. Of the latter, the one which answers to the lower pump _l_, goes through the upper piston, whose rod is _i_: and the pistons are both constructed in the manner shewn in fig. 2; that is to say, the piston has no _body_, fitting the pump barrel: but a triangular bar _x_, going diagonally across the pump barrel, (which is square) and carrying two wings or valves _y z_; which, both together, fill the barrel _when down_, and leave it as empty as possible when up, by which motion the chains _a e_ are slackened. Further, these pistons, with their rods, are heavy enough to raise the pedals, the instant the man raises his feet in any degree: so that, by a proper combination of the motions of his hands and feet, he can let down a given piston, and begin again it’s ascending motion before his effort has wholly ceased on the other pedal. A mean this, of producing a constant and equable rising motion in the column of water through the pumps _k l_; and a mean also, of doing more work with a given fatigue, than would be _possible_ in a pump whose motions were merely reciprocal, and the water of which, in rising, would be subject to any unequable or convulsive motions.

In general, this portable pump was made (many years ago) with a view to being easily carried to any field or garden, bordering on a river, and worked on it’s bank; the flexible suction pipe _p_ being thrown into the river, or a well, as occasion might require. To this end, the whole frame (as is evident from the figure) can be folded up into a kind of _faggot_: and thus it’s transport from place to place, be made perfectly commodious.

OF THE BISECTING COMPASSES.

It _often_ happens, that from a central line, (in drawing for example) we want to set off, quickly, many equal distances on each side; or between two given lines we want a central line; to perform either of which operations, is the use of the Instrument just mentioned.

It is represented in Plate 44. figs. 3 and 4, where _A B_ is the central _point_, being cylindrical in the greatest part of it’s length, and conical at _E B_. It slides correctly in two _cannons_ or swivels _E_ & _A_, which also have two short axes or trunnions, on which _first_, the double compass joints _C D_ turn; and second, the _two_ pairs of arms _F G_. I have called these cannons, _swivels_, that I may shew their construction, by referring to figure 1 in Plate 30--which describes the swivel of the _forcing Machine_; and which will give a complete idea of what is here intended. From this construction it will appear evident, that the point _A B_, (Plate 44) will be always found in the middle, between the two points, of the outer legs of the compasses; and _that_ whether the question is to take two equal distances from a central point, or to _bisect_ a given line or distance at one operation. The point or style now _slides_ in the two swivels _A_ and _E_; but the Instrument might be so constructed, as for it to follow the rising motion of the middle joint (_E_), and thus to keep the three joints in the same horizontal line: but I think a small perpendicular motion of the said _style_, would be always desirable in the Machine, as a drawing Instrument.

OF A MUSICIAN’S PITCH-FORK, _With variable Tones_.

This device is shewn, in two positions, at figs. 1 and 2 of Plate 45. In it’s present application, it is intended to produce a whole octave on the diatonic scale: and therefore, the unsupported ends of the fork are just half as long as they would become if the sliding handle _A_, were drawn to the bottom end of the branches _c d_. For, again, the fixing screw _C_, and it’s box _D_ are fastened to this sliding handle by one or two screws, (_s_) so as to be always ready to press the branches against the enclosed slide _A B_, at whatever place the intended tone may be found. Now, the branches _a c_, _b d_, spring out of a common trunk _c d_, which is pierced with a square hole, exactly fitting this sliding handle _A B_; and the latter is marked, at proper distances, with lines across it, each of which (placed opposite the mark _c d_) gives such a length to the remaining branches _a b_, as to make them sound the note desired. Thus, the line l, brought to _c d_, lengthens the branches _a b_, to (nearly) 53 parts, from 50 at which they are _now_ fixed; the whole length _a c_, being 100. This, and the following divisions would, of course, follow any desired _temperament_, according to the will of the tuner: but I have supposed them founded on the equi-harmonic scale; and thus will the successive intervals to be set off on the slide _B A_, be as follows: (while the corresponding notes will be those expressed in the table.)

In the state represented by the figures 1 and 2, the line a _B_, is 5000; being one half of the whole length _a b_, _c d_.

To form the Sharp 7th. it becomes 5297 the distance _c d_ 1, being 297. „ greater 6th. „ 5946 „ 1-2, „ 649. „ „ 5th. „ 6674 „ 2-3, „ 728. „ „ 4th. „ 7491 „ 3-4, „ 817. „ „ 3rd. „ 7937 „ 4-5, „ 446. „ „ 2nd. „ 8909 „ 5-6, „ 972. „ the fundamental note 10000 „ 6-7, „ 1091.

The above lengths 1 2, 2 3, &c. have been measured off on the slide _A B_, as nearly as possible, or at least with precision enough to give the idea: and the rest I must leave the detail of, to those musical readers who may feel interested in the subject.

OF AN ESSAY, _To obtain a Level at Sea_.

I have done right in calling these attempts “essays”: and if I had said “immature attempts,” they would have been better designated. Yet, having promised them to my readers, I cannot now withhold them, although, from want of opportunity of trial, I can do little more than _talk_ of their supposed properties.

The first essay, as shewn in fig. 3 of Plate 45, is a _mental deduction_ from a device which I executed in 1801, and brought before the public at the exhibition then given, by the French government, of the produce of national _industrie_. It was, nothing more than a _pendulum_, made with a view to lengthen, considerably, the going of a given clock, without altering the wheels. To that end, the weight or bob, was a heavy bar _C D_, suspended diagonally on two points _A B_, placed at a distance from each other, exactly equal to the length of the said bar: and _that_ by the double cross-bars _B C_ and _A D_, of a length sufficient to make the whole assume a form exactly square: where it may be noted--that were this figure _longer_ than high, the curve of vibration would have two points of inflexion, and the bar _would not_ place itself horizontally at last; and that were it narrower and _higher_, that curve would assume a form more like, though still distant from, the arc of a circle. In the present case, such was the effect of this disposition of things, that the centre of gravity of the bar described, in vibrating, a curve _E C D F_, the lower form of which, was so near to a _horizontal line_, that the _times_ of vibration were immensely prolonged; so much indeed, as to represent a common pendulum of several thousand feet in height; and to give a proportionate slowness to any mechanism with which it should have been connected. In fact, this line is so minutely different from such horizontal line, that it is wholly included in the thickness of the _drawn-line_ _C D_: nor becomes visible but near it’s two ends _C D_, when it begins to rise, and _then_ rises faster than that described by a _short_ common pendulum.

In fine, this curve itself is formed by continually bisecting the line or bar _C D_, and drawing lines from it’s centre of gravity, thus found in one of it’s positions, to the same in another position, till the curve _E C D_, &c. arises from this process.

It follows, then, from the nature of this curve, (or pair of curves) that the time of vibration of this pendulum is the _longer_, the _shorter_ the arcs are, in which it vibrates; and that, when the vibrations have attained a certain _length_, compared with the height to which the centre of gravity rises, the _time_ becomes considerably shorter. I shall not now pursue this idea, because it is at once an abstruse question, and at the same time one of uncertain utility--I mean that it’s use is problematical as a pendulum: since the _time_ of a vibration depends on it’s _length_, which cannot _easily_ be determined by any invariable method. I shall, however, add two things on this subject, by way of land mark; the one, that the balance-wheel of a watch has power enough to drive this pendulum, heavy as it is;--and the other, that I have _seen_ it make (for many hours together) vibrations of _half a minute’s duration!_ In a word, this is one of the subjects, which untoward circumstances have prevented me from bringing to maturity--but which I owe to my subscribers, and the public, in any, or every state, to which I have brought them.