The common process would be as follows:--

From 768

Subtract 357

----

Remainder 411

The _arithmetical complement_ of 357, or the number by which it falls

short of 1000, is 643. Now, if this number be added to 768, and the

first figure on the left be struck out of the sum, the process will be

as follows:--

To 768

Add 643

----

Sum 1411

----

Remainder sought 411

The principle on which this process is founded is easily explained. In

the latter process we have first added 643, and then subtracted 1000. On

the whole, therefore, we have subtracted 357, since the number actually

subtracted exceeds the number previously added by that amount.

Since, therefore, subtraction may be effected in this manner by

addition, it follows that the calculation of all serieses, so far as an

order of differences can be found in them which continues constant, may

be conducted by the process of addition alone.

It also appears from what has been stated, that each addition consists

only of two operations. However numerous the figures may be of which the

several pairs of numbers to be thus added may consist, it is obvious

that the operation of adding them can only consist of repetitions of the

process of adding one digit to another; and of carrying one from the

column of inferior units to the column of units next superior when

necessary. If we would therefore reduce such a process to machinery, it

would only be necessary to discover such a combination of moving parts

as are capable of performing these two processes of _adding_ and _carrying_

on two single figures; for, this being once accomplished, the process of

adding two numbers, consisting of any number of digits, will be effected

by repeating the same mechanism as often as there are pairs of digits to

be added. Such was the simple form to which Mr Babbage reduced the

problem of discovering the calculating machinery; and we shall now

proceed to convey some notion of the manner in which he solved it.

For the sake of illustration, we shall suppose that the table to be

calculated shall consist of numbers not exceeding six places of figures;

and we shall also suppose that the difference of the fifth order is the

constant difference. Imagine, then, six rows of wheels, each wheel

carrying upon it a dial-plate like that of a common clock, but

consisting of _ten_ instead of _twelve_ divisions; the several divisions

being marked 1, 2, 3, 4, 5, 6, 7, 8, 9, 0. Let these dials be supposed

to revolve whenever the wheels to which they are attached are put in

motion, and to turn in such a direction that the series of increasing

numbers shall pass under the index which appears over each dial:--thus,

after 0 passes the index, 1 follows, then 2, 3, and so on, as the dial

revolves. In Fig. 1 are represented six horizontal rows of such dials.

Fig. 1.

The method of differences, as already explained, requires, that in

proceeding with the calculation, this apparatus should perform

continually the addition of the number expressed upon each row of dials,

to the number expressed upon the row immediately above it. Now, we shall

first explain how this process of addition may be conceived to be

performed by the motion of the dials; and in doing so, we shall consider

separately the processes of addition and carriage, considering the

addition first, and then the carriage.

Let us first suppose the line D^1 to be added to the line T. To

accomplish this, let us imagine that while the dials on the line D^1 are

quiescent, the dials on the line T are put in motion, in such a manner,

that as many divisions on each dial shall pass under its index, as there

are units in the number at the index immediately below it. It is evident

that this condition supposes, that if 0 be at any index on the line D^1,

the dial immediately above it in the line T shall not move. Now the

motion here supposed, would bring under the indices on the line T such a

number as would be produced by adding the number D^1 to T, neglecting all

the carriages; for a carriage should have taken place in every case in

which the figure 9 of any dial in the line T had passed under the index

during the adding motion. To accomplish this carriage, it would be

necessary that the dial immediately on the left of any dial in which 9

passes under the index, should be advanced one division, independently

of those divisions which it may have been advanced by the addition of

the number immediately below it. This effect may be conceived to take

place in either of two ways. It may be either produced at the moment

when the division between 9 and 0 of any dial passes under the index; in

which case the process of carrying would go on simultaneously with the

process of adding; or the process of carrying may be postponed in every

instance until the process of addition, without carrying, has been

completed; and then by another distinct and independent motion of the

machinery, a carriage may be made by advancing one division all those

dials on the right of which a dial had, during the previous addition,

passed from 9 to 0 under the index. The latter is the method adopted in

the calculating machinery, in order to enable its inventor to construct

the carrying machinery independent of the adding mechanism.

Having explained the motion of the dials by which the addition,

excluding the carriages of the number on the row D^1, may be made to the

number on the row T, the same explanation may be applied to the number

on the row D^2 to the number on the row D^1; also, of the number D^3 to the

number on the row D^2, and so on. Now it is possible to suppose the

additions of all the rows, except the first, to be made to all the rows

except the last, simultaneously; and after these additions have been

made, to conceive all the requisite carriages to be also made by

advancing the proper dials one division forward. This would suppose all

the dials in the scheme to receive their adding motion together; and,

this being accomplished, the requisite dials to receive their carrying

motions together. The production of so great a number of simultaneous

motions throughout any machinery, would be attended with great

mechanical difficulties, if indeed it be practicable. In the calculating

machinery it is not attempted. The additions are performed in two

successive periods of time, and the carriages in two other periods of

time, in the following manner. We shall suppose one complete revolution

of the axis which moves the machinery, to make one complete set of

additions and carriages; it will then make them in the following

order:--

The first quarter of a turn of the axis will add the second, fourth, and

sixth rows to the first, third, and fifth, omitting the carriages; this

it will do by causing the dials on the first, third, and fifth rows, to

turn through as many divisions as are expressed by the numbers at the

indices below them, as already explained.

The second quarter of a turn will cause the carriages consequent on the

previous addition, to be made by moving forward the proper dials one

division.

(During these two quarters of a turn, the dials of the first, third, and

fifth row alone have been moved; those of the second, fourth, and sixth,

have been quiescent.)

The third quarter of a turn will produce the addition of the third and

fifth rows to the second and fourth, omitting the carriages; which it

will do by causing the dials of the second and fourth rows to turn

through as many divisions as are expressed by the numbers at the indices

immediately below them.

The fourth and last quarter of a turn will cause the carriages

consequent on the previous addition, to be made by moving the proper

dials forward one division.

This evidently completes one calculation, since all the rows except the

first have been respectively added to all the rows except the last.

To illustrate this: let us suppose the table to be computed to be that

of the fifth powers of the natural numbers, and the computation to have

already proceeded so far as the fifth power of 6, which is 7776. This

number appears, accordingly, in the highest row, being the place

appropriated to the number of the table to be calculated. The several

differences as far as the fifth, which is in this case constant, are

exhibited on the successive rows of dials in such a manner, as to be

adapted to the process of addition by alternate rows, in the manner

already explained. The process of addition will commence by the motion

of the dials in the first, third, and fifth rows, in the following

manner: The dial A, fig. 1, must turn through one division, which will

bring the number 7 to the index; the dial B must turn through three

divisions, which will 0 bring to the index; this will render a carriage

necessary, but that carriage will not take place during the present

motion of the dial. The dial C will remain unmoved, since 0 is at the

index below it; the dial D must turn through nine divisions; and as, in

doing so, the division between 9 and 0 must pass under the index, a

carriage must subsequently take place upon the dial to the left; the

remaining dials of the row T, fig. 1, will remain unmoved. In the row D^2

the dial A^2 will remain unmoved, since 0 is at the index below it; the

dial B^2 will be moved through five divisions, and will render a

subsequent carriage on the dial to the left necessary; the dial C^2 will

be moved through five divisions; the dial D^2 will be moved through three

divisions, and the remaining dials of this row will remain unmoved. The

dials of the row D^4 will be moved according to the same rules; and the

whole scheme will undergo a change exhibited in fig. 2; a mark (*) being

introduced on those dials to which a carriage is rendered necessary by

the addition which has just taken place.

Fig. 2.

The second quarter of a turn of the moving axis, will move forward

through one division all the dials which in fig. 2 are marked (*), and

the scheme will be converted into the scheme expressed in fig. 3.

Fig. 3.

In the third quarter of a turn, the dial A^1, fig. 3, will remain

unmoved, since 0 is at the index below it; the dial B^1 will be moved

forward through three divisions; C^1 through nine divisions, and so

on; and in like manner the dials of the row D^3 will be moved forward

through the number of divisions expressed at the indices in the row D^4.

This change will convert the arrangement into that expressed in fig. 4,

the dials to which a carriage is due, being distinguished as before by

(*).

Fig. 4.

The fourth quarter of a turn of the axis will move forward one division

all the dials marked (*); and the arrangement will finally assume the

form exhibited in fig. 5, in which the calculation is completed. The

first row T in this expresses the fifth power of 7; and the second

expresses the number which must be added to the first row, in order to

produce the fifth power of 8; the numbers in each row being prepared for

the change which they must undergo, in order to enable them to continue

the computation according to the method of alternate addition here

adopted.

Fig. 5.

Having thus explained what it is that the mechanism is required to do,

we shall now attempt to convey at least a general notion of some of the

mechanical contrivances by which the desired ends are attained. To

simplify the explanation, let us first take one particular

instance--the dials B and B^1, fig. 1, for example. Behind the dial B^1

is a bolt, which, at the commencement of the process, is shot between

the teeth of a wheel which drives the dial B: during the first quarter

of a turn this bolt is made to revolve, and if it continued to be

engaged in the teeth of the said wheel, it would cause the dial B to

make a complete revolution; but it is necessary that the dial B should

only move through three divisions, and, therefore, when three divisions

of this dial have passed under its index, the aforesaid bolt must be

withdrawn: this is accomplished by a small wedge, which is placed in a

fixed position on the wheel behind the dial B^1, and that position is

such that this wedge will press upon the bolt in such a manner, that at

the moment when three divisions of the dial B have passed under the

index, it shall withdraw the bolt from the teeth of the wheel which it

drives. The bolt will continue to revolve during the remainder of the

first quarter of a turn of the axis, but it will no longer drive the

dial B, which will remain quiescent. Had the figure at the index of the

dial B^1 been any other, the wedge which withdraws the bolt would have

assumed a different position, and would have withdrawn the bolt at a

different time, but at a time always corresponding with the number under

the index of the dial B^1: thus, if 5 had been under the index of the

dial B^1, then the bolt would have been withdrawn from between the teeth

of the wheel which it drives, when five divisions of the dial B had

passed under the index, and so on. Behind each dial in the row D^1 there

is a similar bolt and a similar withdrawing wedge, and the action upon

the dial above is transmitted and suspended in precisely the same

manner. Like observations will be applicable to all the dials in the

scheme here referred to, in reference to their adding actions upon those

above them.

There is, however, a particular case which here merits notice: it is the

case in which 0 is under the index of the dial from which the addition

is to be transmitted upwards. As in that case nothing is to be added, a

mechanical provision should be made to prevent the bolt from engaging in

the teeth of the wheel which acts upon the dial above: the wedge which

causes the bolt to be withdrawn, is thrown into such a position as to

render it impossible that the bolt should be shot, or that it should

enter between the teeth of the wheel, which in other cases it drives.

But inasmuch as the usual means of shooting the bolt would still act, a

strain would necessarily take place in the parts of the mechanism, owing

to the bolt not yielding to the usual impulse. A small shoulder is

therefore provided, which puts aside, in this case, the piece by which

the bolt is usually struck, and allows the striking implement to pass

without encountering the head of the bolt or any other obstruction. This

mechanism is brought into play in the scheme, fig. 1, in the cases of

all those dials in which 0 is under the index.

Such is a general description of the nature of the mechanism by which

the adding process, apart from the carriages, is effected. During the

first quarter of a turn, the bolts which drive the dials in the first,

third, and fifth rows, are caused to revolve, and to act upon these

dials, so long as they are permitted by the position of the several

wedges on the second, fourth, and sixth rows of dials, by which these

bolts are respectively withdrawn; and, during the third quarter of a

turn, the bolts which drive the dials of the second and fourth rows are

made to revolve and act upon these dials so long as the wedges on the

dials of the third and fifth rows, which withdraw them, permit. It will

hence be perceived, that, during the first and third quarters of a turn,

the process of addition is continually passing upwards through the

machinery; alternately from the even to the odd rows, and from the odd

to the even rows, counting downwards.

We shall now attempt to convey some notion of the mechanism by which the

process of carrying is effected during the second and fourth quarters of

a turn of the axis. As before, we shall first explain it in reference to

a particular instance. During the first quarter of a turn the wheel B^2,

fig. 1, is caused by the adding bolt to move through five divisions; and

the fifth of these divisions, which passes under the index, is that

between 9 and 0. On the axis of the wheel C^2, immediately to the left of

B^2, is fixed a wheel, called in mechanics a ratchet wheel, which is

driven by a claw which constantly rests in its teeth. This claw is in

such a position as to permit the wheel C^2 to move in obedience to the

action of the adding bolt, but to resist its motion in the contrary

direction. It is drawn back by a spiral spring, but its recoil is

prevented by a hook which sustains it; which hook, however, is capable

of being withdrawn, and when withdrawn, the aforesaid spiral spring

would draw back the claw, and make it fall through one tooth of the

ratchet wheel. Now, at the moment that the division between 9 and 0 on

the dial B^2 passes under the index, a thumb placed on the axis of this

dial touches a trigger which raises out of the notch the hook which

sustains the claw just mentioned, and allows it to fall back by the

recoil of the spring, and to drop into the next tooth of the ratchet

wheel. This process, however, produces no immediate effect upon the

position of the wheel C^2, and is merely preparatory to an action

intended to take place during the second quarter of a turn of the moving

axis. It is in effect a memorandum taken by the machine of a carriage to

be made in the next quarter of a turn.

During the second quarter of a turn, a finger placed on the axis of the

dial B^2 is made to revolve, and it encounters the heel of the

above-mentioned claw. As it moves forward it drives the claw before it:

and this claw, resting in the teeth of the ratchet wheel fixed upon the

axis of the dial C^2 drives forward that wheel, and with it the dial. But

the length and position of the finger which drives the claw limits its

action, so as to move the claw forward through such a space only as will

cause the dial C^2 to advance through a single division; at which point

it is again caught and retained by the hook. This will be added to the

number under its index, and the requisite carriage from B^2 to C^2 will be

accomplished.

In connexion with every dial is placed a similar ratchet wheel with a

similar claw, drawn by a similar spring, sustained by a similar hook,

and acted upon by a similar thumb and trigger; and therefore the

necessary carriages, throughout the whole machinery, take place in the

same manner and by similar means.

During the second quarter of a turn, such of the carrying claws as have

been allowed to recoil in the first, third, and fifth rows, are drawn up

by the fingers on the axes of the adjacent dials; and, during the fourth

quarter of a turn, such of the carrying claws on the second and fourth

rows as have been allowed to recoil during the third quarter of a turn,

are in like manner drawn up by the carrying fingers on the axes of the

adjacent dials. It appears that the carriages proceed alternately from

right to left along the horizontal rows during the second and fourth

quarters of a turn; in the one, they pass along the first, third, and

fifth rows, and in the other, along the second and fourth.

There are two systems of waves of mechanical action continually flowing

from the bottom to the top; and two streams of similar action constantly

passing from the right to the left. The crests of the first system of

adding waves fall upon the last difference, and upon every alternate one

proceeding upwards; while the crests of the other system touch upon the

intermediate differences. The first stream of carrying action passes

from right to left along the highest row and every alternate row, while

the second stream passes along the intermediate rows.

Such is a very rapid and general outline of this machinery. Its wonders,

however, are still greater in its details than even in its broader

features. Although we despair of doing it justice by any description

which can be attempted here, yet we should not fulfil the duty we owe to

our readers, if we did not call their attention at least to a few of the

instances of consummate skill which are scattered, with a prodigality

characteristic of the highest order of inventive genius, throughout this

astonishing mechanism.

In the general description which we have given of the mechanism for

_carrying_, it will be observed, that the preparation for every carriage

is stated to be made during the previous addition, by the disengagement

of the carrying claw before mentioned, and by its consequent recoil,

urged by the spiral spring with which it is connected; but it may, and

does, frequently happen, that though the process of addition may not

have rendered a carriage necessary, one carriage may itself produce the

necessity for another. This is a contingency not provided against in the

mechanism as we have described it: the case would occur in the scheme

represented in fig. 1, if the figure under the index of C^2 were 4

instead of 3. The addition of the number 5 at the index of C^3 would, in

this case, in the first quarter of a turn, bring 9 to the index of C^2:

this would obviously render no carriage necessary, and of course no

preparation would be made for one by the mechanism--that is to say, the

carrying claw of the wheel D^2 would not be detached. Meanwhile a

carriage upon C^2 has been rendered necessary by the addition made in the

first quarter of a turn to B^2. This carriage takes place in the ordinary

way, and would cause the dial C^2, in the second quarter of a turn, to

advance from 9 to 0: this would make the necessary preparation for a

carriage from C^2 to D^2. But unless some special arrangement was made for

the purpose, that carriage would not take place during the second

quarter of a turn. This peculiar contingency is provided against by an

arrangement of singular mechanical beauty, and which, at the same time,

answers another purpose--that of equalizing the resistance opposed to

the moving power by the carrying mechanism. The fingers placed on the

axes of the several dials in the row D^2, do not act at the same instant

on the carrying claws adjacent to them; but they are so placed, that

their action may be distributed throughout the second quarter of a turn

in regular succession. Thus the finger on the axis of the dial A^2 first

encounters the claw upon B^2, and drives it through one tooth immediately

forwards; the finger on the axis of B^2 encounters the claw upon C^2 and

drives it through one tooth; the action of the finger on C^2 on the claw

on D^2 next succeeds, and so on. Thus, while the finger on B^2 acts on C^2,

and causes the division from 9 to 0 to pass under the index, the thumb

on C^2 at the same instant acts on the trigger, and detaches the carrying

claw on D^2, which is forthwith encountered by the carrying finger on C^2,

and driven forward one tooth. The dial D^2 accordingly moves forward one

division, and 5 is brought under the index. This arrangement is

beautifully effected by placing the several fingers, which act upon the

carrying claws, _spirally_ on their axes, so that they come into action in

regular succession.

We have stated that, at the commencement of each revolution of the

moving axis, the bolts which drive the dials of the first, third, and

fifth rows, are shot. The process of shooting these bolts must therefore

have taken place during the last quarter of the preceding revolution;

but it is during that quarter of a turn that the carriages are effected

in the second and fourth rows. Since the bolts which drive the dials of

the first, third, and fifth rows, have no mechanical connexion with the

dials in the second and fourth rows, there is nothing in the process of

shooting those bolts incompatible with that of moving the dials of the

second and fourth rows: hence these two processes may both take place

during the same quarter of a turn. But in order to equalize the

resistance to the moving power, the same expedient is here adopted as

that already described in the process of carrying. The arms which shoot

the bolts of each row of dials are arranged spirally, so as to act

successively throughout the quarter of a turn. There is, however, a

contingency which, under certain circumstances, would here produce a

difficulty which must be provided against. It is possible, and in fact

does sometimes happen, that the process of carrying causes a dial to

move under the index from 0 to 1. In that case, the bolt, preparatory to

the next addition, ought not to be shot until after the carriage takes

place; for if the arm which shoots it passes its point of action before

the carriage takes place, the bolt will be moved out of its sphere of

action, and will not be shot, which, as we have already explained, must

always happen when 0 is at the index: therefore no addition would in

this case take place during the next quarter of a turn of the axis;

whereas, since 1 is brought to the index by the carriage, which

immediately succeeds the passage of the arm which ought to bolt, 1

should be added during the next quarter of a turn. It is plain,

accordingly, that the mechanism should be so arranged, that the action

of the arms, which shoot the bolts successively, should immediately

follow the action of those fingers which raise the carrying claws

successively; and therefore either a separate quarter of a turn should

be appropriated to each of those movements, or if they be executed in

the same quarter of a turn, the mechanism must be so constructed, that

the arms which shoot the bolts successively, shall severally follow

immediately after those which raise the carrying claws successively. The

latter object is attained by a mechanical arrangement of singular

felicity, and partaking of that elegance which characterises all the

details of this mechanism. Both sets of arms are spirally arranged on

their respective axes, so as to be carried through their period in the

same quarter of a turn; but the one spiral is shifted a few degrees, in

angular position, behind the other, so that each pair of corresponding

arms succeed each other in the most regular order,--equalizing the

resistance, economizing time, harmonizing the mechanism, and giving to

the whole mechanical action the utmost practical perfection.

The system of mechanical contrivances by which the results, here

attempted to be described, are attained, form only one order of

expedients adopted in this machinery;--although such is the perfection

of their action, that in any ordinary case they would be regarded as

having attained the ends in view with an almost superfluous degree of

precision. Considering, however, the immense importance of the purposes

which the mechanism was destined to fulfil, its inventor determined that

a higher order of expedients should be superinduced upon those already

described; the purpose of which should be to obliterate all small errors

or inequalities which might, even by remote possibility, arise, either

from defects in the original formation of the mechanism, from inequality

of wear, from casual strain or derangement,--or, in short, from any

other cause whatever. Thus the movements of the first and principal

parts of the mechanism were regarded by him merely as a first, though

extremely nice approximation, upon which a system of small corrections

was to be subsequently made by suitable and independent mechanism. This

supplementary system of mechanism is so contrived, that if one or more

of the moving parts of the mechanism of the first order be slightly out

of their places, they will be forced to their exact position by the

action of the mechanical expedients of the second order to which we now

allude. If a more considerable derangement were produced by any

accidental disturbance, the consequence would be that the supplementary

mechanism would cause the whole system to become locked, so that not a

wheel would be capable of moving; the impelling power would necessarily

lose all its energy, and the machine would stop. The consequence of this

exquisite arrangement is, that the machine will either calculate

rightly, or not at all.

The supernumerary contrivances which we now allude to, being in a great

degree unconnected with each other, and scattered through the machinery

to a certain extent, independent of the mechanical arrangement of the

principal parts, we find it difficult to convey any distinct notion of

their nature or form.

In some instances they consist of a roller resting between certain

curved surfaces, which has but one position of stable equilibrium, and

that position the same, however the roller or the curved surfaces may

wear. A slight error in the motion of the principal parts would make

this roller for the moment rest on one of the curves; but, being

constantly urged by a spring, it would press on the curved surface in

such a manner as to force the moving piece on which that curved surface

is formed, into such a position that the roller may rest between the two

surfaces; that position being the one which the mechanism should have. A

greater derangement would bring the roller to the crest of the curve, on

which it would rest in instable equilibrium; and the machine would

either become locked, or the roller would throw it as before into its

true position.

In other instances a similar object is attained by a solid cone being

pressed into a conical seat; the position of the axis of the cone and

that of its seat being necessarily invariable, however the cone may

wear: and the action of the cone upon the seat being such, that it

cannot rest in any position except that in which the axis of the cone

coincides with the axis of its seat.

Having thus attempted to convey a notion, however inadequate, of the

calculating section of the machinery, we shall proceed to offer some

explanation of the means whereby it is enabled, to print its

calculations in such a manner as to preclude the possibility of error in

any individual printed copy.

On the axle of each of the wheels which express the calculated number of

the table T, there is fixed a solid piece of metal, formed into a curve,

not unlike the wheel in a common clock, which is called the _snail_. This

curved surface acts against the arm of a lever, so as to raise that arm

to a higher or lower point according to the position of the dial with

which the snail is connected. Without entering into a more minute

description, it will be easily understood that the snail may be so

formed that the arm of the lever shall be raised to ten different

elevations, corresponding to the ten figures of the dial which may be

brought under the index. The opposite arm of the lever here described

puts in motion a solid arch, or sector, which carries ten punches: each

punch bearing on its face a raised character of a figure, and the ten

punches bearing the ten characters, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0. It will

be apparent from what has been just stated, that this _type sector_ (as it

is called) will receive ten different attitudes, corresponding to the

ten figures which may successively be brought under the index of the

dial-plate. At a point over which the type sector is thus moved, and

immediately under a point through which it plays, is placed a frame, in

which is fixed a plate of copper. Immediately over a certain point

through which the type sector moves, is likewise placed a _bent lever_,

which, being straightened, is forcibly pressed upon the punch which has

been brought under it. If the type sector be moved, so as to bring under

the bent lever one of the steel punches above mentioned, and be held in

that position for a certain time, the bent lever, being straightened,

acts upon the steel punch, and drives it against the face of the copper

beneath, and thus causes a sunken impression of the character upon the

punch to be left upon the copper. If the copper be now shifted slightly

in its position, and the type sector be also shifted so as to bring

another punch under the bent lever, another character may be engraved on

the copper by straightening the bent lever, and pressing it on the punch

as before. It will be evident, that if the copper was shifted from right

to left through a space equal to two figures of a number, and, at the

same time, the type sector so shifted as to bring the punches

corresponding to the figures of the number successively under the bent

lever, an engraved impression of the number might thus be obtained upon

the copper by the continued action of the bent lever. If, when one line

of figures is thus obtained, a provision be made to shift the copper in

a direction at right angles to its former motion, through a space equal

to the distance between two lines of figures, and at the same time to

shift it through a space in the other direction equal to the length of

an entire line, it will be evident that another line of figures might be

printed below the first in the same manner.

The motion of the type sector, here described, is accomplished by the

action of the snail upon the lever already mentioned. In the case where

the number calculated is that expressed in fig. 1, the process would be

as follows:--The snail of the wheel F^1, acting upon the lever, would

throw the type sector into such an attitude, that the punch bearing the

character 0 would come under the bent lever. The next turn of the moving

axis would cause the bent lever to press on the tail of the punch, and

the character 0 would be impressed upon the copper. The bent lever being

again drawn up, the punch would recoil from the copper by the action of

a spring; the next turn of the moving axis would shift the copper

through the interval between two figures, so as to bring the point

destined to be impressed with the next figure under the bent lever. At

the same time, the snail of the wheel E would cause the type sector to

be thrown into the same attitude as before, and the punch would be

brought under the bent lever; the next turn would impress the figure

beside the former one, as before described. The snail upon the wheel D

would now come into action, and throw the type sector into that position

in which the punch bearing the character 7 would come under the bent

lever, and at the same time the copper would be shifted through the

interval between two figures; the straightening of the lever would next

follow, and the character 7 would be engraved. In the same manner, the

wheels C, B, and A would successively act by means of their snails; and

the copper being shifted, and the lever allowed to act, the number

007776 would be finally engraved upon the copper: this being

accomplished, the calculating machinery would next be called into

action, and another calculation would be made, producing the next number

of the Table exhibited in fig. 5. During this process the machinery

would be engaged in shifting the copper both in the direction of its

length and its breadth, with a view to commence the printing of another

line; and this change of position would be accomplished at the moment

when the next calculation would be completed: the printing of the next

number would go on like the former, and the operation of the machine

would proceed in the same manner, calculating and printing alternately.

It is not, however, at all necessary--though we have here supposed it,

for the sake of simplifying the explanation--that the calculating part

of the mechanism should have its action suspended while the printing

part is in operation, or _vice versa_; it is not intended, in fact, to be

so suspended in the actual machinery. The same turn of the axis by which

one number is printed, executes a part of the movements necessary for

the succeeding calculation; so that the whole mechanism will be

simultaneously and continuously in action.

Of the mechanism by which the position of the copper is shifted from

figure to figure, from line to line, we shall not attempt any

description. We feel that it would be quite vain. Complicated and

difficult to describe as every other part of this machinery is, the

mechanism for moving the copper is such as it would be quite impossible

to render at all intelligible, without numerous illustrative drawings.

The engraved plate of copper obtained in the manner above described, is

designed to be used as a mould from which a stereotyped plate may be

cast; or, if deemed advisable, it may be used as the immediate means of

printing. In the one case we should produce a table, printed from type,

in the same manner as common letter-press printing; in the other an

engraved table. If it be thought most advisable to print from the

stereotyped plates, then as many stereotyped plates as may be required

may be taken from the copper mould; so that when once a table has been

calculated and engraved by the machinery, the whole world may be

supplied with stereotyped plates to print it, and may continue to be so

supplied for an unlimited period of time. There is no practical limit to

the number of stereotyped plates which may be taken from the engraved

copper; and there is scarcely any limit to the number of printed copies

which may be taken from any single stereotyped plate. Not only,

therefore, is the numerical table by these means engraved and

stereotyped with infallible accuracy, but such stereotyped plates are

producible in unbounded quantity. Each plate, when produced, becomes

itself the means of producing printed copies of the table, in accuracy

perfect, and in number without limit.

Unlike all other machinery, the calculating mechanism produces, not the

object of consumption, but the machinery by which that object may be

made. To say that it computes and prints with infallible accuracy, is to

understate its merits:--it computes and fabricates _the means_ of

printing with absolute correctness and in unlimited abundance.

For the sake of clearness, and to render ourselves more easily

intelligible to the general reader, we have in the preceding explanation

thrown the mechanism into an arrangement somewhat different from that

which is really adopted. The dials expressing the numbers of the tables

of the successive differences are not placed, as we have supposed them,

in horizontal rows, and read from right to left, in the ordinary way;

they are, on the contrary, placed vertically, one below the other, and

read from top to bottom. The number of the table occupies the first

vertical column on the right, the units being expressed on the lowest

dial, and the tens on the next above that, and so on. The first

difference occupies the next vertical column on the left; and the

numbers of the succeeding differences occupy vertical columns,

proceeding regularly to the left; the constant difference being on the

last vertical column. It is intended in the machine now in progress to

introduce six orders of differences, so that there will be seven columns

of dials; it is also intended that the calculations shall extend to

eighteen places of figures: thus each column will have eighteen dials.

We have referred to the dials as if they were inscribed upon the faces

of wheels, whose axes are horizontal and planes vertical. In the actual

machinery the axes are vertical and the planes horizontal, so that the

edges of the _figure wheels_, as they are called, are presented to the

eye. The figures are inscribed, not upon the dial-plate, but around the

surface of a small cylinder or barrel, placed upon the axis of the

figure wheel, which revolves with it; so that as the figure wheel

revolves, the figures on the barrel are successively brought to the

front, and pass under an index engraved upon a plate of metal

immediately above the barrel. This arrangement has the obvious practical

advantage, that, instead of each figure wheel having a separate axis,

all the figure wheels of the same vertical column revolve on the same

axis; and the same observation will apply to all the wheels with which

the figure wheels are in mechanical connexion. This arrangement has the

further mechanical advantage over that which has been assumed for the

purposes of explanation, that the friction of the wheel-work on the axes

is less in amount, and more uniformly distributed, than it could be if

the axes were placed in the horizontal position.

A notion may therefore be formed of the front elevation of the

calculating part of the mechanism, by conceiving seven steel axes

erected, one beside another, on each of which shall be placed eighteen

wheels,[12] five inches in diameter, having cylinders or barrels upon

them an inch and a half in height, and inscribed, as already stated,

with the ten arithmetical characters. The entire elevation of the

machinery would occupy a space measuring ten feet broad, ten feet high,

and five feet deep. The process of calculation would be observed by the

alternate motion of the figure wheels on the several axes. During the

first quarter of a turn, the wheels on the first, third, and fifth axes

would turn, receiving their addition from the second, fourth, and sixth;

during the second quarter of a turn, such of the wheels on the first,

third, and fifth axes, to which carriages are due, would be moved

forward one additional figure; the second, fourth, and sixth columns of

wheels being all this time quiescent. During the third quarter of a

turn, the second, fourth, and sixth columns would be observed to move,

receiving their additions from the third, fifth, and seventh axes; and

during the fourth quarter of a turn, such of these wheels to which

carriages are due, would be observed to move forward one additional

figure; the wheels of the first, third, and fifth columns being

quiescent during this time.

[Footnote 12: The wheels, and every other part of the mechanism except

the axes, springs, and such parts as are necessarily of steel, are

formed of an alloy of copper with a small portion of tin.]

It will be observed that the wheels of the seventh column are always

quiescent in this process; and it may be asked, of what use they are,

and whether some mechanism of a fixed nature would not serve the same

purpose? It must, however, be remembered, that for different tables

there will be different constant differences; and that when the

calculation of a table is about to commence, the wheels on the seventh

axis must be moved by the hand, so as to express the constant

difference, whatever it may be. In tables, also, which have not a

difference rigorously constant, it will be necessary, after a certain

number of calculations, to change the constant difference by the hand;

and in this case the wheels of the seventh axis must be moved when

occasion requires. Such adjustment, however, will only be necessary at

very distant intervals, and after a considerable extent of printing and

calculation has taken place; and when it is necessary, a provision is

made in the machinery by which notice will be given by the sounding of a

bell, so that the machine may not run beyond the extent of its powers of

calculation.

Immediately behind the seven axes on which the figure wheels revolve,

are seven other axes; on which are placed, first, the wheels already

described as driven by the figure wheels, and which bear upon them the

wedge which withdraws the bolt immediately over these latter wheels, and

on the same axis is placed the adding bolt. From the bottom of this bolt

there projects downwards the pin, which acts upon the unbolting wedge by

which the bolt is withdrawn: from the upper surface of the bolt proceeds

a tooth, which, when the bolt is shot, enters between the teeth of the

adding wheel, which turns on the same axis, and is placed immediately

above the bolt: its teeth, on which the bolt acts, are like the teeth of

a crown wheel, and are presented downwards. The bolt is fixed upon this

axis, and turns with it; but the adding wheel above the bolt, and the

unbolting wheel below it, both turn upon the axis, and independently of

it. When the axis is made to revolve by the moving power, the bolt

revolves with it; and so long as the tooth of the bolt remains inserted

between those of the adding wheel, the latter is likewise moved; but

when the lower pin of the bolt encounters the unbolting wedge on the

lower wheel, the tooth of the bolt is withdrawn, and the motion of the

adding wheel is stopped. This adding wheel is furnished with spur teeth,

besides the crown teeth just mentioned; and these spur teeth are engaged

with those of that unbolting wheel which is in connexion with the

adjacent figure wheel to which the addition is to be made. By such an

arrangement it is evident that the revolution of the bolt will

necessarily add to the adjacent figure wheel the requisite number.

It will be perceived, that upon the same axis are placed an unbolting

wheel, a bolt, and an adding wheel, one above the other, for every

figure wheel; and as there are eighteen figure wheels there will be

eighteen tiers; each tier formed of an unbolting wheel, a bolt, and an

adding wheel, placed one above the other; the wheels on this axis all

revolving independent of the axis, but the bolts being all fixed upon

it. The same observations, of course, will apply to each of the seven

axes.

At the commencement of every revolution of the adding axes, it is

evident that the several bolts placed upon them must be shot in order to

perform the various additions. This is accomplished by a third set of

seven axes, placed at some distance behind the range of the wheels,

which turn upon the adding axes: these are called _bolting axes_. On these

bolting axes are fixed, so as to revolve with them, a bolting finger

opposite to each bolt; as the bolting axis is made to revolve by the

moving power, the bolting finger is turned, and as it passes near the

bolt, it encounters the shoulder of a hammer or lever, which strikes the

heel of the bolt, and presses it forward so as to shoot its tooth

between the crown teeth of the adding wheel. The only exception to this

action is the case in which 0 happens to be at the index of the figure

wheel; in that case, the lever or hammer, which the bolting finger would

encounter, is, as before stated, lifted out of the way of the bolting

finger, so that it revolves without encountering it. It is on the

bolting axes that the fingers are spirally arranged so as to equalize

their action, as already explained.

The same axes in the front of the machinery on which the figure wheels

turn, are made to serve the purpose of _carrying_. Each of these bear a

series of fingers which turn with them, and which encounter a carrying

claw, already described, so as to make the carriage: these carrying

fingers are also spirally arranged on their axes, as already described.

Although the absolute accuracy which appears to be ensured by the

mechanical arrangements here described is such as to render further

precautions nearly superfluous, still it may be right to state, that,

supposing it were possible for an error to be produced in calculation,

this error could be easily and speedily detected in the printed tables:

it would only be necessary to calculate a number of the table taken at

intervals, through which the mechanical action of the machine has not

been suspended, and during which it has received no adjustment by the

hand: if the computed number be found to agree with those printed, it

may be taken for granted that all the intermediate numbers are correct;

because, from the nature of the mechanism, and the principle of

computation, an error occurring in any single number of the table would

be unavoidably entailed, in an increasing ratio, upon all the succeeding

numbers.

We have hitherto spoken merely of the practicability of executing by the

machinery, when completed, that which its inventor originally

contemplated--namely, the calculating and printing of all numerical

tables, derived by the method of differences from a constant difference.

It has, however, happened that the actual powers of the machinery

greatly transcend those contemplated in its original design:--they not

only have exceeded the most sanguine anticipations of its inventor, but

they appear to have an extent to which it is utterly impossible, even

for the most acute mathematical thinker, to fix a probable limit.

Certain subsidiary mechanical inventions have, in the progress of the

enterprise, been, by the very nature of the machinery, suggested to the

mind of the inventor, which confer upon it capabilities which he had

never foreseen. It would be impossible even to enumerate, within the

limits of this article, much less to describe in detail, those

extraordinary mechanical arrangements, the effects of which have not

failed to strike with astonishment every one who has been favoured with

an opportunity of witnessing them, and who has been enabled, by

sufficient mathematical attainments, in any degree to estimate their

probable consequences.

As we have described the mechanism, the axes containing the several

differences are successively and regularly added one to another; but

there are certain mechanical adjustments, and these of a very simple

nature, which being thrown into action, will cause a difference of any

order to be added any number of times to a difference of any other

order; and that either proceeding backwards or forwards, from a

difference of an inferior to one of a superior order, and _vice versa_.[13]

[Footnote 13: The machine was constructed with the intention of tabulating

the equation Delta^{7}_{u} = 0, but, by the means

above alluded to, it is capable of tabulating such equations as the

following: Delta^{7}u = a Delta u, Delta^{7}u = aDelta^{3}u,

Delta^{7}u = units figure of Delta u.]

Among other peculiar mechanical provisions in the machinery is one by

which, when the table for any order of difference amounts to a certain

number, a certain arithmetical change would be made in the constant

difference. In this way a series may be tabulated by the machine, in

which the constant difference is subject to periodical change; or the

very nature of the table itself may be subject to periodical change, and

yet to one which has a regular law.

Some of these subsidiary powers are peculiarly applicable to

calculations required in astronomy, and are therefore of eminent and

immediate practical utility: others there are by which tables are

produced, following the most extraordinary, and apparently capricious,

but still regular laws. Thus a table will be computed, which, to any

required extent, shall coincide with a given table, and which shall

deviate from that table for a single term, or for any required number of

terms, and then resume its course, or which shall permanently alter the

law of its construction. Thus the engine has calculated a table which

agreed precisely with a table of square numbers, until it attained the

hundred and first term, which was not the square of 101, nor were any of

the subsequent numbers squares. Again, it has computed a table which

coincided with the series of natural numbers, as far as 100,000,001, but

which subsequently followed another law. This result was obtained, not

by working the engine through the whole of the first table, for that

would have required an enormous length of time; but by showing, from the

arrangement of the mechanism, that it must continue to exhibit the

succession of natural numbers, until it would reach 100,000,000. To save

time, the engine was set by the hand to the number 99999995, and was

then put in regular operation. It produced successively the following

numbers.[14]

99,999,996

99,999,997

99,999,998

99,999,999

100,000,000

100,010,002

100,030,003

100,060,004

100,100,005

100,150,006

&c. &c.

[Footnote 14: Such results as this suggest a train of reflection on the

nature and operation of general laws, which would lead to very curious

and interesting speculations. The natural philosopher and astronomer

will be hardly less struck with them than the metaphysician and

theologian.]

Equations have been already tabulated by the portion of the machinery

which has been put together, which are so far beyond the reach of the

present power of mathematics, that no distant term of the table can be

predicted, nor any function discovered capable of expressing its general

law. Yet the very fact of the table being produced by mechanism of an

invariable form, and including a distinct principle of mechanical

action, renders it quite manifest that _some_ general law must exist in

every table which it produces. But we must dismiss these speculations:

we feel it impossible to stretch the powers of our own mind, so as to

grasp the probable capabilities of this splendid production of combined

mechanical and mathematical genius; much less can we hope to enable

others to appreciate them, without being furnished with such means of

comprehending them as those with which we have been favoured. Years must

in fact elapse, and many enquirers direct their energies to the

cultivation of the vast field of research thus opened, before we can

fully estimate the extent of this triumph of matter over mind. 'Nor is

it,' says Mr Colebrooke, 'among the least curious results of this

ingenious device, that it affords a new opening for discovery, since it

is applicable, as has been shown by its inventor, to surmount novel

difficulties of analysis. Not confined to constant differences, it is

available in every case of differences that follow a definite law,

reducible therefore to an equation. An engine adjusted to the purpose

being set to work, will produce any distant term, or succession of

terms, required--thus presenting the numerical solution of a problem,

even though the analytical solution be yet undetermined.' That the

future path of some important branches of mathematical enquiry must now

in some measure be directed by the dictates of mechanism, is

sufficiently evident; for who would toil on in any course of analytical

enquiry, in which he must ultimately depend on the expensive and

fallible aid of human arithmetic, with an instrument in his hands, in

which all the dull monotony of numerical computation is turned over to

the untiring action and unerring certainty of mechanical agency?

It is worth notice, that each of the axes in front of the machinery on

which the figure wheels revolve, is connected with a bell, the tongue of

which is governed by a system of levers, moved by the several figure

wheels; an adjustment is provided by which the levers shall be

dismissed, so as to allow the hammer to strike against the bell,

whenever any proposed number shall be exhibited on the axis. This

contrivance enables the machine to give notice to its attendants at any

time that an adjustment may be required.

Among a great variety of curious accidental properties (so to speak)

which the machine is found to possess, is one by which it is capable of

solving numerical equations which have rational roots. Such an equation

being reduced (as it always may be) by suitable transformations to that

state in which the roots shall be whole numbers, the values 0, 1, 2, 3,

&c., are substituted for the unknown quantity, and the corresponding

values of the equation ascertained. From these a sufficient number of

differences being derived, they are set upon the machine. The machine

being then put in motion, the table axis will exhibit the successive

values of the formula, corresponding to the substitutions of the

successive whole numbers for the unknown quantity: at length the number

exhibited on the table axis will be 0, which will evidently correspond

to a root of the equation. By previous adjustment, the bell of the table

axis will in this case ring and give notice of the exhibition of the

value of the root in another part of the machinery.

If the equation have imaginary roots, the formula being necessarily a

maximum or minimum on the occurrence of such roots, the first difference

will become nothing; and the dials of that axis will under such

circumstances present to the respective indices. By previous adjustment,

the bell of this axis would here give notice of a pair of imaginary

roots.

Mr Colebrooke speculates on the probable extension of these powers of

the machine: 'It may not therefore be deemed too sanguine an

anticipation when I express the hope that an instrument which, in its

simpler form, attains to the extraction of roots of numbers, and

approximates to the roots of equations, may, in a more advanced state of

improvement, rise to the approximate solution of algebraic equations of

elevated degrees. I refer to solutions of such equations proposed by La

Grange, and more recently by other annalists, which involve operations

too tedious and intricate for use, and which must remain without

efficacy, unless some mode be devised of abridging the labour, or

facilitating the means of its performance. In any case this engine tends

to lighten the excessive and accumulating burden of arithmetical

application of mathematical formulæ, and to relieve the progress of

science from what is justly termed by the author of this invention, the

overwhelming encumbrance of numerical detail.'

Although there are not more than eighteen figure wheels on each axis,

and therefore it might be supposed that the machinery was capable of

calculating only to the extent of eighteen decimal places; yet there are

contrivances connected with it, by which, in two successive

calculations, it will be possible to calculate even to the extent of

thirty decimal places. Its powers, therefore, in this respect, greatly

exceed any which can be required in practical science. It is also

remarkable, that the machinery is capable of producing the calculated

results _true to the last figure_. We have already explained, that when

the figure which would follow the last is greater than 4, then it would

be necessary to increase the last figure by 1; since the excess of the

calculated number above the true value would in such case be less than

its defect from it would be, had the regularly computed final figure

been adopted: this is a precaution necessary in all numerical tables,

and it is one which would hardly have been expected to be provided for

in the calculating machinery.

As might be expected in a mechanical undertaking of such complexity and

novelty, many practical difficulties have since its commencement been

encountered and surmounted. It might have been foreseen, that many

expedients would be adopted and carried into effect, which farther

experiments would render it necessary to reject; and thus a large source

of additional expense could scarcely fail to be produced. To a certain

extent this has taken place; but owing to the admirable system of

mechanical drawings, which in every instance Mr Babbage has caused to be

made, and owing to his own profound acquaintance with the practical

working of the most complicated mechanism, he has been able to predict

in every case what the result of any contrivance would be, as perfectly

from the drawing, as if it had been reduced to the form of a working

model. The drawings, consequently, form a most extensive and essential

part of the enterprise. They are executed with extraordinary ability and

precision, and may be considered as perhaps the best specimens of

mechanical drawings which have ever been executed. It has been on these,

and on these only, that the work of invention has been bestowed. In

these, all those progressive modifications suggested by consideration

and study have been made; and it was not until the inventor was fully

satisfied with the result of any contrivance, that he had it reduced to

a working form. The whole of the loss which has been incurred by the

necessarily progressive course of invention, has been the expense of

rejected drawings. Nothing can perhaps more forcibly illustrate the

extent of labour and thought which has been incurred in the production

of this machinery, than the contemplation of the working drawings which

have been executed previously to its construction: these drawings cover

above a thousand square feet of surface, and many of them are of the

most elaborate and complicated description.

One of the practical difficulties which presented themselves at a very

early stage in the progress of this undertaking, was the impossibility

of bearing in mind all the variety of motions propagated simultaneously

through so many complicated trains of mechanism. Nothing but the utmost

imaginable harmony and order among such a number of movements, could

prevent obstructions arising from incompatible motions encountering each

other. It was very soon found impossible, by a mere act of memory, to

guard against such an occurrence; and Mr Babbage found, that, without

some effective expedient by which he could at a glance see what every

moving piece in the machinery was doing at each instant of time, such

inconsistencies and obstructions as are here alluded to must continually

have occurred. This difficulty was removed by another invention of even

a more general nature than the calculating machinery itself, and

pregnant with results probably of higher importance. This invention

consisted in the contrivance of a scheme of _mechanical notation_ which is

generally applicable to all machinery whatsoever; and which is exhibited

on a table or plan consisting of two distinct sections. In the first is

traced, by a peculiar system of signs, the origin of every motion which

takes place throughout the machinery; so that the mechanist or inventor

is able, by moving his finger along a certain line, to follow out the

motion of every piece from effect to cause, until he arrives at the

prime mover. The same sign which thus indicates the _source_ of motion

indicates likewise the _species_ of motion, whether it be continuous or

reciprocating, circular or progressive, &c. The same system of signs

further indicates the nature of the mechanical connexion between the

mover and the thing moved, whether it be permanent and invariable (as

between the two arms of a lever), or whether the mover and the moved are

separate and independent pieces, as is the case when a pinion drives a

wheel; also whether the motion of one piece necessarily implies the

motion of another; or when such motion in the one is interrupted, and in

the other continuous, &c.

The second section of the table divides the time of a complete period of

the machinery into any required number of parts; and it exhibits in a

map, as it were, that which every part of the machine is doing at each

moment of time. In this way, incompatibility in the motions of different

parts is rendered perceptible at a glance. By such means the contriver

of machinery is not merely prevented from introducing into one part of

the mechanism any movement inconsistent with the simultaneous action of

the other parts; but when he finds that the introduction of any

particular movement is necessary for his purpose, he can easily and

rapidly examine the whole range of the machinery during one of its

periods, and can find by inspection whether there is any, and what

portion of time, at which no motion exists incompatible with the desired

one, and thus discover a _niche_, as it were, in which to place the

required movement. A further and collateral advantage consists in

placing it in the power of the contriver to exercise the utmost possible

economy of _time_ in the application of his moving power. For example,

without some instrument of mechanical enquiry equally powerful with that

now described, it would be scarcely possible, at least in the first

instance, so to arrange the various movements that they should be all

executed in the least possible number of revolutions of the moving axis.

Additional revolutions would almost inevitably be made for the purpose

of producing movements and changes which it would be possible to

introduce in some of the phases of previous revolutions: and there is no

one acquainted with the history of mechanical invention who must not be

aware, that in the progressive contrivance of almost every machine the

earliest arrangements are invariably defective in this respect; and that

it is only by a succession of improvements, suggested by long

experience, that that arrangement is at length arrived at, which

accomplishes all the necessary motions in the shortest possible time. By

the application of the mechanical notation, however, absolute perfection

may be arrived at in this respect; even before a single part of the

machinery is constructed, and before it has any other existence than

that which it obtains upon paper.

Examples of this class of advantages derivable from the notation will

occur to the mind of every one acquainted with the history of mechanical

invention. In the common suction-pump, for example, the effective agency

of the power is suspended during the descent of the piston. A very

simple contrivance, however, will transfer to the descent the work to be

accomplished in the next ascent; so that the duty of four strokes of the

piston may thus be executed in the time of two. In the earlier

applications of the steam-engine, that machine was applied almost

exclusively to the process of pumping; and the power acted only during

the descent of the piston, being suspended during its ascent. When,

however, the notion of applying the engine to the general purposes of

manufacture occurred to the mind of Watt, he saw that it would be

necessary to cause it to produce a continued rotatory motion; and,

therefore, that the intervals of intermission must be filled up by the

action of the power. He first proposed to accomplish this by a second

cylinder working alternately with the first; but it soon became apparent

that the blank which existed during the upstroke in the action of the

power, might be filled up by introducing the steam at both ends of the

cylinder alternately. Had Watt placed before him a scheme of mechanical

notation such as we allude to, this expedient would have been so

obtruded upon him that he must have adopted it from the first.

One of the circumstances from which the mechanical notation derives a

great portion of its power as an instrument of investigation and

discovery, is that it enables the inventor to dismiss from his thoughts,

and to disencumber his imagination of the arrangement and connexion of

the mechanism; which, when it is very complex (and it is in that case

that the notation is most useful), can only be kept before the mind by

an embarrassing and painful effort. In this respect the powers of the

notation may not inaptly be illustrated by the facilities derived in

complex and difficult arithmetical questions from the use of the

language and notation of algebra. When once the peculiar conditions of

the question are translated into algebraical signs, and 'reduced to an

equation,' the computist dismisses from his thoughts all the

circumstances of the question, and is relieved from the consideration of

the complicated relations of the quantities of various kinds which may

have entered it. He deals with the algebraical symbols, which are the

representatives of those quantities and relations, according to certain

technical rules of a general nature, the truth of which he has

previously established; and, by a process almost mechanical, he arrives

at the required result. What algebra is to arithmetic, the notation we

now allude to is to mechanism. The various parts of the machinery under

consideration being once expressed upon paper by proper symbols, the

enquirer dismisses altogether from his thoughts the mechanism itself,

and attends only to the symbols; the management of which is so extremely

simple and obvious, that the most unpractised person, having once

acquired an acquaintance with the signs, cannot fail to comprehend their

use.

A remarkable instance of the power and utility of this notation occurred

in a certain stage of the invention of the calculating machinery. A

question arose as to the best method of producing and arranging a

certain series of motions necessary to print and calculate a number. The

inventor, assisted by a practical engineer of considerable experience

and skill, had so arranged these motions, that the whole might be

performed by twelve revolutions of the principal moving axis. It seemed,

however, desirable, if possible, to execute these motions by a less

number of revolutions. To accomplish this, the engineer sat down to

study the complicated details of a part of the machinery which had been

put together; the inventor at the same time applied himself to the

consideration of the arrangement and connexion of the symbols in his

scheme of notation. After a short time, by some transposition of

symbols, he caused the received motions to be completed by eight turns

of the axis. This he accomplished by transferring the symbols which

occupied the last four divisions of his scheme, into such blank spaces

as he could discover in the first eight divisions; due care being taken

that no symbols should express actions at once simultaneous and

incompatible. Pushing his enquiry, however, still further, he proceeded

to ascertain whether his scheme of symbols did not admit of a still more

compact arrangement, and whether eight revolutions were not more than

enough to accomplish what was required. Here the powers of the practical

engineer completely broke down. By no effort could he bring before his

mind such a view of the complicated mechanism as would enable him to

decide upon any improved arrangement. The inventor, however, without any

extraordinary mental exertion, and merely by sliding a bit of ruled

pasteboard up and down his plan, in search of a vacancy where the

different motions might be placed, at length contrived to pack all the

motions, which had previously occupied eight turns of the handle, into

five turns. The symbolic instrument with which he conducted the

investigation, now informed him of the impossibility of reducing the

action of the machine to a more condensed form. This appeared by the

fulness of every space along the lines of compatible action. It was,

however, still possible, by going back to the actual machinery, to

ascertain whether movements, which, under existing arrangements, were

incompatible, might not be brought into harmony. This he accordingly

did, and succeeded in diminishing the number of incompatible conditions,

and thereby rendered it possible to make actions simultaneous which were

before necessarily successive. The notation was now again called into

requisition, and a new disposition of the parts was made. At this point

of the investigation, this extraordinary instrument of mechanical

analysis put forth one of its most singular exertions of power. It

presented to the eye of the engineer two currents of mechanical action,

which, from their nature, could not be simultaneous; and each of which

occupied a complete revolution of the axis, except about a twentieth;

the one occupying the last nineteen-twentieths of a complete revolution

of the axis, and the other occupying the first nineteen-twentieths of a

complete revolution. One of these streams of action was, the successive

picking up by the carrying fingers of the successive carrying claws; and

the other was, the successive shooting of nineteen bolts by the nineteen

bolting fingers. The notation rendered it obvious, that as the bolting

action commenced a small space below the commencement of the carrying,

and ended an equal space below the termination of the carrying, the two

streams of action could be made to flow after one another in one and the

same revolution of the axis. He thus succeeded in reducing the period of

completing the action to four turns of the axis; when the notation again

informed him that he had again attained a limit of condensed action,

which could not be exceeded without a further change in the mechanism.

To the mechanism he again recurred, and soon found that it was possible

to introduce a change which would cause the action to be completed in

three revolutions of the axis. An odd number of revolutions, however,

being attended with certain practical inconveniences, it was considered

more advantageous to execute the motions in four turns; and here again

the notation put forth its powers, by informing the inventor, _through

the eye_, almost independent of his mind, what would be the most elegant,

symmetrical, and harmonious disposition of the required motions in four

turns. This application of an almost metaphysical system of abstract

signs, by which the motion of the hand performs the office of the mind,

and of profound practical skill in mechanics alternately, to the

construction of a most complicated engine, forcibly reminds us of a

parallel in another science, where the chemist with difficulty succeeds

in dissolving a refractory mineral, by the alternate action of the most

powerful acids, and the most caustic alkalies, repeated in

long-continued succession.

This important discovery was explained by Mr Babbage, in a short paper

read before the Royal Society, and published in the Philosophical

Transactions in 1826.[15] It is to us more a matter of regret than

surprise, that the subject did not receive from scientific men in this

country that attention to which its importance in every practical point

of view so fully entitled it. To appreciate it would indeed have been

scarcely possible, from the very brief memoir which its inventor

presented, unaccompanied by any observations or arguments of a nature to

force it upon the attention of minds unprepared for it by the nature of

their studies or occupations. In this country, science has been

generally separated from practical mechanics by a wide chasm. It will be

easily admitted, that an assembly of eminent naturalists and physicians,

with a sprinkling of astronomers, and one or two abstract

mathematicians, were not precisely the persons best qualified to

appreciate such an instrument of mechanical investigation as we have

here described. We shall not therefore be understood as intending the

slightest disrespect for these distinguished persons, when we express

our regret, that a discovery of such paramount practical value, in a

country preeminently conspicuous for the results of its machinery,

should fall still-born and inconsequential through their hands, and be

buried unhonoured and undiscriminated in their miscellaneous

transactions. We trust that a more auspicious period is at hand; that

the chasm which has separated practical from scientific men will

speedily close; and that that combination of knowledge will be effected,

which can only be obtained when we see the men of science more

frequently extending their observant eye over the wonders of our

factories, and our great practical manufacturers, with a reciprocal

ambition, presenting themselves as active and useful members of our

scientific associations. When this has taken place, an order of

scientific men will spring up, which will render impossible an oversight

so little creditable to the country as that which has been committed

respecting the mechanical notation.[16] This notation has recently

undergone very considerable extension and improvement. An additional

section has been introduced into it; designed to express the process of

circulation in machines, through which fluids, whether liquid or

gaseous, are moved. Mr Babbage, with the assistance of a friend who

happened to be conversant with the structure and operation of the

steam-engine, has illustrated it with singular felicity and success in

its application to that machine. An eminent French surgeon, on seeing

the scheme of notation thus applied, immediately suggested the

advantages which must attend it as an instrument for expressing the

structure, operation, and circulation of the animal system; and we

entertain no doubt of its adequacy for that purpose. Not only the

mechanical connexion of the solid members of the bodies of men and

animals, but likewise the structure and operation of the softer parts,

including the muscles, integuments, membranes, &c.; the nature, motion,

and circulation of the various fluids, their reciprocal effects, the

changes through which they pass, the deposits which they leave in

various parts of the system; the functions of respiration, digestion,

and assimilation,--all would find appropriate symbols and

representatives in the notation, even as it now stands, without those

additions of which, however, it is easily susceptible. Indeed, when we

reflect for what a very different purpose this scheme of symbols was

contrived, we cannot refrain from expressing our wonder that it should

seem, in all respects, as if it had been designed expressly for the

purposes of anatomy and physiology.

[Footnote 15: Phil. Trans. 1820, Part III. p. 250, on a method of

expressing by signs the action of machinery.]

[Footnote 16: This discovery has been more justly appreciated by

scientific men abroad. It was, almost immediately after its publication,

adopted as the topic of lectures, in an institution on the Continent for

the instruction of Civil Engineers.]

Another of the uses which the slightest attention to the details of this

notation irresistibly forces upon our notice, is to exhibit, in the form

of a connected plan or map, the organization of an extensive factory, or

any great public institution, in which a vast number of individuals are

employed, and their duties regulated (as they generally are or ought to

be) by a consistent and well-digested system. The mechanical notation is

admirably adapted, not only to express such an organized connexion of

human agents, but even to suggest the improvements of which such

organization is susceptible--to betray its weak and defective points,

and to disclose, at a glance, the origin of any fault which may, from

time to time, be observed in the working of the system. Our limits,

however, preclude us from pursuing this interesting topic to the extent

which its importance would justify. We shall be satisfied if the hints

here thrown out should direct to the subject the attention of those who,

being most interested in such an enquiry, are likely to prosecute it

with greatest success.

One of the consequences which has arisen in the prosecution of the

invention of the calculating machinery, has been the discovery of a

multitude of mechanical contrivances, which have been elicited by the

exigencies of the undertaking, and which are as novel in their nature as

the purposes were novel which they were designed to attain. In some

cases several different contrivances were devised for the attainment of

the same end; and that among them which was best suited for the purpose

was finally selected: the rejected expedients--those overflowings or

waste of the invention--were not, however, always found useless. Like

the _waste_ in various manufactures, they were soon converted to purposes

of utility. These rejected contrivances have found their way, in many

cases, into the mills of our manufacturers; and we now find them busily

effecting purposes, far different from any which the inventor dreamed

of, in the spinning-frames of Manchester.[17]

[Footnote 17: An eminent and wealthy retired manufacturer at Manchester

assured us, that on the occasion of a visit to London, when he was

favoured with a view of the calculating machinery, he found in it

mechanical contrivances, which he subsequently introduced with the

greatest advantage into his own spinning-machinery.]

Another department of mechanical art, which has been enriched by this

invention, has been that of _tools_. The great variety of new forms which

it was necessary to produce, created the necessity of contriving and

constructing a vast number of novel and most valuable tools, by which,

with the aid of the lathe, and that alone, the required forms could be

given to the different parts of the machinery with all the requisite

accuracy.

The idea of calculation by mechanism is not new. Arithmetical

instruments, such as the calculating boards of the ancients, on which

they made their computations by the aid of counters--the _Abacus_, an

instrument for computing by the aid of balls sliding upon parallel

rods--the method of calculation invented by Baron Napier, called by him

_Rhabdology_, and since called _Napier's bones_--the Swan Pan of the

Chinese--and other similar contrivances, among which more particularly

may be mentioned the Sliding Rule, of so much use in practical

calculations to modern engineers, will occur to every reader: these may

more properly be called _arithmetical instruments_, partaking more or less

of a mechanical character. But the earliest piece of mechanism to which

the name of a 'calculating machine' can fairly be given, appears to have

been a machine invented by the celebrated Pascal. This philosopher and

mathematician, at a very early age, being engaged with his father, who

held an official situation in Upper Normandy, the duties of which

required frequent numerical calculations, contrived a piece of mechanism

to facilitate the performance of them. This mechanism consisted of a

series of wheels, carrying cylindrical barrels, on which were engraved

the ten arithmetical characters, in a manner not very dissimilar to that

already described. The wheel which expressed each order of units was so

connected with the wheel which expressed the superior order, that when

the former passed from 9 to 0, the latter was necessarily advanced one

figure; and thus the process of carrying was executed by mechanism: when

one number was to be added to another by this machine, the addition of

each figure to the other was performed by the hand; when it was required

to add more than two numbers, the additions were performed in the same

manner successively; the second was added to the first, the third to

their sum, and so on.

Subtraction was reduced to addition by the method of arithmetical

complements; multiplication was performed by a succession of additions;

and division by a succession of subtractions. In all cases, however, the

operations were executed from wheel to wheel by the hand.[18]

[Footnote 18: See a description of this machine by Diderot, in the

_Encyc. Method._; also in the works of Pascal, tom. IV., p. 7; Paris,

1819.]

This mechanism, which was invented about the year 1650, does not appear

ever to have been brought into any practical use; and seems to have

speedily found its appropriate place in a museum of curiosities. It was

capable of performing only particular arithmetical operations, and these

subject to all the chances of error in manipulation; attended also with

little more expedition (if so much), as would be attained by the pen of

an expert computer.

This attempt of Pascal was followed by various others, with very little

improvement, and with no additional success. Polenus, a learned and

ingenious Italian, invented a machine by which multiplication was

performed, but which does not appear to have afforded any material

facilities, nor any more security against error than the common process

of the pen. A similar attempt was made by Sir Samuel Moreland, who is

described as having transferred to wheel-work the figures of _Napier's

bones_, and as having made some additions to the machine of Pascal.[19]

[Footnote 19: Equidem Morelandus in Anglia, tubæ stentoriæ author,

Rhabdologiam ex baculis in cylindrulos transtulit, et additiones

auxiliares peragit in adjuncta machina additionum Pascaliana.]

Grillet, a French mechanician, made a like attempt with as little

success. Another contrivance for mechanical calculation was made by

Saunderson. Mechanical contrivances for performing particular

arithmetical processes were also made about a century ago by Delepréne

and Boitissendeau; but they were merely modifications of Pascal's,

without varying or extending its objects. But one of the most remarkable

attempts of this kind which has been made since that of Pascal, was a

machine invented by Leibnitz, of which we are not aware that any

detailed or intelligible description was ever published. Leibnitz

described its mode of operation, and its results, in the Berlin

Miscellany,[20] but he appears to have declined any description of its

details. In a letter addressed by him to Bernoulli, in answer to a

request of the latter that he would afford a description of the

machinery, he says, 'Descriptionem ejus dare accuratam res non facilis

foret. De effectu ex eo judicaveris quod ad multiplicandum numerum sex

figurarum, _e.g._ rotam quamdam tantum sexies gyrari necesse est, nulla

alia opera mentis, nullis additionibus intervenientibus; quo facto,

integrum absolutumque productum oculis objicietur.'[21] He goes on to

say that the process of division is performed independently of a

succession of subtractions, such as that used by Pascal.

[Footnote 20: Tom. I., p. 317.]

[Footnote 21: _Com. Epist._ tom. I., p. 289.]

It appears that this machine was one of an extremely complicated nature,

which would be attended with considerable expense of construction, and

only fit to be used in cases where numerous and expensive calculations

were necessary.[22] Leibnitz observes to his correspondent, who required

whether it might not be brought into common use, 'Non est facta pro his

qui olera aut pisculos vendunt, sed pro observatoriis aut cameris

computorum, aut aliis, qui sumptus facile ferunt et multo calculo

egent.' Nevertheless, it does not appear that this contrivance, of which

the inventor states that he caused two models to be made, was ever

applied to any useful purpose; nor indeed do the mechanical details of

the invention appear ever to have been published.

[Footnote 22: Sed machinam esse sumptuosam et multarum rotarum instar

horologii: Huygenius aliquoties admonuit ut absolvi curarem; quod non

sine magno sumptu tædioque factum est, dum varie mihi cum opificibus

fuit conflictandum.--_Com. Epist._]

Even had the mechanism of these machines performed all which their

inventors expected from them, they would have been still altogether

inapplicable for the purposes to which it is proposed that the

calculating machinery of Mr Babbage shall be applied. They were all

constructed with a view to perform particular arithmetical operations,

and in all of them the accuracy of the result depended more or less upon

manipulation. The principle of the calculating machinery of Mr Babbage

is perfectly general in its nature, not depending on any _particular

arithmetical operation_, and is equally applicable to numerical tables of

every kind. This distinguishing characteristic was well expressed by Mr

Colebrooke in his address to the Astronomical Society on this invention.

'The principle which essentially distinguishes Mr Babbage's invention

from all these is, that it proposes to calculate a series of numbers

following any law, by the aid of differences, and that by setting a few

figures at the outset; a long series of numbers is readily produced by a

mechanical operation. The method of differences in a very wide sense is

the mathematical principle of the contrivance. A machine to add a number

of arbitrary figures together is no economy of time or trouble, since

each individual figure must be placed in the machine; but it is

otherwise when those figures follow some law. The insertion of a few at

first determines the magnitude of the next, and those of the succeeding.

It is this constant repetition of similar operations which renders the

computation of tables a fit subject for the application of machinery. Mr

Babbage's invention puts an engine in the place of the computer; the

question is set to the instrument, or the instrument is set to the

question, and by simply giving it motion the solution is wrought, and a

string of answers is exhibited.' But perhaps the greatest of its

advantages is, that it prints what it calculates; and this completely

precludes the possibility of error in those numerical results which pass

into the hands of the public. 'The usefulness of the instrument,' says

Mr Colebrooke, 'is thus more than doubled; for it not only saves time

and trouble in transcribing results into a tabular form, and setting

types for the printing of the table, but it likewise accomplishes the

yet more important object of ensuring accuracy, obviating numerous

sources of error through the careless hands of transcribers and

compositors.'

Some solicitude will doubtless be felt respecting the present state of

the calculating machinery, and the probable period of its completion. In

the beginning of the year 1829, Government directed the Royal Society to

institute such enquiries as would enable them to report upon the state

to which it had then arrived; and also whether the progress made in its

construction confirmed them in the opinion which they had formerly

expressed,--that it would ultimately prove adequate to the important

object which it was intended to attain. The Royal Society, in accordance

with these directions, appointed a Committee to make the necessary

enquiry, and report. This Committee consisted of Mr Davies Gilbert, then

President, the Secretaries, Sir John Herschel, Mr Francis Baily, Mr

Brunel, engineer, Mr Donkin, engineer, Mr G. Rennie, engineer, Mr

Barton, comptroller of the Mint, and Mr Warburton, M.P. The voluminous

drawings, the various tools, and the portion of the machinery then

executed, underwent a close and elaborate examination by this Committee,

who reported upon it to the Society.

They stated in their report, that they declined the consideration of the

principle on which the practicability of the machinery depends, and of

the public utility of the object which it proposes to attain; because

they considered the former fully admitted, and the latter obvious to all

who consider the immense advantage of accurate numerical tables in all

matters of calculation, especially in those which relate to astronomy

and navigation, and the great variety and extent of those which it is

professedly the object of the machinery to calculate and print with

perfect accuracy;--that absolute accuracy being one of the prominent

pretensions of the undertaking, they had directed their attention

especially to this point, by careful examination of the drawings and of

the work already executed, and by repeated conferences with Mr Babbage

on the subject;--that the result of their enquiry was, that such

precautions appeared to have been taken in every part of the

contrivance, and so fully aware was the inventor of every circumstance

which might by possibility produce error, that they had no hesitation in

stating their belief that these precautions were effectual, and that

whatever the machine would do, it would do truly.

They further stated, that the progress which Mr Babbage had then made,

considering the very great difficulties to be overcome in an undertaking

of so novel a kind, fully equalled any expectations that could

reasonably have been formed; and that although several years had elapsed

since the commencement of the undertaking, yet when the necessity of

constructing plans, sections, elevations, and working drawings of every

part; of constructing, and in many cases inventing, tools and machinery

of great expense and complexity, necessary to form with the requisite

precision parts of the apparatus differing from any which had previously

been introduced in ordinary mechanical works; of making many trials to

ascertain the value of each proposed contrivance; of altering,

improving, and simplifying the drawings;--that, considering all these

matters, the Committee, instead of feeling surprise at the time which

the work has occupied, felt more disposed to wonder at the possibility

of accomplishing so much.

The Committee expressed their confident opinion of the adequacy of the

machinery to work under all the friction and strain to which it can be

exposed; of its durability, strength, solidity, and equilibrium; of the

prevention of, or compensation for, wear by friction; of the accuracy of

the various adjustments; and of the judgment and discretion displayed by

the inventor, in his determination to admit into the mechanism nothing

but the very best and most finished workmanship; as a contrary course

would have been false economy, and might have led to the loss of the

whole capital expended on it.

Finally, considering all that had come before them, and relying on the

talent and skill displayed by Mr Babbage as a mechanist in the progress

of this arduous undertaking, not less for what remained, than on the

matured and digested plan and admirable execution of what is completed,

the Committee did not hesitate to express their opinion, that in the

then state of the engine, they regarded it as likely to fulfil the

expectations entertained of it by its inventor.

This report was printed in the commencement of the year 1829. From that

time until the beginning of the year 1833, the progress of the work has

been slow and interrupted. Meanwhile many unfounded rumours have

obtained circulation as to the course adopted by Government in this

undertaking; and as to the position in which Mr Babbage stands with

respect to it. We shall here state, upon authority on which the most

perfect reliance may be placed, what have been the actual circumstances

of the arrangement which has been made, and of the steps which have been

already taken.

Being advised that the objects of the projected machinery were of

paramount national importance to a maritime country, and that, from its

nature, it could never be undertaken with advantage by any individual as

a pecuniary speculation, Government determined to engage Mr Babbage to

construct the calculating engine for the nation. It was then thought

that the work could be completed in two or three years; and it was

accordingly undertaken on this understanding about the year 1821, and

since then has been in progress. The execution of the workmanship was

confided to an engineer by whom all the subordinate workmen were

employed, and who supplied for the work the requisite tools and other

machinery; the latter being his own property, and not that of

Government. This engineer furnished, at intervals, his accounts, which

were duly audited by proper persons appointed for that purpose. It was

thought advisable--with a view, perhaps, to invest Mr Babbage with a

more strict authority over the subordinate agents--that the payments of

these accounts of the engineer should pass through his hands. The amount

was accordingly from time to time issued to him by the Treasury, and

paid over to the engineer. This circumstance has given rise to reports,

that he has received considerable sums of money as a remuneration for

his skill and labour in inventing and constructing this machinery. Such

reports are altogether destitute of truth. He has received, neither

directly nor indirectly, any remuneration whatever;--on the contrary,

owing to various official delays in the issues of money from the

Treasury for the payment of the engineer, he has frequently been obliged

to advance these payments himself, that the work might proceed without

interruption. Had he not been enabled to do this from his private

resources, it would have been impossible that the machinery could have

arrived at its present advanced state.

It will be a matter of regret to every friend of science to learn, that,

notwithstanding such assistance, the progress of the work has been

suspended, and the workmen dismissed for more than a year and a half;

nor does there at the present moment appear to be any immediate prospect

of its being resumed. What the causes may be of a suspension so

extraordinary, of a project of such great national and universal

interest,--in which the country has already invested a sum of such

serious amount as L.15,000,--is a question which will at once suggest

itself to every mind; and is one to which, notwithstanding frequent

enquiries, in quarters from which correct information might be expected,

we have not been able to obtain any satisfactory answer. It is not true,

we are assured, that the Government object to make the necessary

payments, or even advances, to carry on the work. It is not true, we

also are assured, that any practical difficulty has arisen in the

construction of the mechanism;--on the contrary, the drawings of all

the parts of it are completed, and may be inspected by any person

appointed on the part of Government to examine them.[23] Mr Babbage is

known as a man of unwearied activity, and aspiring ambition. Why, then,

it may be asked, is it that he, seeing his present reputation and future

fame depending in so great a degree upon the successful issue of this

undertaking, has nevertheless allowed it to stand still for so long a

period, without distinctly pointing out to Government the course which

they should adopt to remove the causes of delay? Had he done this (which

we consider to be equally due to the nation and to himself), he would

have thrown upon Government and its agents the whole responsibility for

the delay and consequent loss; but we believe he has not done so. On the

contrary, it is said that he has of late almost withdrawn from all

interference on the subject, either with the Government or the engineer.

Does not Mr Babbage perceive the inference which the world will draw

from this course of conduct? Does he not see that they will impute it to

a distrust of his own power, or even to a consciousness of his own

inability to complete what he has begun? We feel assured that such is

not the case; and we are anxious, equally for the sake of science, and

for Mr Babbage's own reputation, that the mystery--for such it must be

regarded--should be cleared up; and that all obstructions to the

progress of the undertaking should immediately be removed. Does this

supineness and apparent indifference, so incompatible with the known

character of Mr Babbage, arise from any feeling of dissatisfaction at

the existing arrangements between himself and the Government? If such be

the actual cause of the delay, (and we believe that, in some degree, it

is so,) we cannot refrain from expressing our surprise that he does not

adopt the candid and straightforward course of declaring the grounds of

his discontent, and explaining the arrangement which he desires to be

adopted. We do not hesitate to say, that every reasonable accommodation

and assistance ought to be afforded him. But if he will pertinaciously

abstain from this, to our minds, obvious and proper course, then it is

surely the duty of Government to appoint proper persons to enquire into

and report on the present state of the machinery; to ascertain the

causes of its suspension; and to recommend such measures as may appear

to be most effectual to ensure its speedy completion. If they do not by

such means succeed in putting the project in a state of advancement,

they will at least shift from themselves all responsibility for its

suspension.

[Footnote 23: Government has erected a fire-proof building, in which it

is intended that the calculating machinery shall be placed when

completed. In this building are now deposited the large collection of

drawings, containing the designs, not only of the part of the machinery

which has been already constructed, but what is of much greater

importance, of those parts which have not yet been even modelled. It is

gratifying to know that Government has shown a proper solicitude for the

preservation of those precious but perishable documents, the loss or

destruction of which would, in the event of the death of the inventor,

render the completion of the machinery impracticable.]