At another part of the machine a series of number cards, resembling those of Jacquard, but delivered to and computed by the machine itself, can be placed. These can be called for by the Engine itself in any order in which they may be placed, or according to any law the Engine may be directed to use. Hence the condition (b) is fulfilled, viz. an unlimited number of constants can be inserted in the machine in an unlimited time.

I propose in the Engine I am constructing to have places only for a 1000 constants, because I think it will be more than sufficient. But if it were required to have 10, or even a 100 times that number, it would be quite possible to make it, such is the simplicity of its structure of that portion of the Engine.

Thus it appears that the whole of the conditions which enable a finite machine to make calculations of unlimited extent are fulfilled in the A. E. The means I have adopted are uniform. I have converted the infinity of space, which was required by the conditions of the problem, into the infinity of time. The means I have employed are in daily use in the art of weaving patterns.

As soon as an A. E. exists, it will necessarily guide the future course of the science. Whenever any result is sought by its aid, the question will then arise-By what course of calculation can these results be arrived at by the machine in the shortest time?

Having thus completely mastered the details of the proposed Analytical Engine, Mr. Babbage then completed the drawings of the Difference Engine No. 2. In the mean time certain portions of the machine had been completed, and were in working order. These latter remained in Mr. Babbage's possession for some time previous to their removal to King's College. During this period many persons of great scientific eminence saw these parts in actual operation. On one occasion there were present Dr. Lloyd, then Provost of Trinity College, and Dr. Robinson, of Armagh. Mr. Babbage proceeds to tell us what took place:

I then proceeded to explain the mechanism of the Engine, and to cause it to calculate T. One of the party remarked two axes in front of the machine which had not hitherto been performing any work, and inquired for what purpose they were so placed. I informed him that these axes had been so placed in order to illustrate a series of calculations of the most complicated kind, to which they contributed. I observed that the T. thus formed were of so artificial and abstract a nature that I could not foresee the time when they would be of any use. This remark additionally excited their curiosity, and they requested me to set the machine at work to compute such a T. Having taken a simple case of this kind, I set the Engine to do its work, and then told them, That it was now prepared to count the natural numbers; but that it would only obey this law as far as the millionth term. That after that term it would commence a series, following a different, but known law, for a very long period. That after this new law had been fulfilled for another long period, it would then suddenly abandon it, and calculate the term of a series following another new law, and so on throughout all time. Of course it was impossible to verify these assertions by making the machine actually go through the calculations; but after having made the Engine count the natural numbers for some time, I proceeded to point out the fact that it was impossible, by its very structure, that the machine could record any but the natural numbers before it reached the number 999,990. This I made evident to my friends by showing them the actual structure of the Engine. Having demonstrated this to their entire satisfaction, I put the machine on to the number 999,990, and continued to work the Engine, when the result I had predicted soon arrived. After the millionth term a new law was taken up, and my friends were convinced that it must, from the very structure of the machine, continue for a very long time, and then inevitably give place to another new law, and so on throughout all time.

He then reverts to the Analytical Engine; but we had better let Mr. Babbage pursue his own narrative:

When they were quite satisfied about this fact, I observed that in a new engine, which I was then contemplating, it would be possible to set it so that: 1. It should calculate a T. for any given length of time according to any given law. 2. That at the termination of that time it should cease to compute a T. according to that law; but that it should commence a new T. according to any other given law that might be desired, and should then continue this computation for any other given period. 3. That this succession of a new law, coming in and continuing during any desired time, and then giving place to other new laws, in endless but unknown succession, might be continued indefinitely. remarked that I did not conceive the time could ever arrive when the results of such calculations would be of any utility. I added, however, that they offered a striking parallel with, although at an immeasurable distance from, the successive creations of animal life, as developed by the vast epochs of geological time...

I continued the subject, and pointed out the application of the same reasoning to the nature of miracles. The same machine could be set in such a manner that these laws might exist for any assigned number of times, whether large or small; also that it was not necessary that these laws should be different, but the same law might, when the machine was set, be ordered to re-appear, after any desired interval. Thus we might suppose an observer watching the machine, to see a known law continually fulfilled, until after a lengthened period, when a new law has been appointed to come in. This new law might after a single instance cease, and the first law might again be restored, and continue for another interval, when the second law might again govern the machine as before for a single instance, and then give place to the original law. This property of a mere piece of mechanism may have a parallel to the laws of human life. . . .

But the workings of machinery run parallel to those of the intellect. The Analytical Engine might be so set, that at definite periods, known only to its maker, a certain lever might become movable during the calculations then making. The consequence of moving it might be to cause the then existing law to be violated for one or more times, after which the orig. law would resume its reign. . . . It does not clearly appear how much of the Analytical Engine was ever actually constructed. Certain portions of Difference Engine No. 2 appeared also available for the A. E. In Passages from the Life of a Philosopher, pub. 1864, Mr. Babbage says [p. 449]. "If I survive some few years longer, the Analytical Engine will exist, and its works will afterwards be spread over the world." He died in Oct. 1871, never having completed the A. E.; but he had prepared for the press a work thereon, which we notice under date 1864.

The next machine we have to notice is one of Russian invention, by M. STAFFEL. The precise date of its invention we cannot ascertain. The mechanism is 18in. in length, 9in. in breadth, and 4in. in height. It consists of 3 rows of vertical cylinders: the first row contains 13; the 2nd 7; and the 3rd 7. Upon each of the cylinders in the first

row are 10 notches, corresponding with the units 1 to 10. Within each of these cylinders is a small pulley, in connexion with a lever, set in motion by a slider, which, when the cylinder has been turned from either 9 to o, or o to 9, sets in motion the lever, and communicates its action to wheels which carry over the figures. The pulley connected with the cylinder the furthest from the handle, is in connexion with the hammer of a bell. The purpose of this bell is to give warning to the operator on committing an error, and constitutes a most important add. to the machine, particularly in the operation of division. Upon each of the cylinders in the 2nd row 10 units are placed. These 7 cylinders are so fixed upon their axes, that they can bodily be moved right and left, and fixed at any part, so that the cyphers on the two cylinders can be made to correspond. This cylinder is furnished with a spike, which lays hold of and works the third row of cylinders. The internal communication of each of the parts is brought about by means of a connecting wheel, furnished with 9 movable pegs, which are set in motion by means of an excentric incision in the dial.

The machine is capable of performing addition, subtraction, multiplication, and division; and of extracting the square root. The operation of addition is performed as follows: By simply placing one line of numbers upon the second row of cylinders (the index pointing to addition), and turning the handle till it stops, these numbers are trans. almost instantly to the first row of cylinders, and so on successively till all the numbers to be added are trans., and their sum is shown on the top row. In performing subtraction, the first part of the operation is the same as in addition, but on placing the 2nd line of of figures on the 2nd row of cylinders, the pointer being placed to subtraction, the handle is turned the opposite way, or against the motion of the sun, and the difference of the two numbers is shown on the upper line. The operation of multiplication is performed by placing the multiplier and the multiplicand on the 2nd and 3rd rows of cylinders, and then, the index pointing to multiplication, the product will be found on the first cylinder. The operation of division is very similar, excepting that the handle is turned as in subtraction.

In the performance of the square root, the following add. mechanism is brought into play. Between every division of the cylinder, in row 2, a small wheel is placed, and near it a projecting piece which acts upon a lever. When the projecting piece is near the word "rod" engraved on the cylinder, on turning the handle the figures increase by 1. This by other mechanism is connected with the other two rows of cylinders. The operation of the square root is performed directly, without any guessing at numbers; but is comparatively rather a long process.

M. Staffel has also invented a small machine for the performance of the add. and subtraction of fractions, whose denominators are 10, 12, and 15. By enlarging the machine, this number could be increased, and the power of the instrument extended. [See 1851.]

About 1850 M. THOMAS (de Colmar) invented a small machine adapted for the performance of the first four rules of arithmetic, and indirectly capable of being made to extract the square root. The instrument consists of two rows of cylinders, the first row containing 16, the 2nd 8—the former are movable, the operation at each step being changed tenfold. The principle of the instrument is that multiplication is in reality the continual addition of itself as many times as there are units in the multiplier; and division that of continued subtraction of the divisor. The instrument is adapted for the multiplication of numbers whose product is expressed by less than 16 figures. To multiply 5321 by 3256 the following is the process: The first number is placed on one series of cylinders; the number 6 is placed on one of the cylinders of the 2nd row. On the handle being turned (in this machine always in the same direction), the number 31,926 appears; the upper row is moved through one division; the handle turned again, and so on till in a very short time the number 17,325, 176 appears. [See 1851.]

This instrument, now called the "Arithmometer," and which is about 18in. long, by 6 in. wide, and 11⁄2 in. deep, has been greatly improved since it was first invented; and it is now in very general use in England and in France. [See 1871.]

HERR WERTHEIMER has invented several calculating machines, adapted for the performance of addition and subtraction of numbers and moneys of this and other countries. Each machine consists of a box, with a metal plate divided into 9 indexes, with semicircular notches, under which are placed a succession of holes. Round the indexes numbers are engraved, and the semicircular notches are furnished with teeth, and a pointer to insert between the notches, for the purpose of bringing the notch opposite any particular figure, from right to left. This latter operation is attended with some hazard, and may cause inaccuracy. For this and other reasons the machines have not come into general They are however very ingenious. [See 1851.]

use.

M. SCHILT, a Swiss, has invented a simple calculating machine, or instrument, which can perform the first operation of arithmetic only.

M. LALANNE, a Frenchman, has invented a calculating rule, upon new principles. It consists of a graphic table formed entirely of right lines, with which all calculations usually performed by the sliding rule can be performed to within 1-2001 of the true result. In 1851 came about the great gathering of the mechanical and other arts of the world.

A department was instituted for "Philosophical Instruments, and processes depending on their use," known as Class X. In this department was included calculating machines. The jury appointed to report upon this class contained the following among its 12 names -Sir David Brewster, Sir John Herschel, Mr. James Glaisher. Neither Babbage's nor Scheutz's machines were exhibited-indeed the latter was not then finally completed. Regarding Babbage's machine, then for several years past deposited at King's College, it is impossible to account for its omission: it may have arisen from official indifference; from jealousy; or from shame at its incomplete condition. Confining themselves therefore simply to the machines which were exhibited, the jury gave the first place to Staffel's, which on examination seems to combine accuracy with economy of time, and works easily and directly." Again, "upon the whole it must be considered that Mr. Staffel has made an instrument possessed of considerable powers, and that great praise is due to him. The double motion of the handle, as well as the warning bell, are important improvements." Prize medal awarded. M. Thomas (de Colmar) “exhibits the next best calculating machine in the Exhibition, and has combined the two essentials of economy of time and accuracy of results." Again, on trying the machine, the number I was almost instantaneously taken from 10,000, giving the difference 9999 accurately; the performance of this operation is generally a severe test to these machines." Prize medal awarded. Regarding Herr Wertheimer, the jury say, "The machines are ingenious, but they are much wanting in the essentials of such machines, economy of time, and unerring accuracy." They were awarded Honourable Mention. The like was awarded to M. Schilt, and to M. Lalanne. Dr. Roget's sliding scale (as improved by Brooker) was also exhibited.

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In 1852 Mr. Willich, author of the well-known tables bearing his name, said, "We have but little hope that the splendid prospect opened by Mr. Babbage's calculating machine will ever be realized, the aid of Gov. having been withdrawn." He then adds: Is there no chivalrous millionnaire in this country anxious to immortalize his name by being associated with the successful carrying out of Mr. Babbage's calculating machine? A slice of a million would be well bestowed to obtain such a result." No one has yet come forward.

By 1853 the machines of the MESSRS. SCHEUTZ was finally completed, on the principles of the working model which had been prepared 10 years previously; and which we have already described. The difficulties in the way of its completion had been very considerable. In 1851, after a further inspection by a Committee of the Royal Academy, Herr Geo. Scheutz had applied to his Gov. for means to construct a larger and more perfect machine. This application was refused. Afterwards, however, the Diet for Stockholm did grant a sum of £280, upon condition that the machine should be completed before the end of 1853. It was so completed; after which a further £280 was voted, making in all £560.

In 1854 the inventors brought their machine to England, and it was first exhibited at Bermondsey, at the manufactory of Messrs. Bryan Donkin & Co. In 1855 the machine was exhibited in the Paris International Exhibition, and the inventors obtained a gold medal. Mr. W. Gravatt, an English engineer, and F.R.S., took great interest in the invention, and introduced it to the notice of the Royal So. The machine was brought back to Lond., and was set to work to print tables. The following is an authentic description of it, and its capabilities:

The size of the whole machine when on its proper stand and protected by its cover is about that of a small square pianoforte. The calculating portion of the machine, which appears in the front of the drawing, consists of a series of 15 upright steel axes passing down the middle of 5 horizontal rows of silver-coated numbering rings, 15 in each row. Each ring being supported by and turning concentrically on its own brass shelf, having with it a hole rather less than the largest diameter of the ring. Round the cylindrical surface of each ring are engraved the ordinary numerals from o to 9, one of which, in each position of the ring, appears in front, so that the successive numbers shown in any horizontal row of rings may be read from left to right, as in ordinary writing. The upper row exhibits the number or answer resulting from the calculation of 15 places of figures, the first 8 of which the machine stereotypes. The numbers seen in the 2nd row of rings constitute the first order of differences, also to 15 places of figures, if that number be required; and the 3rd, 4th, and 5th row of rings in like manner exhibit the 2nd, 3rd, and 4th order of differences. Any row can be set by hand, so as to present to the eye any number expressed according to the decimal scale of rotation-such as the number 987654321056789, the first 8 figures of which, if in the uppermost row, would, on being calculated by the machine, be immediately stereotyped. But by simply changing a ring in each of two of the vertical columns, the machine can be made to exhibit and to calculate numbers expressed in the mixed senary system of notation, as in that of degrees, minutes, seconds, and decimals of a second. Thus, for instance, if the result 874324687356402 were indicated, in the upper row of rings, it would be stereotyped 87 degrees, 43 minutes, 24'69 seconds.

While this process is going on, the argument proper to each result is at the same time also stereotyped in its proper place; nothing more being required for that purpose than to set each row of figure rings to differences previously calculated from the proper formula, and to place a strip of sheet lead on the slide of the printing apparatus; then by turning the handle (to do which requires no greater power than that which is exerted in turning that of a small barrel organ), the whole T. required is calculated and stereo-moulded in the lead. By this expression is meant that the strip of lead is made into a beautiful stereotype mould, from which any number of sharp stereotype plates can be produced ready for the working of an ordinary printing press.

At the average rate of working the machine, 120 lines per hour of arguments and results are calculated, and actually stereotyped ready for the press. It is found on trial that the machine calculates and stereotypes, without chance of error, 24 pages of figures in the same time that a skilful compositor would take merely to set up the types for one single page.

The machine was shortly afterwards purchased for 1000 by Mr. Rathbone, an American merchant, and by him presented to the Dudley Observatory at Albany, N. Y., where it still remains. Mr. Babbage was not slow to bear his testimony to the perfection and in some respects the originality of the machine.

In 1854 Mr. W. T. Thomson read before the Inst. of Act. a paper on Decimal Numeration and Decimal Coinage. The paper, which is printed in vol. iv. of Assu. Mag., exhibits much quaint scholarship, of which we have been glad to make some use. It contains a division, "Aids to Calculation," coming within the scope of our present art.

The Paris Exposition Universal of 1855 was remarkable for the number and ingenuity of the machines which performed arithmetical operations. Pre-eminently above all others stood the Swedish machine. It is honourable to France (says Mr. Babbage), that its highest reward was deservedly given to the inventor of that machine; whilst it is somewhat remarkable that the English Commissioners appointed to report upon the French Exhibition omitted all notice of these Calculating Machines.

In the Journal of the So. of Arts, 27 April, 1855, there appeared a brief description of Scheutz's machine, which developes one feature not previously noted:

The machine calculates to 16 figures, but prints to 8 only; and by a singularly ingenious, and at the same time simple, contrivance, the 8th figure in the T. is printed, not in all cases as calculated, but with a correction when required, for the 9th and subsequent figures omitted in the T. Thus whenever the 9th figure as calculated amounts to 5 or more, it is more accurate that the 8th or final figure in the T. should be printed by the addition of one: this the machine accomplishes.

In 1856 there were pub.: (1) Observations by Charles Babbage, on the Mechanical Notation of Scheutz's Difference Engine, prepared and drawn up by his Son, Major Henry Prevost Babbage, addressed to the Inst. of Civil Engineers. The same is pub. in the Minutes of Proceedings of that So. vol. 15. (2) Observations addressed to the Royal So. on the Swedish Tabulating Machine of Geo. Scheuts. This latter paper we believe was not by Mr. Babbage.

In the Journal of the So. of Arts, 3rd July, 1857, there was an account of Scheutz's machine from which we have drawn some of the preceding details.

It had been a matter of deep regret on the part of many of our leading scientific men that Scheutz's machine had ever been allowed to leave these shores. The more so as there was at the time work required to be done, which it could have accomplished. We may here quote Dr. Farr:

At that time it appeared to be desirable to construct a new life T. from the materials accumulated at the Gen.-Reg. office by the regis. of births and deaths in 17 years (1838-54), and by the two enumerations of the pop. of E. and W. in 1841 and 1851. The T. for single lives, and the various combinations for joint lives, male and female, involve a great deal of numerical computation; and as it was found that the calculations of the series, thrown into a form which is described elsewhere [paper read before Royal So., 7th April, 1859], could be performed by the machine, the Reg.-Gen. was pleased to bring the matter under the notice of Sir Geo. Lewis, then Sec. of State for the Home Depart., and in doing so he pointed out the importance which had been justly attached by the most scientific men of the country, by H.M. Gov., and by Parl., to the machine of Mr. Babbage, for which, though it had not been completed, £17,000 of money had been granted, besides the money expended by Mr. Babbage himself. The Astronomer-Royal concurred with the Reg.-Gen. in

advising H.M. Gov. to order a new machine.

The request was granted. A contract was entered into with MR. SCHEUTZ and the MESSRS. DONKIN, who agreed to construct a new machine, with several improvements, for the sum of £1200. In the work several new tools were required, and workmen had to be specially instructed. From this expense the contractors did not shrink. The machine was completed, and was reported to be superior to the first.

Mr. Bryan Donkin reported that the machine consists of about 4320 pieces, of which 2054 were screws; 364 compose the chain; and 902 constituted the other parts of the mechanism. The weight, exclusive of the case, is about 10 cwt. The machine was shaken out of order on its way from the factory to Somerset House. It was, however, soon set in order, and put to work. [See 1862 and 1864.]

In January, 1860, MR. JARDINE HENRY brought before the Royal So. of Arts, in Edin. an instrument which he had invented for the construction of Life Annu. T. without the use of logarithms. His instrument accomplished by a single movement all multiplications necessary in forming L. Annu. Commutation T. We can only give a brief description of the invention. A right-angled triangle with two equal sides is divided into 10,000 equal parts. Lines are drawn from the left hand, where zero stands to the numbers in the perpendicular side, representing the numbers alive at the end of each year from birth to death, say out of 10,000 persons born. A vertical sliding scale on T, also divided into 10,000 equal parts, is adjusted so as to slide upon the triangle. The principal use of the instrument was said to be to furnish Joint Life Tables. It was not said to arrive at perfect accuracy; but its results were "sufficiently correct for all practical purposes." From 400 to 600 values could be read off the instrument with complete ease; and the labour of constructing T. compared with the use of logarithms reduced to one-fourth. [See 1867.] In the International Exhibition in London, in 1862, there were exhibited [Class XIII.] several calculating machines, or arithmetical instruments, of which we have not previously made any mention, and concerning which we have very few accurate details.

The first of these is the invention of HERR WIBERG, of Malmö, Sweden. It is a small difference engine of cylindrical form, in which the difference axes are arranged round the

circumference of a circle, in place of lying in one plane, as in the machines of Messrs. Babbage and Scheutz. This machine, however, was so much deranged in its transit to the Exhibition, that the jury had no means of testing its mode of action. Herr Wiberg also exhibited a smaller calculating machine, like the other of a circular form, very compactly arranged, and very neatly executed. It was presumed to be for the purposes of multiplication and division; but no precise information could be obtained.

M. C. X. THOMAS exhibited several well-constructed machines for multiplying to the extent of 7 figures by 7. These seem to be the same we have spoken of as the invention of M. Thomas de Colmar. Medal awarded.

SIGNOR T. GONNELLA, of Florence, exhibited a calculating machine of very simple form and construction, but the jury considered "probably of little practical utility." Mr. Babbage's Difference Engine No. 1 (as far as completed) was also exhibited. The jury, consisting of 13 members, among whom were Sir David Brewster, Mr. James Glaisher, and Prof. Wheatstone, say in their report:

These eminently ingenious and practically useful contrivances have undergone considerable development since the former Exhibition of 1851; but that progress, as it will presently appear, is not completely represented in the present Exhibition. Calculating machines, as they at present exist, are essentially of two kinds. In the simpler form the operation of addition is performed by causing a figure wheel to advance a given number of unit spaces by moving through the same number of spaces or wheel with which it is in gear. The process of multiplication is merely the repetition of successive additions; and subtraction and division are merely the inverse processes of the former.

...

Then follows a short description of Babbage's and Scheutz's machines, in which occurs the following, "It must suffice to observe that in the engine of Messrs. Scheutz these arrangements [by which the number on any given wheel is transferred to the wheel above it] are more simple, and apparently not less efficacious than in that of Mr. Babbage."

Scheutz and Donkin's machine was not exhibited. It was indeed in use at the time, calculating and printing portions of the English Life T. No. 3. A description of it and examples of its work were distributed, and many scientific men visited and saw it in operation during the Exhibition. It may be be seen at Somerset House now, by any properly accredited person. In the description so circulated occur the following passages : The machine has been extensively tried, and it has upon the whole answered every expectation. But it is a delicate instrument, and requires considerable skill in the manipulation. It approaches infallibility in certain respects, but it is not infallible, except in very skilful hands. The weakest point of the machine is the printing apparatus, and that admits of evident improvement. The machine calculates and print series of a particular kind; and to the execution of these operations its utility is therefore limited. Its scope is less ambitious than the new analytical machine for which Mr. Babbage abandoned his first invention, as that machine seeks to embrace the whole field of analysis. [See 1864.] In 1864 there was announced for pub. by the late Mr. Babbage: Hist. of the Analytical Engine. The vol. was to contain a reprint of chapters 5-8 of the Passages from the Life of a Philosopher. Also a reprint of translation of General Menabrea's Sketch, etc. [See 1842.] We believe this work never was pub.

In the same year there was published the English Life Table: Tables of the Lifetimes, Annu. and Prems.; with an Intro. by Wm. Farr, M.D., etc. In a letter to the Reg.-Gen., forming such Introduction, Dr. Farr says: "Several of the series were calculated by Scheutz's machine. . It gave us an opportunity of testing its working powers in England, where Mr. Babbage explained the principles, and first demonstrated the practicability of performing certain calculations and printing the results by machinery." The machine was employed to introduce the element of int. into the various T. In an appendix [p. cxxxix] the learned Doctor enters upon further details, while also replying to a complaint of Mr. Babbage regarding the non-exhibition of the machine, by which circumstance the latter considered the constructors lost a medal, and many scientific men were disappointed. Dr. Farr says that the work upon which the machine was employed was much required; and that quietude was essential to the proper conduct of its operations : The machine required incessant attention. The differences had to be inserted at the proper terms of the various series; checking was required; and when the machine got out of order it had to be set right.... The idea had been as beautifully embodied in metal by Mr. Bryan Donkin as it had been conceived by the genius of its inventors; but it was untried. So its work had to be watched with anxiety, and its arithmetical music had to be elicited by frequent tuning and skilful handling in the quiet most congenial to such productions. This vol. is the result; and thus-if I may use the expressionthe soul of the machine is exhibited in a series of T. which are submitted to the criticism of consummate judges of this kind of work in England and in the world. If their approving testimony be won, it will be some compensation to the English workmen-the firm of Messrs. Donkin, and the Messrs. Scheutz, for the loss of a medal at the Exhibition of 1862.

It will be generally admitted that this beautifully printed and useful vol. of between 700 and 800 pages, mainly of T.-although not all the produce of the machine-must remain a very enduring monument of its usefulness; and it ought not to be forgotten that it is prob. to Dr. Farr that we really owe the existence of this particular machine.

In 1864 also, Dr. Farr read a paper before the Brit. Asso. at Bath, on Life Tables, by the Swedish Calculating Machine-with Photographs by A. Claudet; and at the same meeting Major-Gen. Hannyngton read: Some Remarks on the French Calculating Machine [M. Thomas de Colmar's]. Abstracts of these papers were not printed in the Official Rep. In the Companion to the (Brit.) Almanack, 1866, there is a paper by Mr. F. J. Williams, The Swedish Calculating Machine at the General Regis. Office, Somerset House; wherein is a very clearly written hist. of the machine, and of its performances. He also points out