C

CABLE. The great rope of a ship to which the anchor is fastened. Iron chain cables are said to have been used by the Veneti in the time of Cæsar, or 57 years before the Christian era. These latter were only introduced into the English Navy in 1812. In 1785 a special Act of Parl. was passed-25 Geo. III. c. 56—to prevent deceits and frauds in the manufacture of cables and cordage for ships. In 1864 an Act was passed-27 & 28 Vict. c. 27authorizing the testing of cables and anchors.

CADAVER (from Cado, to fall).-A corpse or dead body. Hence the term Cadaverous, expressive of great exhaustion.

One

CADDOW, JOHN, Underwriter of Maritime Marine Ins. Co., Liverpool, since 1868. CADIZ. A maritime port in Spain [anciently Gadiz-the Roman Gades].—It was at a former period a place of considerable commercial and maritime importance. hundred vessels of the Spanish Armada were destroyed in its port, 1587, by Sir Francis Drake. The Consulado of Cadiz was only estab. in 1680; but it had long previously been possessed of regulations for governing its ins. contracts. The following is a form of marine pol. in use in 1618:

In the name of God, Amen. We, the underwritten, do acknowledge and oblige ourselves to insure you, A. B., or any goods loaded by you, or by any other person or persons for you: And we also insure you on all the charge or charges of this ins. The which said merchandize go registered in the Royal Register, and at the risk of A. B., in the ship N., Captain C. D., or any other who shall go master in her. And the said ship being loaded, let her prosecute her present voyage successfully unto her destined port in the Indies, and there arrived in safety, and the goods unloaded from the said ship, in any boat or boats, until delivered safe ashore. And it is agreed that the said ship may, and do, make what stops she will, or may judge proper, as well unavoidable as voluntary, entering into and going out of any port or ports, delivering or receiving any goods, though not altering the voyage, except to join some company: And if any risk or damage happens, we declare, that on producing a certificate of it, made with or without the party, or by a person that shall not have been made a party in the place where the ship shall have been lost, or in any other port: and after 6 months are past, to be counted from the day that the policy was signed, we will freely pay, and immediately disburse and deposit in the power of the shipper, or the person insured, all that we shall have underwrote, or that part of the damage which shall touch us on giving us sufficient and satisfactory security to return us 33 p.c. if such payment shall be wrong made, and the ship should not appear: that is we are to pay in a year and a half from the ship's sailing out of port, and not appearing in that time: and the year and a half is to be counted from the ship's departure from the port, and not from the time the policy was signed. And it is to be understood that the first and last of us are proportionably to run the risk of what the lading shall be worth, and the surplus of the cargo's value must be left out, according to the Ordinance. And in this manner, and with these conditions, we are content to run the said risk. And for a compliance we oblige our persons and effects; and give full power to the Justice of the Contratacion House of this City of Seville, and to any other Justices of these Kingdoms, to oblige us to comply: and we renounce our own proper rights and privileges, and the Law Si convenerit, and submit ourselves to the customs and jurisdiction of the said Judges, Officers, and all the other Justices, and to the Prior and Consuls, which are or henceforward shall be of the University of the Shippers and Merchants trading to the Indies, of the City of Seville: that by all rigour of Law, as well by way of execution, as in any other manner, they compel and force us to observe and perform them, as if it was anything judged and determined by a definitive sentence pronounced by a competent judge in a contradictory judgment, and consented to by us, and each of us, and passed as a determined thing.

Magens gives a form of pol. in use in 1725, in which the penalty of 33 p.c. is altogether omitted. The subs. of the underwriter at the last-named date was in the following form:

I am content to run the risk in the said ship, which God preserve and keep, in conformity to this pol. for 100 Dollons of two Escudos of gold each, and am paid the prem. in ready money, at the rate of ...p.c. Dated at Cadiz, this of 1725.

He also gives a form of bottomry bond on ships, and another form on goods. CADOGAN, CHARLES, was Sec. of General Live Stock from 1854 down to the date of its liq. CÆSARIAN OPERATION, OR SECTION (Hysterotomia).-A surgical operation whereby the fætus, which can neither make its way into the world by the ordinary or natural passage, nor be extracted by the application of art-whether the mother and fœtus be yet alive, or whether one of them be dead-is released by an incision in the abdomen and through the uterus, with a view to save the lives of both or either.

By most men the life of the mother has been considered of the greatest importance, and therefore, as the Cæsarian operation is full of danger to her, no Brit. practitioner will perform it when delivery can, by destruction of the child, be procured per vias naturales. There are, I think, histories of 23 cases where this operation has been performed in Brit.; out of these only one woman has been saved, but 11 children have been preserved. On the Continent, however, where the operation has been performed more frequently, and often in more favourable circumstances, the number [proportion?] of fatal cases is much less. The operation itself, though dangerous in its consequences and formidable in its appearance, is by no means difficult to perform.-Burn, Principles of Midwifery.

Cooper's Surgical Dict. (ed. 1861) contains a T. which, out of 2009 cases, gives a mort. of 55'4 p.c. of the mothers, and 29'45 p.c. of the children. The deaths in England from this cause were-in 1865, 4; 1866, 3; 1867, 4.

CAINES, GEORGE, pub. in New York, in 1802, Lex Mercatoria Americana; or, An Inquiry into the Law Merchant of the United States on several Heads of Commercial Importance. The work treats incidentally of marine ins., but is not regarded as of much authority. CALCAGUI, DR. FRANCISCO.—In 1822 he compiled A Bill of Mort. for the City of Palermo, which was pub. in 1823. [BILLS OF MORT.]

CALCULATING MACHINES.-Ever since men began to compute, endeavours have been made to facilitate calculations, or to perform them altogether, by means of mechanical

contrivances. The history of these would afford its author abundant and interesting materials. The hands and fingers offer the first and readiest help in computing. We can not only count on the fingers, but even perform complicated calculations.-Dr.Zillmer. 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 Shwan-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.-Dr. Lardner, in Edin. Review, July, 1834.

Calculating machines comprise various pieces of mechanism for assisting the human mind in executing the operations of arithmetic. Some few of these perform the whole operation without any mental attention, when once the given numbers have been put into the machine. Others require a moderate portion of mental attention: these latter are generally of much simpler construction than the former, and, it may also be added, are less useful. The simplest way of deciding to which of these two classes any calculating machine belongs is, ask its maker-Whether, when the numbers on which it is to operate are placed in the instrument, it is capable of arriving at its result by the mere motion of a spring, a descending weight, or any other constant force? If the answer be in the affirmative, the machine is really automatic; if otherwise, it is not self-acting. Of the various machines I have had occasion to examine, many of those for addition and subtraction have been found to be automatic. Of machines for multiplication and division, which have come under my examination, I cannot at present recall one to my memory as absolutely fulfilling this condition.-Babbage's Passages from the Life of a Philosopher, 1864.

We propose here mainly to confine our attention to CALCULATING MACHINES, but we must also take a passing note of ARITHMETICAL INSTRUMENTS.

Unquestionably the most ancient Arithmetical Instrument is the Abacus. It is simply an oblong frame, divided by a certain number of wires placed upright or across, upon which wires small ivory balls or beads are strung. Commencing from the bottom wire each above it has a progressive ten-fold value. By this simple contrivance very extensive operations may be computed, with great rapidity. This instrument has been used successively by the Greeks, Romans [Tabula Logistica], Russians, Germans, French, etc. -indeed by most of the Eastern nations.

The Chinese Shwan-Pan is but a variation of the Abacus. Whether it ranks before the European invention in point of date, we cannot determine. In point of power, by means of a simple subdivision, it is greatly in advance of all European varieties. Sir John Bowring, after a long official residence in China, speaks in the most unqualified terms of its use, and of the marvellous accuracy with which calculations are performed by its aid. The first recorded attempt at an Arithmetical Instrument in Gt. Brit. is that made by Napier, the inventor of Logarithms, about 1614. As already stated, the instrument is known as "Napier's Bones." It is simply a movable multiplication T. The multiplicand is written on the top of a rod or other movable slip, its multiples in lines belowthe units being separated from the tens by diagonal lines; and these slips are sufficiently numerous to allow of the formation of any number by their initial figures. If the multiplicand be, for example, 43429448, slips are arranged showing that number at the top, and then in any of the horizontal lines its multiple may be had by carrying the tens on one slip to the units of that on its right. In this way the computor obtains the successive lines of his product: these he has to write down and add together in the usual way. Mr. Edward Sang, writing of this contrivance as recently as 1871, says: "I am not acquainted with any other contrivance for showing the product of two numerical factors." Again: "It must not, however, be thought that Nepair's rods [Mr. Sang always calls him Nepair, for which there is authority] were of no use: in his day men learned to count after they were grown old; and Indian numerals were novelties, and the multiplication table was by no means at the finger-ends of computors; thus the rods were of real use," etc.

The first Calculating Machine of which we find any mention is one invented by that eminent philosopher PASCAL, about 1650. He, being then about 19 years of age, and engaged with his father, who held an official position 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. 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.

It is very doubtful if this machine was ever brought into any practical use. Dr. Lardner estimates its value as follows: "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 computor.'

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. In 1663 SIR SAMUEL MORELAND constructed a very complete and well-executed machine for answering all questions in plain trigonometry. In 1666 he constructed a small calculating machine of the simplest order for adding together any number of separate sums of money, providing the total was under £100,000. It would appear that all Moreland really did, was to transfer to wheel-work the figures of Napier's bones; and to have made some additions to the machine of Pascal.

M. GRILLET, a French mechanician, made a like attempt, prob. about this date, but with no great success.

The

About 1672, LEIBNITZ, the great mathematician and philosopher, invented a calculating machine. We have never seen any description of it. One of the Bernouillis applied to him to describe it; but his account of it was most meagre. He says, however, that the process of division was performed independently of a succession of subtractions, such as that used by Pascal. There is reason to believe that the machine was one of an extremely complicated nature; attended with considerable expense of construction; and only fit to be used in cases where numerous and expensive calculations were necessary. inventor stated that he had caused two models to be made of his machine; but we cannot find that it was ever applied to any useful purpose. Hutton says that both the great French minister, Colbert, and the Academy of Sciences, approved of Leibnitz's invention. Early in the 18th century an arithmetical instrument was invented by DR. NICHOLAS SAUNDERSON, Professor of Mathematics in Cambridge University. The peculiar circumstance attending this invention was, that the learned Doctor was entirely blind-rendered so by an attack of smallpox in his childhood; and this contrivance was designed by himself to aid him in his peculiar difficulties; and by its aid he constantly performed very intricate calculations with great rapidity. His "Calculating Table" was a smooth thin board, a little more than a foot square, raised upon a small frame, so as to lie hollow; which board was divided into a great number of little squares, by lines intersecting one another perpendicularly, and parallel to the sides of the T.-the parallel ones only one-tenth of an inch from each other; so that every square inch of the T. was thus divided into 100 little squares. At every point of intersection the board was perforated by small holes, capable of receiving a pin; for it was by the help of pins, stuck up to the head through these holes, that he expressed his numbers. He used two sorts of pins; a larger and a smaller sort; at least their heads were different, and might easily be distinguished by feeling. Of these pins he had a large quantity in two boxes, with their points cut off, which always stood ready before him when he calculated. A writer who was familiar with his process says: "He could place and displace his pins with incredible nimbleness and facility, much to the pleasure and surprise of all the beholders. He could even break off in the middle of a calculation, and resume it when he pleased: and could presently know the condition of it, by only drawing his fingers gently over the Table."-Hutton's Math. Dict.

About this period also M. DELEPRENE and M. BOITISSENDEAU invented several mechanical contrivances for performing particular arithmetical processes. These were, however, merely modifications of Pascal's, "without varying or extending its objects." About the middle of the same [18th] century, VISCOUNT MAHON [afterwards Earl Stanhope] invented a small arithmetical machine. In 1775 the same noble inventor made a larger machine, to add, subtract, multiply, and divide. In 1777 he produced another somewhat similar machine, of a somewhat different construction, for the same operations. In vol. i. of Machines et Inventions approuvées par l'Académie Royal des Sciences there is a description of the Abacus Rhabdologicus, a variation of Napier's. In vol. xlvi. of Phil. Trans. there is an account of an ingenious instrument of computation invented by MR. GAMALIEL Somethwest, where the inventor remarks that computations by it are much quicker and easier than by the pen; are less burdensome to the memory; and can be performed by blind persons, or in the dark as well as in the light.

Before passing from these earlier machines to a more modern phase of invention, we may with advantage again quote Dr. Lardner:

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.

PROF. BABBAGE, the next inventor whom we have to mention, being thus introduced to us, we may at once proceed to speak of his performances. It seems to have occurred to him as early as 1812 or 1813, that T. of logarithms might be calculated by machinery. We propose to draw from his own record-Passages from the Life of a Philosopher- such details as may best expound his efforts, and at the same time aid in a general understanding of this interesting subject:

I considered that a machine to execute the more isolated operations of arithmetic would be com. paratively of little value unless it were very easily set to do its work, and unless it executed not only accurately, but with great rapidity, whatever it was required to do. On the other hand, the method of differences supplied a general principle by which all tables might be computed through limited intervals by one uniform process. Again, the method of differences required the use of mechanism for addition only. In order, however, to insure accuracy in the printed T., it was necessary that the machine which computed T. should also set them up in type, or else supply a mould in which stereotype plates of those T. could be cast.

I now began to sketch out arrangements for accomplishing the several partial processes which were required. The arithmetical part must consist of two distinct processes-the power of adding one digit to another, and also of carrying the tens to the next digit, if it should be necessary. The first idea was, naturally, to add each digit successively. This, however, would occupy much time if the numbers added together consisted of many places of figures. The next step was to add all the digits of the two numbers, each at the same instant, but reserving a certain mechanical memorandum whenever a carriage became due. These carriages were then to be executed successively. Having made various drawings, I now began to make models of some portions of the machine, to see how they would act. Each number was to be expressed upon wheels placed upon an axis; there being one wheel for each figure in the number operated upon.

He then tells us how his first experiments failed; and the cause of the failure. He proceeds:

The next step was to devise means for printing the T. to be computed by this machine. My first plan was to put together movable type. I proposed to make metal boxes, each containing 3000 types of one of the ten digits. These types were to be made to pass out one by one from the bottom of their boxes, when required, by the computing part of the machine. But here a new difficulty arose. The attendant who put the types into the boxes might, by mistake, put a wrong type in one or more of them This cause of error I removed in the following manner :-There are usually certain notches in the side of the type. I caused these notches to be so placed that all the types of any given digit possessed the same characteristic notches, which no other type had. Thus, when the boxes were filled, by passing a small wire down these peculiar notches, it would be impeded in its passage, if there were included in the row a single wrong figure. Also if any digit were turned upside down, it would be indicated by the stoppage of the testing wire. One notch was reserved as common to every species of type..

...

By means of this common notch, precautions were taken to prevent disaster after the type was finally set :

Another plan for printing the T. was to place the ordinary printing type round the edges of wheels. Then as each successive number was produced by the arithmetical part, the type-wheels would move down upon a plate of soft composition, upon which the tabular number would be impressed. This mould was formed of a mixture of plaster of Paris, with other materials, so as to become hard in the course of a few hours. The first difficulty arose from the impression of one tabular number on the mould being distorted by the succeeding one. I was not then aware of the very slight depth of impression from the type would be quite sufficient.

Another series of experiments were, however, made for the purpose of punching the computed numbers upon copper plate. A special machine was contrived and constructed, which might be called a co-ordinate machine, because it moved the copper plate and steel punches in the direction of three rectangular co-ordinates. This machine was afterwards found very useful for many other purposes.... In the end Mr. Babbage prepared various sketches, prob. answering each of the ends here described. Between the years 1820 and 1822 he actually constructed a DIFFERENCE ENGINE--the first which had ever been constructed. This, for the sake of distinction, we shall call Difference Engine No. 1.

About 1815 DR. ROGET invented a sliding scale of involution, known by his name. The instrument consists of one fixed and one movable scale, like a sliding rule. On the slide a line is logometrically divided, the divisions of one half being from 1 to 10, and repeated on the second half in the same order. The fixed scale is graduated in such a manner that each of its own divisions is set against its own respective logarithm on the slider; and consequently, all the numbers on the slider will be situated immediately under those numbers in the fixed scale of which they are the logarithms. Thus 3 on the fixed scale will stand under 100, and so on. The instrument is adapted to perform the operations of involution and evolution. [See 1851.]

In 1822 the following pub. appeared :—(1) Note respecting the Application of Machinery to the Calculation of Mathematical Tables. This appeared in the Memoirs of the Astronomical So. (2) A Letter to Sir H. Davy, P.R.S., on the Application of Machinery to the purpose of Calculating and Printing Mathematical Tables. (3) On the Theoretical Principles of the Machinery for Calculating Tables. This appeared in Brewster's Edin. Journ. of Science. Each of the above papers were from the pen of Charles Babbage. (4) Address to the Astronomical So. by Henry Thomas Colebrooke, Esq., F.R.S., President, on Presenting the first Gold Medal of the So. to Charles Babbage, Esq., for the Invention of the Calculating Engine.

In the above letter to Sir Humphry Davy, Mr. Babbage said his machine would "calculate tables governed by laws which have not been hitherto shown to be explicitly determinable, or solve equations for which analytical methods of solution have not yet been contrived." He further said that the machine would take from the several boxes containing type the numbers which it calculated and place them side by side: thus

becoming at the same time a substitute for the compositor and the computor, by which means all error in copying as well as printing is removed.

In his address to the Astronomical So. Mr. Colebrooke said:

The principle which essentially distinguishes Mr. Babbage's invention from all these [the inventions which had preceded him] 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 computor; 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.

Regarding the printing its own Tables Mr. Colebrooke says:

The usefulness of the instrument 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 insuring accuracy, obviating numerous sources of error through the careless hands of transcribers and compositors.

No sooner was the Difference Engine No. I completed, than Mr. Babbage received instructions to construct another and more comprehensive one, for and at the expense of the the English Gov. This [Difference Engine No. 2] he commenced in 1823. It was proposed that this new engine should have six orders of differences, each consisting of about 20 places of figures; and also that it should print the tables it computed. The printing might be by either of the processes already described. While the construction of this second machine is in hand we must proceed with our chronicle. [See 1836.]

In 1824 there appeared in the Memoirs of the Astronomical So. a paper by Charles Babbage, Observations on the Application of Machinery to the Computations of Mathematical Tables.

In 1829 there was pub. a Report by the Committee appointed by the Council of the Royal So. to consider the subject referred in a Communication received by them from the Treasury, respecting Mr. Babbage's Calculating Engine, and to Report thereupon. This Committee, which had been appointed at the instance of the Gov., 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. We can only give an abstract of the report:

They had declined the consideration of the principle on which the practicability of the machinery depended, and of the public utility of the object which it proposed to attain; because they considered the former fully admitted, and the latter obvious to all who considered the immense advantage of accurate numerical tables in all matters of calculation-especially those which related 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 inquiry was, that such precautions appear 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 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 of 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 surprised at the time which the work had 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 could 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 was 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.

It would be difficult to imagine a much stronger expression of opinion, and this too by men thoroughly competent to form a practical judgment. The work continued to progress, but in a very slow and interrupted manner, until 1833, when it became entirely relinquished.

In the Edin. Review, for July, 1834, appeared an art. by Dr. Lardner, mainly consisting of a description of the scientific appliances combined in the construction of Mr.