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bodies under the term. An actuary, as now understood, is a person who is trained to apply the doctrine of mathematical prob. to the affairs of life. The classes of problems with which he has to deal embrace all monetary questions that involve a consideration of the separate or combined effect of int. and prob.

An actuary is now regarded as a necessary officer of every asso. transacting life, annuity, or rev. bus. He may be either a resident actuary, a term applied to persons holding a fixed appointment with any particular asso.; or he may be a consulting actuary, whose services are at the disposal of any person or asso. requiring the same. [ACTUARIES, CON SULTING.] The title of actuary can scarcely be said to properly belong to any person in Gt. Brit. who is not a member of the Inst. of Actuaries of Gt. Brit. and Ireland, or of the Faculty of Actuaries in Scotland.

Mr. Wm. Morgan was probably the first resident actuary appointed. He became act. of the Equitable in 1774. Dr. Price addressed the following remarks to that So. on the duties and the importance of the office of actuary.

There are no questions the solution of which requires a stricter attention, or greater skill in investigation, than some in the doctrine of assu. Difficult questions are sometimes brought to the So.; and the Directors, not being themselves mathematicians, are under a necessity, in making their demands, of being governed by their Actuary: and should he happen to be unqualified, he must make mistakes, and either the public or the So. will be injured. In short, the So. can scarcely be sensible enough of the importance of both abilities and probity in the servants it employs; nor therefore of the particular reason there is for guarding their places against the applications of candidates who in any future vacancies may endeavour to intrude themselves by their connexions or influence.

It was in 1819 that the profession of the actuary came to be specially recognized by the Government. This came about in two forms. First by the appointment of Mr. John Finlaison to the office of actuary to the Commissioners of the National Debt; and second, by enacting (59 Geo. III. c. 128, sec. 2) that the Tables and Rules of all Friendly Societies should be "approved by two persons at least, known to be professional actuaries, or persons skilled in calculation," as fit and proper, according to the most correct calculation of which the nature of the case would admit. (See 1846.)

In 1826, Mr. Babbage said in his Comparative View, speaking of the actuaries of the then offices:

The degree of knowledge possessed by persons so situated at the different Inst. is exceedingly various, passing through all degrees, from the most superficial acquirements, derived merely from the routine of an office, up to the most profound knowledge of the subject.

These differences in degree of attainments are not peculiar to the profession of the actuary.

The requirement of an actuarial certificate to the Tables, etc., of F. Sos. enacted in 1819, was superseded by the law of 1829; but in 1846 there was enacted the 9 & 10 Vict. c. 27, sec. 13 of which provided as follows:

After the passing of this Act, the Reg. of F. Sos. in England and Scotland shall not certify the rules of any F. So, estab. after the passing of this Act, for the purpose of securing any benefit depending on the laws of sickness or mort., unless such So. shall adopt a Table which shall have been certified to be a Table which may be safely and fairly adopted for such purpose under the hand of the actuary to the Commissioners for the Reduction of the National Debt, or of some person who shall have been for at least five years an actuary to some Life Ins. Co. in Lond., Edin., or Dublin, and the name of the actuary by whom any such Table shall have been certified shall be set forth in the rules, and printed at the foot of all copies of such Tables printed for the use of the So. (See 1850.)

By the 13 & 14 Vict. c. 115, the enactments of 1819 and 1846 are modified, and the employment of an actuary in relation to F. Sos. is rendered optional, except that the Reg. is not to grant a "certificate to any So. assu. to any member thereof a certain annuity deferred or immediate, unless the Tables of Contributions payable for such kind of assu. shall have been certified by an actuary as aforesaid, or furnished by the Reg.' But if the Rules and Tables were certified by an actuary as provided by the act of 1846, then the So. was to be designated a "certified" So.

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By 15 & 16 Vict. c. 80 (1852), an act to abolish the office of master in ordinary of the High Court of Chancery, and to make provision for the more speedy and efficient despatch of the bus. of the said Court, authority is given (sec. 42) to any judge of the Court to obtain the assistance of "actuaries or other scientific persons" the better to enable such Court or judge to determine any matter at issue in any cause or proceeding, and to act upon the certificate of such persons. Under this authority the opinions of actuaries are very constantly required by the Court.

In 1853 a gool deal of attention was drawn to the subject of the training and qualification of actuaries, by reason of the Select Com. on Assu. Asso., which sat in that year, taking some notice of the question.

Mr. Samuel Brown, in a paper read before the Inst. (Assu. Mag. vol. iv., p. 93), took occasion to say :

I apprehend that the real bus. of the actuary is the reasoning on all events to which the mathematics of prob. can be applied, and reducing the conclusions to a form in which they can be practically used for the public benefit. His study is the doctrine of averages; and though his functions have been hitherto confined in a great measure to subjects relating to the assu. of human life, there are evidently many other topics to which in time his attention ought to be directed. The discovery of the mathematical laws of events will eventually be recognized as the sole means of bringing uncertainty to certainty, and out of irregularity deducing order. Whilst men depend wholly on their individual experience and skill, without consulting the laws deduced by mathematics from a large collection of

facts, they will often be astonished, as they frequently are now in Fire and Marine Assu., by fluctuations which upset all their rules of practice, but which the mathematician, if he had been furnished with the previous results of their experience, would have predicted with almost unerring certainty. Dr. Farr, in the Twelfth Ann. Rep. of the Reg.-Gen., pub. that same year, said: The whole commerce of the country turns on contingencies which demand the application of scientific observation and calculation; and as English agriculture has its chemists, English commerce must, to keep pace with it, ultimately employ actuaries to calculate the risks which are now only roughly guessed at; and thus extend the sphere of an important class of scientific men, at present almost peculiar to this country.

And then turning to the present rather than the future, added the following: There is so much of peculiarity in every Assu. So., and such skill required in determining what charge should be laid on the net premium, what reserve should be laid up, what constitutes the safety of a particular Office, what should be sacrificed to extend the transactions, what should be strenuously resisted to save a So. from imminent danger or insolvency, and what should be adopted to give families the greatest benefits, the public the greatest confidence in Ins. Sos.-as demand from the actuary great technical and mathematical skill, besides integrity, consummate judgment, courage and prudence.

In the same year Mr. H. W. Porter read before the Inst. of Actuaries an able paper On some points connected with the Education of an Actuary (Assu. Mag. vol. iv., p. 108). In the preparation of the present work we think it will be found that we certainly have not exceeded the scope of inquiry which the author of that paper considered should form the groundwork of the education of an actuary. We commend the careful study of that paper to all who contemplate entering into the profession. We content ourselves with the following extract here:

The model actuary, then, as a statist, collects and arranges the materials for his mort. table; as a mathematician he constructs, accommodates, and corrects it, according to scientific principles; and from this course he calculates his Tables of annuities and of prems. His knowledge of the nature of diseases, and of their effect upon certain constitutions and under different conditions, enables him to co-operate with the physician; and thus the medical knowledge of that officer is combined with the statistical element in the hands of the actuary, and the knowledge of both is thus made practically useful. His legal knowledge, if sound, may save the Co. much expense-his sphere of usefulness is enlarged, and he becomes a valuable coadjutor of the legal adviser of his Co. As a scholar, the actuary is continually in request. As a man of business his services are invaluable. In the term "business" I include a knowledge of Finance.

Mr. David Maclagan, in his address to the Actuarial So. of Edin., in 1867, said:

I claim for the profession of an actuary a very high place indeed. Measured by the issues which depend upon its accurate details, and still more upon the soundness of the principles on which these details proceed, the importance of our profession may be stated in very strong terms. It deals with enormous figures in finance, and it is entrusted with the interests of generations of men. It concerns itself with the minutiae of apparently trifling matters of routine, with fractional and almost infinitesimal considerations; but it also manipulates and fructifies gigantic sums, and apportions them periodically among thousands of recipients who are literally helpless in its hands.

The charter of incorp. of the Faculty of Actuaries of Scot. granted 1868, thus sets forth the duties of an actuary :

Firstly, to take care that the inst. under his charge, or which may at any time desire his opinion and advice, is founded on a safe basis, both as regards the rate of mort, assumed for any particular country, class, or sex, and the rate of int. at which it may be calculated the money entrusted to the care of such inst. can be safely improved; secondly, to ascertain from time to time, as the inst. makes progress, by appropriate calculations, whether the rate of mort. actually experienced, and the rate of int. realized, are in accordance with the data assumed: for the performance of these duties it is evident that not only a sound knowledge of mathematical principles is required, but also the practical application of financial judgment and experience:... in addition to the requirements of Life Assu. Inst., the profession of Actuary is largely called into requisition, in the same manner as that of advocate or barrister, in advising and directing the public in regard to a great variety of pecuniary interests, frequently involving interests of large amount.

The Life Assu. Cos. Act, 1870, requires an investigation into the affairs of all Asso. transacting Life bus., to be made by "an actuary" periodically; but does not define who shall be regarded as an actuary for such purpose. We believe the attempt once or twice made legally to define an actuary led to a complete failure. This need not be so. A short act of Incorp. for the Institute might settle this vexed question.

After what has been already said here, it may seem superfluous to add that an actuary must be something more than simply a mathematician. That he must be a mathematician admits of no question; but with that qualification ever so largely developed, and nothing more than that, he never becomes an actuary in the sense here implied. The other qualifications are sound judgment and enlarged knowledge of business affairs-sagacity. The latter can only be obtained with and from experience; the judgment should be inherent. We will quote from two authorities in point: Mr. Porter said in the paper already quoted : Those who have been in the habit of seeing that class of cases which arise in the private practice of an actuary, and particularly in that of actuaries of Rev. Ins. Cos.,-and which are of a far higher order than ordinary Assu. Office calculations,-must be well aware that in many cases judgment, both as to the treatment of the case, and as to the adoption of results when arrived at by calculation, or the modification of those results, is no unimportant aid to the actuary; indeed, cases may and do arise in practice, the result of which untempered by judgment would be absurd.

Mr. Charles Jellicoe remarked in 1855 (Assu. Mag. vol. vi., p. 66):

From what has been said, it will be apparent that in questions of this kind a great deal of judgment and discretion must always be required from the actuary, and that it is not possible to lay down any general rule which will altogether obviate such requirement.

Hence, and happily, calculating machines can never entirely take the place of men.

ACUTE DISEASES.-Diseases of considerable severity, rapid progress, and short duration, as distinguished from chronic, or long-continued diseases. Diseases were formerly distinguished into morbi acutissimi, very acute, lasting only three or four days; morbi subacutissimi, lasting seven days; and morbi subacuti, lasting from twenty to forty days.— Hoblyn's Dict. of Med. Terms.

ADAMANT FIRE and Life Assu. Co. projected in 1852, but never attained the honour of comp. regis. The Co. was promoted by Mr. Fred. Lawrence, who first regis. it as the Alleviator. Its proposed cap. was £100,000, in shares of £1.

ADAMS, John, pub. in 1787 The Mathematician's Companion, or a Table of Logarithms from 1 to 10,860, with an introduction to Decimal and Logarithmic Arithmetic.

ADAMS, THOMAS, was Sec. of Coal Trade Mut. and several other Marine Clubs at South Shields, in 1845, and for some years subsequent.

AD INTERIM, in the mean time. As ad interim dividends, pending the declaration of ordinary dividends.

ADDISON, COLONEL H. R., was manager of the Phonix Life during the years 1856-7. ADDITIONS TO BUSINESS.-An Ins. Asso. cannot take up any branch of bus. not orig. provided for in the scheme of its constitution. This was decided in 1824 in the case of Natusch v. Irving, see ALLIANCE F. AND L. In view of this circumstance, it is usual in stating the "objects" for which an asso. is founded, which in the case of every modern Co. has to be set out in detail in the Mem. of Asso. [MEMORANDUM OF ASSO.], to embrace not only the immediate objects of the Asso., but such as may arise in process of time by amalg. or otherwise. Hence the objects of a Life Asso. frequently comprehend the trans. of Fire and Marine Ins. or Accident and Fidelity Guar. bus., although it is only intended at the time to transact life bus. The objects of the Asso. once fixed cannot be altered. [ALTERATIONS.] [OBJECTS.] ADDITIONS TO POLICY.-Reversionary Bonuses declared upon Life policies are termed "Additions to Policy." Mr. Charles Jellicoe advanced the following important query upon this subject in 1856. Should not the add. to a policy, as well as the sum assu., be charged with extra prem. where extra risk is incurred?-adding the following observations: It is remarkable that this is done in very few offices, even when the add. are actually greater than the sum assu. There can be, of course, no good reason for such a practice; the add. are made on the supposition that the circumstances of the life involved will remain the same. If those circumstances are altered, the office should have compensation for the add. risk incurred by the change, or it must be a loser to the extent of the proper prem. to meet it. Assu. Mag., vi., p. 104. ADELPHI Asso. "for the effecting of mut. and the granting of guaranteed assu. on Lives and Survivorships, and the sale of deferred and contingent Life annu. and Endow." This Asso. was projected some years since. It was to have a capital of £500,000, in 10,000 shares of £50. Its preliminary prospectus said:

The prov. committee of the Adelphi Asso. having well considered the various existing schemes of Life Assu., are satisfied that there are strong reasons for believing that notwithstanding the large number of similar Inst., an asso. embracing, and extending, upon safe and equitable principles, the various conveniencies which have hitherto been projected, is yet requisite to supply the wants of, and would be appreciated and supported by the public.

This belief was not realized; the undertaking never reached maturity; the scheme bore a strong family resemblance to the Abacus. Mr. E. Ryley was its consulting actuary. ADJOINING RISKS.-In Fire Ins. houses, buildings, etc., standing so near to the particular risks being ins. as to be likely to communicate fire. Property insurable in itself at easy rates may by reason of its contiguity to combustible materials be deemed hazardous. In France the person in whose premises a fire originates is primâ facie liable for all damage done to adjoining risks.

ADJUDICATION, giving or pronouncing a judgment, sentence, or decree. As adjudicating upon claims; determining or decreeing the amount to be paid. Claims "waiting for adjudication" are those in which all the requirements of the proof have not been complied with.

ADJUST (To).-From the Fr. to make even. To arrange, define, determine, make even, and "settle" the amount payable under a contract of ins. on the occasion of a loss. ADJUSTER.-One whose profession or bus. it is to adjust. [ASSESSOR.] [AVERAGE STATER.] [CLAIM ADJUSTER.]

ADJUSTMENT.-The term is applied in several forms to the business of Ins. We must

deal with it under each head.

In Marine Ins. it signifies the process of ascertaining the amount of the indemnity which the insured, after all allowances and deductions made, is entitled to receive under his policy, and the fixing the proportion which each underwriter is liable to pay. The term "settling," as applied to the adjustment of marine losses, is technical, and sometimes leads to misapprehension; it should be discontinued. Marine losses are usually adjusted by persons specially qualified for the purpose, called average-adjusters, or average-staters, which is indeed a recognized profession. Orginally Marine losses were not payable until one month after adjustment. The Marine Cos. after a time adopted the practice of paying within ten days or a week. The underwriters at Lloyd's adhered to the custom of one month, until June 1870, when a discussion was raised, and on a ballot of members, it was agreed to pay one week after adjustment.

The question has arisen whether, if the underwriter received information after the adjustment, which altered his views of the bona fide character of the loss, and therefore of his liability, he was at liberty to decline to pay. In the case of Hog v. Gouldney, which arose in 1745, the adjustment had been made and endorsed upon the policy as follows: Adjusted the loss on this policy at ninety-eight pounds per cent., which I do agree to pay one month after date.-Henry Gouldney. The plaintiff pleaded that after such adjustments the losses were always paid without further proof, and the Lord Chief Justice considered the endorsement as a note of hand, and said the plaintiff had no need to enter into proof of loss. Later decisions have modified this ruling; and in case of fraud the money can be recovered even after payment. The usual form of endorsement on the policy now is "Settled at £and signed by the underwriter, or in case of a Co.

by the duly authorized officer, or two or more directors.

In Life Ins. the term has no reference to claims.

In Fire Ins. complications equally great with those in Marine Ins. occur, more particularly in relation to "Floating Policies." But such adjustments are usually termed "apportionments," and under that head we shall speak of them. The officer making the apportionment is called an "assessor." [ASSESSOR.]

In Hail and some other branches of Ins. the adjustment of the loss is termed an "assessment," and will be spoken of under that head.

In Cattle Ins. the losses are generally settled through the aid of an "Inspector." ADJUSTMENT OF RIGHTS OF CONTRIBUTORIES, is a process which arises in the winding up an asso. either voluntary or under the Court. The debts being all paid, the surplus has to be disposed of to the contributories by this process. Cos. Act, 1862, secs. 109 and 133. ADJUSTMENT OF TABLES OF MORT.--The process of adjustment or graduation by which a Life Table is made to represent as nearly as possible the progress of a human generation year by year through life, is employed upon the same principle that astronomers "reduce," as it is termed, all their observations to some common event or epoch. "By the term correcting or equating observations for nutation," says Herschel, is always understood in astronomy the getting rid of a periodical cause of fluctuation and presenting a result, not as it was observed, but as it would have been observed had that cause of fluctuation had no existence." The same process has to be employed in the construction of Mort. Tables. A simple instance may be furnished. Between the ages of 15 and 25, and indeed up to later ages, the mort. is kept down in towns by the influx of healthy people (chiefly females) from the country: thus in Lond. the annual mort. amongst young women, between the ages named, is only 6 per 1,000; while in the surrounding counties the mort. at the same age is from 7 to 8 per 1,000; and amongst young men in Lond., at the like age, it is 8 per 1,000; The solution is found in the fact that healthy young women of these ages go from the country into Lond., and other large towns, and obtain situations, and frequently, if they are taken ill, go back into the country to die. The effect is to make towns look more healthy than the country, at these ages. Mort. Tables, constructed upon extensive data from town and country life, would not be materially affected by such fluctuations. Those based upon town observations only are certain to be more or less so, unless subjected to the processes just enumerated. They would, in fact, exhibit fictitious decrements at the ages enumerated if this "correction "--which implies the preceding processes-were omitted.-Ins. Guide and Hand-book.

In 1857, a paper from Mr. Peter Gray on Mr. Gompertz's method for the adjustment of Tables of Mort., was pub. in the Assu. Mag. (vol. vii., p. 121), and therein the writer offered the following remarks:

:

When an observation has been made for the purpose of determining the mort. which has prevailed during a specific time in the community observed upon, it is usually found that the series of prob. of living a year at the various ages thence deduced is very far from conforming to our ideas of what an exponent of the law of mort. ought to be. Instead of a series exhibiting throughout its extent a gradual and progressive change of value in passing from each term to the next, we have one showing but a faint approach to the desired regularity. This is just what, from the circumstances in which such obs. are usually made, we ought to expect. It is not often that the community subjected to obs. is sufficiently extended to furnish us with such a series of average results as can alone fitly figure forth the law of mort. Now if our object is only to ascertain the mort, which has prevailed during the period to which our obs. has been restricted, nothing remains to be done-the series obtained as above is a correct representation of that mort. But there is usually another ulterior object in view. What we generally want is a series to serve as a basis of deductions for the future, and which consequently shall exhibit, not the incidental mort, of a limited period, but the normal mort. (so to speak), which would have been found to prevail had the observation been conducted on more extensive bases. Keeping in view then that we have no other means of arriving at, or rather of approximating to the series in question than by subjecting to treatment the series already obtained, it becomes a matter of importance to determine what is the mode of treatment likely to conduct us to the most satisfactory result. Various methods have been devised and employed by computors who have been engaged in the construction of tables for the adjustment of their results (for so the operation I speak of is termed), and it is one of these that it is the object of the present paper to explain and illustrate.

The method in question is that which was devised by Mr. Gompertz, and given to the world in the Phil. Trans. for 1825. Although so long before the public, it is far from being so well known as it deserves to be.

...

In nearly all the methods of adjustment heretofore employed, with the exception of Mr. Gompertz's, the object chiefly kept in view has been, simply (doing, of course as little violence as possible to the orig. results), to secure some sort of regularity of progression in the series of prob. of living a year; and this without reference to any law in accordance with which this progression ought to be regulated. Mr. Gompertz, on the other hand, sets out by proposing for our acceptance a principle with respect to

the progression of the rate of mort., which, on its being admitted, leads to the method of adjustment of which we speak.

He then proceeds to explain Mr. Gompertz's Law of Mort., and to expound its formulæ, in which it is not necessary to follow him.

Two able papers On Interpolation, Summation, and the Adjustment of Numerical Tables, appear in vol. xi. Assu. Mag. by Mr. Woolhouse.

It will have been gathered from the foregoing that various methods of adjustment have been employed. A controversy has recently (1870) arisen between Mr. Woolhouse and Mr. Filipowski, as to the plan which was adopted in adjusting the NEW EXPERIENCE Tables. Mr. Woolhouse said on this occasion:

I have for many years made the adjustment of tables a special study, and the subject is one the investigation of which is beset by formidable difficulties, which still present to mathematicians an interesting field for future research. The particular method by which the New Experience Tables have been adjusted by me, and which I am assured will be practically useful in other departments of science, is mathematically satisfactory in principle, and the manipulation of the same has proved to be both effective and simple in practice, and such as to warrant its general adoption.

Mr. Filipowski advocated a method altogether different from that which he believed had been adopted. We cannot follow the controversy (see Ins. Record, December, 1870). [GRADUATION.] [MORT. TABLES.]

ADLARD, GEORGE, an English gentleman resident in New York. He has represented several English Ins. Cos. doing bus. in the U.S., viz., the Monarch, the Unity, and more recently the Queen. He has written some able papers on historical subjects, and to him we are indebted for the discovery, in the Register Books of the Privy Council, of the controversy between the two first English Fire Offices, which will be found detailed in our HIST. OF FIRE INS.

ADLER, MARCUS N., M.A., F.I.A., Act. of Life department of Alliance since 1867. Mr. Adler entered that office in 1857, for the purpose of acquiring a practical knowledge of ins. He had studied under the late Professor De Morgan, at University College, and had assisted a son of that gentleman in the estab. of the Mathematical So. In the Alliance he had the good fortune to come under the immediate notice of the then distinguished Act. of the Co., Mr. Gompertz, who discerned and appreciated his attainments. In 1858 Mr. Adler communicated to the Assu. Mag., "Formula for an Approximate Value of Annuities at Simple Interest."

In 1864 Mr. Adler prepared a paper :-Some Considerations on the Government Life Annuities and Life Assu. Bill, in which was contained many suggestions of a practical character. He had the satisfaction of seeing that most of his suggestions were embodied in the measure adopted by the Government. The paper is printed in vol. xii. of Assu. Mag. In 1865, he prepared a further paper :-On Government Annuity and Assu. Rates and Regulations, in which he answered some criticisms on the preceding measure (Assurance Magazine, vol. xii., p. 265).

In 1866 Mr. Adler communicated to the Assu. Mag. (vol. xiii) a very interesting memoir of Mr. Gompertz, F.R.S., which we shall have occasion to notice hereafter. It seemed only appropriate that the man who was ultimately to succeed to the chair of that distinguished mathematician should write his memoir.

In 1868 Mr. Adler read before the Institute an instructive paper on "Ins. bus. in Germany ;" and in 1870, he read before the Working Men's Club Union (under the presidency of Lord Lichfield), an interesting paper on F. Sos.

ADMINISTÉR (To).-To dispose according to law of the estate and effects of a person who who has died intestate—that is, without leaving a will. This is done under the authority of a legal instrument called "Letters of Administration." If these be granted to a male, he is called "Administrator," if to a female she is called "Administratrix." Where there are any legal difficulties as to who shall administer, the process is effected through the aid of the Court of Chancery, in what is termed an "Administration suit." ADMINISTRATION. See LETTERS OF ADMINISTRATION.

ADMIRALTY COURT.-This is a Court of great antiquity. In the reign of Edward I. it was said to have existed "time out of mind." All things arising upon the sea, as causes of merchants and mariners, and whether civil or criminal, were tried before the Lord High Admiral, who was to judge them in a summary way according to the laws of the sea then known. Edward III. appears to have placed the Court upon a better footing in 1357. The rules by which it then came to be governed were the ancient laws, customs, and usages of the sea, including such selections from the laws of Rhodes and Oleron, the Waterrecht of Wisbey, the Hanseatic Ordinances, the Consolato del Mare, the Marine Ordinances of Louis XIV. (1681), and others, which from their natural justice and sound policy obtained generally in the Admiralty Courts of Europe.

Richard II. limited the jurisdiction of the Court. It is probable that previously the Court took cognizance of all causes of a maritime nature, whether arising within the king's dominions or out of them. It would seem to be the proper province of the Court to deal with causes wholly arising upon the main sea, and not within the precincts of any country so that being out of the reach of ordinary Courts of Justice, they are to be remedied by a peculiar court of their own. The judgeship of the Admiralty was constituted in 1514: the judge being styled the Lieutenant of the High Admiral.

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