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24,532 and 27,431; brain diseases undistinguished, 3963 and 5605. This class of diseases constituted a proportion, in the year 1866, of 1233'9 deaths to every 10,000 of the deaths from all causes-viz., cephalitis, 836; apoplexy, 2077; paralysis, 211'9; insanity, 131 chorea, 13; epilepsy, 49.8; convulsions, 553'4; and other brain diseases, 113.1.

Among brain diseases, necrencephalus, or softening of the brain, has of late years rapidly increased. In the ten years 1857-66, 11,685 deaths were registered in E. and W. from this cause-7168 males, and 4517 females. In the first five years, 1857-61, the average annual deaths were 894; whereas in the second period of five years 1862-1866, the deaths averaged 1443 annually. In 1857 the number of persons who died from softening of the brain was 775. In 1866 the number was 1664, of which 78 were under 20 years of age; 191, 25 and under 45; 457, 45 and under 65; 424, 65 and under 75; and ten were aged 75 and upwards. In 1867 the deaths were 1810, of which 1132 were males, and 678 females. The ages at death were about the same as in 1866. BRAITHWAITE, J., was Gen. Man. of the Progress Ins. Co. during its short career, 1867-8. BRAKENRIDGE, Rev. Wм., D.D., F.R.S., addressed, in 1755, a letter to the President of the Royal So., Concerning the Method of Constructing a T. for the Prob. of Life at Lond. The same was pub. in Phil. Trans. that year. In 1756 he addressed another letter to the same So., in which he estimates the number of houses in England; and the same is pub. in the Trans. for that year. In 1757 he made a further communication on the number of houses in Lond. and Middlesex.—See Phil. Trans., vol. 50. [HOUSES.] [POPULATION.] BRAMAH, JOSEPH, described as "of Piccadilly, Lond., Engine Maker," in 1785 obtained a patent for a "hydrostatical machine upon a new construction." It applied to pumps and fire engines. In 1793 he patented" several improvements and additions to a fire engine made by me." Some of Bramah's engines are still in use in Lond. [FIRE ENGINES.] BRANCH PIPES.-A metal pipe, several feet in length, fastened on the end of the hose, and used for directing the water from the fire engine upon the fire. Its invention is prob. coeval with that of fire engines. In 1863 Mr. Lewis Becker applied a stopcock to the branch, for use in the interior of a building, which is said to be a great improvement. BRAND, CHARLES, late Registrar of the Amicable So., pub., in 1775, A Treatise on Assu. and Annu. on Lives, with several objections against Dr. Price's Obs. on the Amicable So. and Others. To which is added, a Short, Easy, and more Concise Method of Calculating the Value of Annu. and Assu. on Lives, than any heretofore pub. This work was reviewed in The Critical Review for the same year, and in that review, in 1776, appeared, A Letter written by this Author in Defence and Explanation of his Work and Principle.

In 1778 he prepared for the So. its Mort. "Experience" from the commencement of the So. a most valuable document.-See AMICABLE SO. EXPERIENCE Tables.

In 1780 he edited an ed. of Smart's Tables, "Now revised, enlarged, and improved, by Charles Brand; to which is added an appendix containing some obs. on the General Prob. of Life."

BRANDENBURG, T. of Mort. FOR.-In the last ed. of Sussmilch's Gotliche Ordnung, pub. 1775, is contained a T. of Mort., "showing the prob. of the duration of human life at all ages in a kingdom at large; deduced from obs. in the Kurmark of Brandenburg, and formed on the supposition that a third of the kingdom consists of inhabitants of towns, and two-thirds of the inhabitants of country parishes and villages." Dr. Price included this in his 4th and 5th eds. of Reversionary Payments, etc. The obs. had been made by Sussmilch upon 1000 children born; but in these were included 42 stillborn, which Dr. Price eliminated. He added the column of "Expectations." The following is the T. as given by Dr. Price:

BRANDENBURG, DUCHY OF, MORT. T. FOR.-Sussmilch.

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This T., it should be further observed, has been formed without any regard to the correction explained in the 4th essay in the former vol. of this work [Rev. Payments]; and on this account (as far as it has been deduced from the numbers dying at every age in the towns of Brandenburg) makes the prob. of living too high in the first stages of life. But it should be likewise attended to that on another account, it makes them in a much greater proportion too low. I mean on account of the great excess of the births above the burials in the country parishes and villages.

BRAZIL. The pop. in 1856 was 7,677,800, and its density per square mile was 2. Pop., 1867, 10,780,000.

BREACH OF TRUST.-A violation of duty by a trustee, executor, or other person in a fiduciary position. A breach of trust was not punishable as a criminal offence until the passing of 20 & 21 Vict. c. 54, in 1857. [FRAUDULENT TRUSTEES ACT.] BREAD, ASSIZE OF; ADULTERATION OF.-The first Stat. for regulating the sale of bread was 3 John, Assessa Panis, A.D. 1203. The chief justiciary and a baker commissioned by the King had the inspection of the assize. -Matthew Paris. The assize was further regulated by Stat. 51 Henry III., 1266; and by 8 Anne, 1710. These Acts were repealed in 1824.

The first direct Act against the Adulteration of Bread was passed in 1822, the 3 Geo. IV. c. cvi.; An Act to repeal the Acts now in force, relating to bread to be sold in the City of Lond. and the Liberties thereof, and within the Weekly B. of Mort., and ten miles of the Royal Exchange; and to provide other regulations for the making and sale of bread, and preventing the adulteration of meal, flour, and bread, within the limits aforesaid. By the 6 & 7 Wm. IV. c. 37 (1836), these provisions were to be extended to the entire kingdom of Gt. Brit. (not Ireland), and bread was thereafter to be sold by weight. By the 1st Vict. c. 28, the regulations as to bread were extended to Ireland. BREAK OF LIFE.-It is a well-known result of all European contributions to V. statistics, that a marked change, the causes of which are but very imperfectly understood, takes place in the law of mort. about the age of 55-so much so, that Dr. Farr, in constructing the English L. T. for the Reg.-Gen., actually used different mathematical laws for the formation of his T. before and after this age; and this period has been called the "break of life."-Professor Gill, Report on N. Y. Mutual, 1851.

BREAKING BULK.-A term formerly used to signify the separation of goods in the hands of

a bailee, which made him liable for felony. Since 24 & 25 Vict. c. 96 (1861), this distinction is immaterial.

BREAST MILK, Want of.-Deaths from this cause, which are too common, are classed under Zymotic, of the order Dietic. The fluctuations are very small, as will be seen by the following figures, applying to ten consecutive years: 1858, 997; 1859, 1017; 1860, 1002; 1861, 970; 1862, 1006; 1863, 1158; 1864, 1253; 1865, 1410; 1866, 1410; 1867, 1437. The numbers appear to be steadily on the increase; over a period of fifteen years ending 1864, they averaged 44 per million of the pop. living. The deaths in 1867 were: Males, 805; Females, 632; and were generally under 1 year of age. BREECHING.-A contrivance in metal in connexion with the working of hose from fire engines, by means of which two streams of water can be directed from one engine; or streams from two engines ejected from one nozzle. The Lond. Assurance Corporation's engines had such an appliance as early as 1828. In 1844 Lord Thurlow regis. a form of breeching by means of which one engine could throw three separate streams of water at once, or three separate engines be worked through one nozzle. [FIRE ENGINES.] BREMIKER, DR., pub., in Berlin, in 1859, Das Risico bei Lebensversicherungen—The risk attaching to the grant of ins. on lives. Mr. Sprague has furnished a translation of this paper for the benefit of the readers of the Assu. Mag. [vol. 16, p. 216.] We shall speak of it under other heads.

BREMNER, HUGH, was agent of the Lond. branch of City of Glasgow L. from opening of the branch in 1845 down to 1852.

BRESLAU, CITY OF.-Breslau is the capital of the province of Silesia; and one of the principal cities in Germany. Our interest centres in it entirely from the fact that from its regis. or bills of mort. were obtained the data for the first Life Table of which we have any record. It is situate on a spacious plain at the confluence of the Ohlau and Oder; bounded on the north by the Trebnitz Mountains; and on the south at a greater distance, by those of Zobten. The streets of the city, which was formerly fortified, are narrow, but the houses for the most part well built. It manufactures gloves, jewelry, silks, woollens, cottons, and stockings. Its pop. in 1710 was 41,000; by 1844, it had increased to 103, 282; by 1846 to 112, 194. We have very little other information concerning the place; except such as we shall give in the next art.

In this city the ann. average births regis. between the years 1717 and 1725 was 1252; of burials 1507. A great proportion of the children died under 10. Sussmilch furnished statistics tending to show that the mort. of children under 5 was very large in this city.— Dr Price.

Years.

Numbers..

Average 1552

The following were the burials for the 6 consecutive years 1720-25. 1720 1721 1722 1723 1724 1725 1816 1482 1791 1321 1466 1441 The city was burned by the Mongols in 1241. BRESLAU TABLE OF MORTALITY.-The formation of this celebrated Table-celebrated because it was the first formed upon actual data scientifically arranged-came about in this wise. The efforts of Graunt and Petty had resulted in mere approximations of the value, or probable duration, of Human Life. The Bills of Mort. which formed the basis of their observations did not then record the ages at death; and the results consequently were very vague and unsatisfactory. This state of matters engaged the attention of scientific men towards the close of the 17th century: and accordingly an effort was made to obtain access to regis. which did record the ages at death. It was found that in the City of Breslau in Silesia such records had been kept, at least during several years; and on the application of Mr. Justell-a member of the Royal Society-to Dr. Newmann, of that city, copies of such registers were obtained. This was in the year 1692. The returns were for the 5 years 1687-91. They comprised a total of 6193 births and 5869 deaths. Having obtained the materials, the next thing was to find a competent mathematician to work upon them. Dr. Halley was at that time a mathematician of great distinction, and he was selected, probably by the Royal Society, for the task. The result of his labours appeared early in the succeeding year under the following title, in a paper submitted to the Royal So., and pub. in Phil. Trans. for 1693: An estimate of the degrees of the Mort. of Mankind, drawn from curious Tables of the births and funerals of the City of Breslau; with an attempt to ascertain the price of annuities upon lives. By E. Halley, F.R.S. It is important to understand the author's own views of the task he had undertaken and performed. Dr. Halley commenced his paper as follows:

The contemplation of the mort. of mankind has, besides the moral, its physical and political uses, both which have been some years since most judiciously consider'd by the curious Sir William Petty, in his natural and political obs, on the B. of Mort. of Lond., owned by Capt. John Graunt. And since, in a like treatise, on the B. of Mort. of Dublin. But the deduction from those B. of Mort. seemed even to their authors to be defective. First: In that the number of the people was wanting. Secondly: That the ages of the people dying was not to be had. And lastly: That both Lond. and Dublin, by reason of the great and casual accession of strangers who die therein (as appeareth in both by the great excess of funerals above the births), rendered them incapable of being standards for this purpose; which requires, if it were possible, that the people we treat of should not at all be changed, but die where they were born, without any adventitious increase from abroad, or decay by migration elsewhere. This defect seems in a great measure to be satisfied by the late curious T. of the B. of Mort. of the City of Breslau, lately communicated to this honourable So. by Mr. Justell, wherein both the ages

and sexes of all that die are monthly delivered, and compared with the number of the births for five years last past, viz. 1687, 88, 89, 90, 91, seeming to be done with all the exactness and sincerity possible. The City of Breslau is the capital City of the Province of Silesia, . . . and very nigh the latitude of Lond. It is very far from the sea, and as much a Mediterranean place as can be desired, whence the confluence of strangers is but small, and the manufacture of Linnen employs chiefly the poor people of the place, as well as of the country round about. . . . For these reasons the people of this City seem most proper for a standard; and the rather for that the births do a small matter exceed the funerals. The only thing wanting is the number of the whole people, which in some measure I have endeavoured to supply by the comparison of the mort. of the people of all ages, which I shall from the said bills trace out with all the accuracy possible.

Then follows the T., the arrangement of which we have slightly modernized. Age Curt., we presume, stands for "Age Current."

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This table Dr. Halley wished in effect to be interpreted thus: that of 1000 children aged 1 year, as many would live to attain the older ages respectively as were denoted by the numbers set opposite to those ages. From this it was to be argued that a child of 1 year old had precisely as many chances out of a thousand of attaining any particular age as there were survivors represented by the Table to attain that age. Nor was this relation confined to children of one year old. For as it was strictly a table representing consecutive survivors, so the " prospection" of a person of any specified age attaining an older specified age was distinctly denoted by as many chances of the number, commencing from such first age, as there were survivors attaining the older age.

Two examples by reference to the Table will suffice: thus, the chances of a child aged 1 year attaining 30 years of age would be represented by 531 chances out of 1000: and the chances of a person aged 20 attaining 40 would be 445 chances out of 598. In the same manner, mutatis mulandis, the chances of living and dying for all ages were easily ascertainable, the number of expectant survivors representing the chances of living, and the remainder, or the number who were not expected to survive, the chances of death.

These principles, self-evident as they may appear, yet really only became so when the Table of Mort. was created and arranged: and thus Dr. Halley by his simple arrangement effected the resolution of many questions by comparative inspection, which previously were wholly incapable of even approximate answers.

The preceding Table seems not only interesting to the general reader as the first complete Table of Mort. upon record, but also as constituting the first real step in the art of life-measurement. It may further be added, as a fair tribute to Dr. Halley's skill, that 150 years of subsequent consideration by the most eminent mathematicians of Europe have only tended to confirm the eligibility of the form primarily chosen, even the most modern Tables of Mort. being still arranged on the same principle.-Farren, 1844.

The reader must not overlook the fact that Graunt had adopted a very similar arrangement in his Table published thirty years previously. [MORT. TABLES.]

The following is an enumeration of the uses to which Dr. Halley considered his Table might be applied:

The first use hereof is to show the proportion of men able to bear arms in any multitude, which are those between 18 and 56 years....

The second use of this T. is to show the differing degrees of mort., or rather vitality, in all ages.... Use III. If it be inquired of what number of years, it is an even lay that a person of any age shall die, this T. readily performs it; for if the number of persons living of the age proposed be halfed, it will be found by the T. at what year the said number is reduced to half by mort.; and that is the age to which it is an even wager that a person of the age proposed shall arrive before he die-as for instance: A person of 30 years of age is proposed, the number of that age is 531, the half thereof is 265, which number I find to be between 57 and 58 years, so that a man of 30 years may reasonably expect to live between 27 and 28 years.

Use IV. By what has been said, the price of ins. upon lives ought to be regulated; and the difference 24

VOL. I.

is discovered between the price of insuring the life of a man of 20 and 50. For example: It being 100 to I that a man of 20 dies not in a year, and but 38 to 1 for a man of 50 years of age.

Use V. On this depends the valuation of annu. upon lives...

Use VI. Two lives are likewise valuable by the same rule. . . .

Use VII. Three lives are proposed.

The subject of Ins. Wagers was strong in the learned Doctor's mind when he wrote this summary. And it must be noted also that he speaks of the "price of ins. upon lives," clearly showing what indeed we now know, that life ins. was a matter of common practice at that period: but the insurances were for specific periods, and were undertaken by individual underwriters, in the same manner as marine policies were then, and are now, written. Dr. Halley adds a supplemental use or reflection, in the following form:

Besides the uses mentioned, it may perhaps not be an unacceptable thing to infer from the same T. how unjustly we repine at the shortness of our lives, and think ourselves wronged if we attain not old age; whereas it appears hereby that one half of those that are born are dead in 17 years' time, 1238 being in that time reduced to 616; so that instead of murmuring at what we call an untimely death, we ought, with patience and unconcern, to submit to that dissolution which is the necessary condition of our perishable materials, and of our nice and frail structure and composition, and to account it as a blessing that we have survived perhaps by many years that period of life whereat the one half of the whole race of mankind does not arrive.-Phil. Trans., No. 198, vol. xvii.

In our art. ANNUITIES UPON LIVES, we have already shown the important bearing which the results of this T. ought to have had upon all financial dealings of that character. To say that the Gov. of the day was very slow to profit by its teachings, although so much of the national finance was accomplished by means of L. annu., or that private individuals profited by using the obvious lessons of the T. to their individual advantages as against the Gov., is only to state that which all who are conversant with our financial history are already aware of. It took some years to make the advantages of a scientific mode of life measurement at all appreciated by those most concerned.

In Edward Lawrence's Dissertation on Estates for Lives, etc. (1730), Halley's Table was inserted and recommended for adoption in preference to the imaginary estimates on lives then current; and in the same year, John Richards, of Exeter, pub. Tables for valuing estates, leasehold and for lives, founded on Halley's estimate, and De Moivre's hypothesis.

În 1752 W. Dodson, F. R.S., submitted to the Royal So. some remarks on the decrement of life exhibited in the Breslau Table; and the same were pub. in the Phil. Trans. of that year.

In 1753 Kerseboom pub.: A view of the relation between the celebrated Dr. Halley's Tables, and the notions of M. de Buffon for estab. a rule for the prob. duration of the life of man. In the same year James Hardy's Complete System of Int. and Annu. contained annu. values deduced from this table.

De Moivre, in the 3rd ed. of his Doctrine of Chances, 1756, said “The first T. is that of Dr. Halley, composed from the bills of mort. in the city of Breslau; the best perhaps as well as the first of its kind; and which will always do honour to the judgment and sagacity of its excellent author." And then, after naming various other T., he returns to the Breslau T., and adds:

We may therefore retain this last as no bad standard for mankind in general, till a better police, in this and other nations, shall furnish the proper data for correcting it; and for expressing the decrements of life more accurately and in larger numbers.

Again :

The celebrated M. de Buffon has lately given us a new T. from the actual obs. of Mons. du Pré de St. Maur, of the French Academy. This gentleman, in order to strike a just mean, takes 3 populous parishes in the city of Paris and so many country villages as furnish him nearly an equal number of lives; and his care and accuracy in that performance have been such as to merit the high approbation of the learned editor.

He then details the steps he had taken for comparing this T. with Halley's, and adds: "There resulted only a mutual confirmation of the two tables; Mr. Du Pré's T. making the lives somewhat better as far as 39 years, and thence a small matter worse than they are by Dr. Halley's.

Benjamin Martin's Decimal Arithmetic, pub. 1763, contained a reprint of Halley's T., and the same indeed may be said of nearly all the works pub. before the appearance of the Northampton T.

It was a very general complaint by the writers of this period that the Breslau T. was not adapted to the purposes of annu. and ins. asso. founded in Lond. ; but the writers did not at all harmonize in their views as to the grounds of its unsuitability. Indeed, on the one hand, it was contended that in the small city of Breslau the value of life must be much greater than its value in the overgrown and plague-smitten city of Lond.; while, on the other hand, it was contended that whatever the faults of Lond. might be, continental life could never be compared in point of healthfulness to that of English life, and it was very doubtful whether all continental cities had not a greater mort than Lond. We shall have occasion to notice some of these statements under LONDON, MORT. T. FOR. The Laudable So. of Annuitants was founded in 1766. In a few years it was found that its promised advantages to its members were much too large in relation to the payments made by them to the So. A controversy arose; it was asserted on behalf of the founders of the So. that they had promised no more than the BRESLAU TABLE would

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