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vol. iv. of Assu. Mag., there is a division, "Aids to Calculation," in which are given some details concerning various arithmetical instruments, from which we have quoted in our art. on CALCULATING MACHINES.

CALCULUS [in Mathematics].—In modern language the term Calculus is employed to denote any branch or any operation of mathematics which requires or may involve numerical calculation, and therefore may be applied to the whole of the mathematical sciences excepting pure geometry. Thus that part of algebra which treats of exponents is called Exponential Calculus. In like manner the phrases Calculus of Definite Integrals; Calculus of Finite Differences; Calculus of Functions; Calculus of Probabilities; Calculus of Variations, etc., etc., are used to denote certain branches of the higher mathematics. -Brande. [DIFFERENTIAL CALCULUS.] [INTEGRAL CALCULUS.] [VARIATIONS.] CALCULUS [in Medicine] (from Calx, a lime or chalk stone).-A solid or unorganized concretion found in various parts of the human body, and commonly called stone or gravel. It is most frequently formed in the urinary organs.

CALCULUS OF FINITE DIFFERENCES.—This calculus was created by Dr. Brook Taylor, a learned English mathematician, in his work Methodus Incrementorum, pub. 1715. In vol. viii. of Assu. Mag. will be found a paper by Mr. W. Curtis Otter, On the Calculus of Finite Differences, and its Application to Problems in the Doctrine of Compound Int. and Certain Annu.

CALCULUS OF PROBABILITIES.-See PROBABILITIES, MATHEMATICAL THEORY OF. CALCUTTA. The capital of Bengal and Brit. India. The first settlement of the English here was made in 1689; became a separate Presidency in 1707. On 20th June, 1756, the fort taken from the English-146 British crammed into the "Black-Hole prison," a dungeon about 18 feet square, from whence only 23 came forth the next morning alive. Retaken by English 1757. The Hooghly river, which runs up to Calcutta, is particularly dangerous for navigation in consequence of the "Bore." On 5th Oct., 1864, a great cyclone, followed by a "bore," did enormous damage to shipping and houses. Nov., 1867, another cyclone; about 30,000 small houses unroofed, and much damage done to shipping.

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In 1850 the pop. of the city was estimated at 413,582. In 1866 a regular census was taken, but not without considerable difficulty, arising from the prejudice of the natives, etc. There were found to be 58,892 houses. The pop. was distributed as follows: Europeans, 11,224; Mussulmans, 113,059; Hindus, 239, 190; the remaining pop. being made up of Eurasian Greeks, Armenians, Asiatics, Jews, Parsees, Africans, and Chinese. The suburbs of the city were estimated at 250,000, making the entire pop. 629,924.

From a report by the Health Officer of the Census Committee it appears that in 1865 there were 304 deaths amongst an aggregate European pop. of 11,224, thus giving the mort. rate as 2'71 p.c. But it has been pointed out that these figures should be taken with reserve, as few Europeans remain to die in Calcutta. That which most materially swells the death-rate of Calcutta is the mort. prevailing amongst common soldiers and sailors, who go ashore into the Lall Bazar and other places of resort, and drinking arrack and other vile compounds, stagger out and remain in the open air all night, thus causing almost certain death. The mort. of Calcutta, reckoned according to Creeds, is: Christians, 519; Hindus, 6:41; Mussulmans, 5.83. The highest ages surviving in reference to nationality were: Europeans, 87; Eurasians, 104; Armenians, 84; Jews, 88; Mussulmans, 100; Hindus, 116.-Tait.

In 1848 Lieut.-Col. Sykes read a paper before the Brit. Asso. at York, On the Pop. and Mort. of Calcutta [reprinted vol. viii., Statistical Journal]. In 1848 Dr. Cuthbert Finch read before Brit. Asso., at Swansea, a paper, Vital Statistics of Calcutta [reprinted vol. xiii., Statistical Journal]. In 1867 Mr. P. M. Tait read before the Brit. Asso., at Dundee, a paper, On the Pop. and Mort. of Calcutta. An abstract of the paper appears in the report of the Asso. for that year, from which we have drawn some of the above facts. Between 1797 and 1810 the following marine offices were founded in Calcutta: Asiatic Ins. Co.; Calcutta Ins. Co.; Calcutta Ins. Office; Ganges Ins. So.; Hindostan Ins. So.; India Ins. Co.; Phenix Ins. So. Many of these were started at that period in consequence of the high rate of duty charged in England, and the monopoly then existing with the two Marine Ins. Corps.

There are various local marine, and F. and L. ins. asso. in the city; and several of the Brit. offices have agencies and transact considerable bus. There is a fire brigade with fire escapes.

Much more information regarding the mort. of Calcutta will be given under INDIA. CALDER, ALEXANDER, was Man. of Ins. Co. of Scotland from 1862 to 1868. CALEDONIAN INSURANCE CO., founded in Edinburgh in 1805, with an authorized cap. of £100,000, in 1000 shares of 100. The cap. was afterwards increased to £150,000; and more recently to £300,000, in shares of the same denomination. The paid-up cap. of the Co. now stands at £29,907 10s.

The first D. of asso. of the Co. was executed in June, 1805, and was regis. in the books of the Council of Session in Scotland on the 9th Aug., 1805. A charter was granted to the Co. under the seal appointed by the Treaty of Union, "to be kept and used in Scotland in place of the great seal formerly used there;" sealed 9th May, 1810.

The first Man. of the Co. was Mr. Wm. Braidwood; the first Sec., Mr. Wm. Dickie. The bus. of the Co. was limited in the first instance to F. ins. only. The first quarter's return of duty amounted to £661 12s. 7d. In 1836 its return for the year had reached £5182. In 1850 it had reached £8106. Further details will be found under FIRE INS. DUTY. Its F. bus. has always been made the subject of careful selection.

By art. of agreement, executed in 1833, and regis. in the books of the Council of Session in Scotland, under date 30th Dec. in that year, it was agreed that L. ins. should be added, "and that from thenceforward the bus. of F. ins. and the bus. of L. ins. should form the bus. of the Co. In 1840 the Co. commenced bus. in Lond.

In 1846 the Co. obtained a special Act of Incorp.-9 & 10 Vict. c. xlv.-An Act for Incorp. the" Caledonian Ins. Co."; for enabling the said Co. to Sue and be Sued, to take and to hold Property; for confirming the Rules and Regulations of the said Co.; and for other purposes relating thereto. This Act received the Royal Assent 18th June, 1846. The Act limits the bus. of the Co. to Gt. Brit. There is a provision regarding the shares of the Co. which we shall speak of under LEGISLATION FOR INS. Asso. Then follow the usual provisions of a D. of Sett. The directors may purchase and sell shares. Clause 62 gives the directors power to make regulations as to participation in profits by pol.holders. Clause 63 relates to settlement of disputes by arbitration. Clause 70 renders the Co. subject to provisions of any General Ins. Act.

Five-sixths of the profits of L. bus. are divided every 7th year among L. pol. of 5 years' duration and upwards. The first division took place in 1843; the last in 1871. The bonuses have been progressive-the last being at the rate of £1 75. p. c. p.a. on sums ins.,

under rev. scale.

The following particulars are given in the 5th schedule concerning the valuation made as at 13th May, 1871:

Each pol. was valued separately by finding the value of the sum assu., and deducting therefrom the value of the future net prems., an add. of one quarter year's int. at 3 p.c. being made to the values on account of the claims of the Co. being payable 3 months after proof of death. For short-period assu. a proportion of the prem. payable was stated as the liability. The annu. were also valued separately. The profits are ascertained every 7 years. Five-sixths thereof belong to the assured, and are divided amongst them by giving to pol. entitled to parti. a bonus at a certain rate p.c. on the sum assu. irrespective of age, for each year's prem. paid since the previous division, if a bonus has already been declared on them; and if no bonus has been added, then for each year's prem. paid since the commencement of the risk; a provision being made for the prospective bonus which is payable when death occurs between the periods of dividing profits. The remaining 6th of the profits falls to the proprietors.


The principles of valuation and distribution of profits are determined by the regulations and bye-laws of the directors. The T. of mort. used in the valuation were: (1). Carlisle T. for assu. (2). Gov. T. (Finlaison) for annu. on single lives. (3). Carlisle T. for special annu. The rates of int. assumed were 3 p.c. on L. pol; 4 p.c. on annu. whole of the loading was reserved for future expenses and profits. The amount of profit ascertained was £73,239. The number of pol. participating was 1747, ins. £721,578. The total number of L. pol. in force was 3818, ins. £1,509, 240. Annu. contracts, 62, involving ann. payments amounting to 1733. The amount of L. funds in hand, £398,011. The aunu. fund, £20,766; together, £418,777. F. fund in hand, including cap. and subject to div., £146,962.

The Co. is under sound and economic management. Its Man. and Act. is Mr. John Moinet; its Sec., Mr. G. H. Fairburn; its Assistant Act., Mr. D. J. Surenne. It has branches in Lond., Dublin, and Glasgow.

CALEDONIAN PLATE-GLASS INS. Co., founded in Glasgow, in 1871, under the Cos. Acts 1862 and 1867, without lim. liability. The authorized cap. of the Co. is £20,000, in shares of £ Mr. W. M'Gavin M'Culloch was the founder, and is the Manager. The prospectus says:

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The object of this Co. is to develope in Scotland the system of plate-glass ins. In the principal cities in England this branch of ins. bus. is daily increasing in importance; and during the last few years the use of plate-glass for the windows both of shops and dwelling-houses has been exceedingly rapid in Scotland; and the necessity for security against the risk of serious loss to which proprietors and tenants are thus exposed has been often felt and expressed. CALENBERG WIDOWS FUND, estab. in 1767 by the States of the Duchy of Calenberg, of which Hanover is the cap. It avoided some of the errors of other inst. of the same period, and charged contributions in regard to the age of its members on admission. terms, however, were only about one-half the sum actually required to make certain the payment of the allowances promised. In 1779 it had no less than 3800 members or subs., whose widows would become entitled to annu. It had also at that date 600 widows to whom annu. were payable. The large number of members were mainly owing to the lowness of the subs., and the authority of the States. Dr. Price drew attention to the prob. distress and disappointment its failure would occasion. We believe his words of warning led to an investigation of the affairs of the asso. by Prof. Nicholas Tetens, of Kiel, of whom we shall have to speak hereafter.

CALENDAR MONTH.-A period of time consisting of the days assigned to each month in the calendar, and therefore variable; and also running from a given date in any one month to a corresponding date in the succeeding month- -as distinguished from the month of 4 weeks, or 28 days.

CALENTURE (from caleo, to be hot).—A violent fever, attended with delirium, incident to persons in hot countries. Under its influence, it is said, sailors imagine the sea to be green fields, and will throw themselves into it, if not restrained.

In the earlier English Bills of Mort. this appeared as one of the causes of death. Thus there are 3 such cases in 1657; and 3 in 1673; 1 in 1681; and 1 in 1708. This is a disease, say the books, in the form of nostalgia, the maladie du pays, or longing for home: a malady capable of producing death among the enthusiastic inhabitants of mountainous countries. Calenture does not appear in the modern bills. CALIFORNIA, INS. LAWS OF STATE OF.-There are several laws in force for regulating the formation of Home Ins. Asso. in this State; and also other Acts for regulating the admission of Foreign Ins. Asso. to transact bus. It will be sufficient that we give a short epitome of the general requirements. No asso. can be formed or admitted with a less cap. than $100,000 held or deposited within the State. Before commencing bus. a certificate from the Ins. Commissioner must be obtained-fee $30. Agent must give bonds for $2000; and be authorized to accept service. The cost of the licence is $400 p.a., payable quarterly. A tax of 2 p.c. is ann. payable on prems. and stamp tax on pol. A statement [on gold basis] is to be made to 31st Dec. each year; and certain fees are to be payable with same. Expenses of ins. department beyond fees to be paid by offices pro rata. Penalty of $3000 in default. Some of the cos. of the Eastern States have transacted a very large bus. in California. We shall speak of the mort. of California under UNITED STATES. The standard for valuation of L. contracts in the ins. department is American Experience T. 4 p.c. int. The legal rates of int. in the State are 7 and 10 p.c. according to the nature of the security. CALISTHENIC (properly kalisthenic, from the Greek, signifying beautiful and strength).— Another term for "gymnastic," as applied to bodily exercise practised for the improvement of health and strength; but preferable as suggestive of beauty and strength. CALLET, MONS. F., pub. in Paris, in 1794, Tables portatives de Logarithms de nombres 1 à 108,000; revues par M. Saigey. A new ed. pub. 1864.

CALLINGHAM, JAMES, one of the Editors and Proprietors of the Ins. Record-Mr. Callingham renders essential service to the ins. profession by means of his rapid and accurate rendering of reports of discussions on the various papers read before the Inst. of Act.

CALLOW, JOHN, was for some years Chief Clerk in the European (No. 2). He pub., in 1865, A Letter to the Shareholders and Policy-Holders of the European Assu. So. on the Subject of its Recent Amalg. with the Brit. Nation Life Assu. Asso. ; wherein he indicated with great sagacity the probable effect of that proceeding upon the European So. CAMBIO MARINO.-A name used in Sweden, and prob. other parts of the North of Europe, for loans on Respondentia, or lending money at maritime int.

CAMBRIAN ASSURANCE Co.-This Co. was projected in 1844; but never got beyond prov. regis.

CAMBRIAN AND GENERAL LIFE INS. Co.-A co. under this title was projected in 1845; but did not proceed beyond prov. regis. It proposed to transact the following branches of bus., viz. fire, hail-storm, life, and cattle.

CAMBRIAN MUT. LIFE ASSU. AND PROV. INSTITUTION.-A co. under this title was projected in 1846, the promoter being Mr. Osmond Lewis. It was never completely regis. CAMBRIAN AND UNIVERSAL INS. CO., founded in 1849, with an authorized cap. of £100,000, in 4000 shares of £25. For "L and F. ins., healthy, invalid, and declined lives assured; marriage dowries and annu. granted," etc., etc. The prosp. said:

Of all asso. calculated to promote the welfare of society none advance higher claims to public support, or stand in a more conspicuous and honourable position than life assu. inst., the benefits of which, though applicable to all classes, are nevertheless not universally diffused among any. However, it is trusted that the period is rapidly approaching when not to ins. will be the exception instead of the rule; and when life ins. will be generally resorted to as affording the wisest, easiest, and best means of shielding families and dependents from the poverty, sorrow, and temptation, which a premature death entails so frequently.

Nothing can be more simple or easy than to effect such an ins.; but nevertheless, as scarcely 200,000 persons are ins. out of 30,000,000, it is highly prob, that these remarks will fall into the hands of many persons altogether ignorant of the course to be adopted, and who may imagine the process intricate

and difficult.

The Co. issued endowment pol. ; half credit; increasing and decreasing rates; limited number of payments; joint lives; declined or invalid lives; and whole-world pol. But its new and important feature, "entirely originating with this Co.," was a scheme of "marriage dowries, life assu. and deferred annu. embraced by one pol." :

It is applicable to both sexes; but by its adoption the two most eventful periods of female life especially are provided for. At a very moderate sacrifice every person having children or dependents is, according to station in life, enabled to secure to them their position in society. Example: A person having a daughter (or son) aged 4 years next birthday, may by one payment of £218 25. 11d., or by an ann. payment of £17 10s., continued only till 21, in case the child should live so long, secure to that daughter £500, payable within 1 month after arrival at 21, should she be previously married; or if marrying after 21, then within 1 month of proof of that event. In case of her non-marriage at 41, she will then be entitled to an annu. of £75, payable half yearly, for the remainder of her life. In the event of her dying unmarried before 21, three-fourths of the prems. paid will be returned to the father or his personal representatives; while in case of the death of the child unmarried between 21

and 41, the above-mentioned sum of £500 will become payable to her representatives. In add, she may at any period after 21, if unmarried, sell to, or raise money from this Co. upon the pol. proportionate to its actual value. By this mode assu. can be virtually effected on the lives of many young persons, who, from a tendency to consumption, delicate constitution, or other serious cause, would be otherwise uninsurable.


The F. bus. was very small, as will be seen by reference to the FIRE DUTY returns hereafter given. The Man. and Sec. of the Co. was Henry Felton; the Assistant Fire Man., John Henry Kock; the Consulting Act., W. E. Hillman. In 1857 the L. bus., which had never been large, was trans. to the Mitre. CAMPBELL, ROBERT, M.A., Advocate, Edinburgh. He pub. in the Philosophical Mag., for Nov., 1859, a paper, On a Test for ascertaining whether an Observed Degree of Uniformity or the Reverse in Tables of Statistics is to be looked upon as remarkable. 1860 he contributed to the Assu. Mag. a paper, On the Composition for Leave to an Assured to Reside Abroad. In the same year he submitted to the Inst. of Act. a paper, On the Stability of the Results based upon Average Calculations considered with Reference to the Number of Transactions embraced. These papers will be found in vols. viii. and ix. of Assu. Mag. They are ably written. We notice them under the respective subjects which they treat. [AVERAGES.] [FOREIGN RESIDENCE.] [STATISTICAL RESULTS.] CAMPBELL, T. COLIN, was Sec. pro tem. of Colonial Foreign and General, 1845. CAMPBELL, WILLIAM, Comptroller of the Legacy Duty, pub., in 1810, The Value of Annu. from £1 to £1000 p.a. on Single Lives from the Age of 1 to 90 Years; with the Number of Years' Purchase each Annu. is worth, and the Rate of Int. the Purchaser receives. With the Amount of the several Rates of the Legacy Duty, Payable according to the Statute on the Value of Annu. [ANNU. ON LIVES.] CAMPBELL'S ACT.-An Act of Parl. passed in 1846, at the instance of the late Lord Campbell, 9 & 10 Vict. c. 93, An Act for Compensating the Families of Persons Killed by Accidents. The Act was amended in 1864. [INJURY.] [NEGLIGENCE.] CAMPHENE.-Rectified oil of turpentine is sold in the shops under this name for burning in lamps. It is very inflammable, burning with a bright white flame, and without a proper supply of air it evolves a dense smoke; hence peculiar lamps (camphene lamps) are required.-Dr. Ure.

In certain classes of fire risks the use of camphene is considered highly dangerous. In the case of Westfal v. Hudson River Fire Ins. Co., tried in N.Y. in 1855, the policy under "Specially Hazardous" contained this clause: "Camphene, spirit gas, or burning fluid, when used in stores or warehouses as a light, subjects the goods therein to an extra charge of 10 cents. per $100, and prem. for such use must be indorsed on pol. ;" and it appearing that camphene had been used in the store ins. up to the time of the fire, without permission or payment of extra charge, it was Held, that the use of it was prohibited, and that the pol. was void. In the case of Harper v. City Ins. Co., tried in N. Y. in 1857, where a condition in the pol. provided that "this Co. will not be liable for any loss occasioned by camphene or other inflammable liquid," it was Held to mean, not that the fire must originate with the camphene, by its own ignition, but as a medium of communication from outside or other cause, thus occasioning a fire which would not have happened but for the presence of that article on the premises. And in the case of Stettiner v. Granite Ins. Co., tried in N. V. in 1858, where a clause in pol. of ins. on "stock of cap fronts and other goods," provided that "lighting the premises ins. by camphene or spirit gas, without written permission in the pol., shall render it void," it was Held to apply to ins. on merchandize as well as on buildings, and to be binding on insured.-Digest of Fire Ins. Decisions.

CAMROUX, F. FERGUSON, was first Sec. of National Loan Fund, 1837. In 1848 he became Sec. of Metropolitan Counties, and remained in that position until the amalg. of the Co. in 1862. He has not since returned to ins. pursuits.

CANADA.-The Province of Canada constitutes an important part of Brit. North America. It formerly consisted of two provinces, viz. Upper and Lower Canada. These and the adjacent provinces of New Brunswick and Nova Scotia are since 1867 united. Returns before this date will not apply to the United Provinces. Canada was first taken by the English in 1628; but it has several times had to be retaken. The French element is still strongly marked in the pop. of Lower Canada—that is, below Montreal on the St. Lawrence river.

If latitude alone determined the temperature of the atmosphere, the climate of Canada would resemble that of central and S. Europe; but through the operation of numerous disturbing influences by which temperature is affected, it more nearly resembles the climates of Norway, Sweden, St. Petersburg, and the S. portions of Iceland-the isothermal line diverging far to the north of the parallels of latitude that connect it with the old continent. Both the heat of summer and the cold of winter are much greater than in the corresponding latitudes of Europe-the thermometer ranging between 102° above, and 36° below the zero of Fah. ; but in the districts adjoining the great lakes on its S. border, the climate is much milder than that of places more remote-a natural consequence of the presence of great expanses of water. The prevailing winds in Canada are the N.E., N. W., and S. W., the last being the most frequent.—Imperial Gazetteer.

The towns and villages were originally constructed nearly entirely of wood, as were the paths in the streets, and not unfrequently the roads. In the towns this state of things is now rapidly changing; and the buildings and warehouses used for the purposes of commerce are equal in solidity and safety of construction with those of any part of Europe. The pop. of Canada has increased very rapidly; the immigration being large and incessant. A great many of the immigrants pass at once into the back country for the purposes of agricultural settlement. In 1857 the pop. of Lower Canada was 1,220,514; and of Upper Canada 1,350,923: together 2,571,437. In 1861 it was estimated at 3,000,000, and Dr. Farr estimated the excess of males over females at about 70,000. The census of 1871 shows that there had been an increase on the pop. of 1861 of 395,265. or 12 79 p.c. The total pop. of the four provinces is placed at 3,484,924; but it seems to be admitted that the figures are much below the mark. However that may be, the

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The pop, of Prince Edward Island was 93,521, against 80,357 in 1861, an increase of 13, 164, or 16:28 p.c. There had been no returns from British Columbia, but the last estimate of its pop. was 10,496, exclusive of natives. The Indian pop. is variously estimated at from 30,000 to 50,000, and the Chinese number 1947.

In a paper in the Journ. of Statistical So., 1849, by Mr. J. T. Dawson, Some Particulars of the Commercial Progress of the Colonial Dependencies of the U. K. during the 20 Years 1827 46, will be found some other details as to the pop. of the provinces.

Fire Ins. For many years several of the Brit. F. ins. offices have had agencies in Canada. Since 1860 the number has very considerably increased. Many of the young English offices have tried their hands here with very poor success. About 1855 or 1856 the Brit. offices then having agencies in Canada, on comparing notes, found almost without exception that their bus. had involved a loss. A gentleman was sent out to investigate the cause and suggest a remedy. Combined action and increased rates followed for a time; but after a few years competition became as rife as ever. Combined action is impossible among agents located so far distant from the seat of management of their cos. Then the inducement of a commission will always lead to the acceptance of some unprofitable risks-unprofitable for the office. The difficulty of efficient supervision of the risks accepted is very great; but it has to be solved before F. ins. in Canada can become profitable.

The competition of the American offices has from time to time presented further difficulties. That is now in a great measure removed. We are glad to see that the subject of rates is again [August, 1872] receiving some attention.

The local Canadian offices have never been very powerful; they are of two classesjoint-stock and mutual- the latter mostly very small. It is only as recently as 1868 that any accurate compilation of the aggregate statistics of F. ins. in Canada has been made. Here are the figures:

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Of this the local mut. offices are believed to have taken in prems. about $170,000; to have issued 20,000 pol. ins. $14,500,000 [pol. generally running 3 years]; to have $36,000,000 at risk; to have sustained 150 losses, and to have paid thereon $110,000, in add. to $5000 in suspense, and $14,000 resisted.

Regarding the prems. received in Canada by each of the Brit. offices, we have no later return than 1869. We give also, for purposes of comparison, the figures of 1868:


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