being also applied to the actions of the body, is by physicians divided into vital, animal, and natural. The vital functions are those necessary to life, and without which the individual cannot subsist; as the motion of the heart, lungs, &c. The natural functions are such as it cannot subsist any considerable time without; as the digestion of the aliment, and its conversion into blood. Under animal functions are included the senses of touching, tasting, &c. memory, judgment, and voluntary motion; without any or all of which an animal may live, but not very comfortably.

The animal functions perform the motion of the body by the action of the muscles; and this action consists chiefly in the shortening the fleshy fibres, which is called contraction, the principal agents of which are the arteries and nerves distributed in the fleshy fibres.

All parts of the body have their own functions, or actions, peculiar to themselves. Life consists in the exercise of these functions, and health in the free and ready exercise of them.

**FUNCTION,** a term used in analytics for an algebraical expression any how compounded of a certain letter or quantity with other quantities or numbers; and the expression is said to be a function of that letter or quantity. Thus $a - 4x,$ or $ax + 3x^2,$ or $2x - a\sqrt{a^2 - x^2},$ or $xc,$ or $c^x,$ is each of them a function of the quantity $x.$

**FUND,** in general, signifies any sum of money appropriated for a particular purpose. Thus, that part of the national revenue which is set apart for the payment of the national debt, is called the sinking fund. But, when we speak of the funds, we generally mean the large sums which have been lent to government, and constitute the national debt; and for which the lenders, or their assignees, receive interest from revenues allotted for that purpose. The term stock is used in the same sense, and is also applied to the sums which form the capital of the bank of England, the East India and South Sea companies; the proprietors of which are entitled to a share of the profits of the respective companies. The practice of funding was introduced by the Venetians and Genoese in the 16th century, and has been adopted since by most of the nations in Europe. Princes had often borrowed money, in former times, to supply their exigencies, and sometimes mortgaged their territories in security; but these loans were generally extorted, and their payment was always precarious; for it depended on the good faith and success of the borrower, and never became a regular burden on posterity. The origin of funds is derived from the peculiar manners and circumstances of modern Europe. Since the invention of gunpowder, and the progress of commerce, the military occupation has become a distinct employment in the hands of mercenaries; the apparatus of war is attended with more expense; and the decision of national quarrels has often been determined by command of money rather than by national bravery. Ambitious princes have therefore borrowed money, in order to carry on their projects with more vigour. Weaker states have been compelled, in self-defence, to apply to the same resource; the wealth introduced by commerce has afforded the means; the regularity of administration, established in consequence of the progress of civility, has increased the confidence of individuals in the public security; the complicated system of modern policy has extended the scenes of war, and prolonged their duration; and the colonies established by mercantile nations have rendered them vulnerable in more points, and increased the expense of defending them.

When a greater sum has been required for the annual expense than could easily be supplied by annual taxes, the government have proposed terms to their own subjects, or foreigners, for obtaining an advance of money by mortgaging the revenue of future years for their indemnification. This mortgage may either be for a limited period, or perpetual. If the sum allotted annually for the benefit of those who advance the money, be considerably greater than the interests of the sums advanced, they may agree to accept of such allowance, for a limited time, as a full equivalent. Thus, they may either agree for the casual produce of the revenue assigned; or a fixed annuity for a greater or less number of years; or a life annuity to themselves or nominees; or an annuity for two or more lives; or an annuity, with the benefit of survivorship, called a tontine, in which scheme, the whole sum to which the original annuitants were entitled continues to be distributed among the survivors.

The establishment of the funds was introduced in Britain at the Revolution; and has since been gradually enlarged, and carried to an amazing extent. The various methods above-mentioned have been used in their turns, but perpetual annuities have been granted for the greatest part; and, even when the money was originally advanced on other conditions, the lenders have been sometimes induced, by subsequent offers, to accept of perpetual annuities, instead of the former terms. The debt for which perpetual annuities are granted, is called the redeemable debt, and the other is called the irredeemable debt. Although the debts thus contracted by government are seldom paid for a long term of years; yet any creditor of the public may obtain money for what is due him when he pleases, by transferring his property in the funds to another; and regular methods are appointed for transacting these transfers in an easy manner. By means of this, the stocks become a kind of circulating capital; and have the same effect, in some respects, as the circulating money in the nation. When a stockholder transfers his share, he may sometimes be able to obtain a greater price than the original value, and at other times be obliged to accept of a less one. The value of the funds depends on the proportion between the interest they bear, and the benefit which may be obtained by applying the money to other purposes. It is influenced by the plenty or scarcity of money, and by the quantity of the public debt; and it is impaired by any event which threatens the safety, or weakens the credit, of the government.

The business of stock-jobbing is founded on the variation of the prices of stock. Persons possessed of real property may buy or sell stock, according to their notion that the value is likely to rise or fall, in expectation of making profit by the difference of price. And a practice has taken place among persons who often possess no property in the funds, to contract for the sale of stock against a future day, at a price now agreed on. For instance: A agrees to sell B £1000 of bank stock, to be transferred, in 20 days, for £1000. A has, in fact, no such stock; but, if the price of bank stock, on the day appointed for the transfer, should be only 118 per cent. A may purchase as much as will enable him to fulfill his bargain for 118£0l. and thus gains 2£l. by the transaction; on the contrary, if the price of bank stock be 125 per cent. he will lose 5£l. The business is generally settled without any actual purchase or transfer of stock, by A paying to B, or receiving from him, the difference between the current price of the stock on the day appointed and the price bargained for.

This practice, which is really nothing else than a wager concerning the price of stock, is contrary to law; yet it is carried on to a great extent. In the language of Exchange Alley, where matters of this kind are transacted, the buyer is called a bull, and the seller a bear. As neither party can be compelled by law to implement these bargains, their sense of honour, and the disgrace and loss of future credit, which attend a breach of contract, are the principles by which the business is supported. When a person declines to pay his loss, he is called a lame duck, and dare never afterwards appear in the Alley. This opprobrious appellation, however, is not bestowed on those whose failure is owing to want of ability, providing they make the same surrender of their property voluntarily, which the law would have exacted if the debt had been entitled to its sanction.

The interest or dividend on the stock is paid half-yearly; and the purchaser has the benefit of the interest due on the stock he buys, from the last term to the time of purchase. Therefore the prices of the stocks rise gradually, ceteris paribus, from term to term, and fall at the term when the interest is paid. In comparing the prices of the different stocks, it is necessary to advert to the term when the last interest was paid; and, allowance being made for this circumstance, the prices of all the government stocks, which bear interest at the same rate, must be nearly the same, as they all depend on the same security. When a loan is proposed, such terms must be offered to the lenders, as may render the transaction beneficial; and this is now regulated by the prices of the old stocks. If the stocks, which bear interest at 4 per cent. fall at par, or rather above, the government may expect to borrow money at that rate; but, if these stocks are under par, the government must either grant a higher interest, or some other advantage to the lenders, in compensation for the difference. For this purpose, besides the perpetual annuity, another annuity has sometimes been granted for life, or for a term of years. Lotteries have frequently been employed to facilitate the loan, by entitling the subscribers to a certain number of tickets, for which no higher price is charged than the exact value distributed in prizes, though their market price is generally 2l. or 3l. higher. Sometimes an abatement of a certain proportion of the capital has been granted, and a lender entitled to hold 100l. stock, though in reality he advanced no more perhaps than 95l.

It belongs to the chancellor of the exchequer to propose the terms of the loan in parliament; and he generally makes a previous agreement with some wealthy merchants, who are willing to advance the money on the terms proposed. The subscribers to the loan deposit a certain part of the sum subscribed; and are bound to pay the rest by instalments, or stated proportions, on appointed days, under pain of forfeiting what they have deposited. For this they are entitled, perhaps, not only to hold their share in the capital, but to an annuity for 10 years, and to the right of receiving a certain number of lottery tickets on advantageous terms. They may sell their capital to one person, their annuity to a second, and their right to the tickets to a third. The value of all these interests together is called omnium; and, in order to obtain a ready subscription, it ought to amount to 102l. or upwards, on 100l. of capital. This difference is called the bonus to the subscribers.

The capital advanced to the public, in the form of transferable stocks, and bearing interest from taxes appropriated for that purpose, is called the funded debt. Besides, there is generally a considerable sum due by government, which is not disposed of in that manner, and therefore is distinguished by the appellation of the unfunded debt. This may rise from any sort of national expense, for which no provision has been made, or for which the provision has proved insufficient. The chief branches are,

1st, Exchequer Bills. These are issued from the exchequer, generally by appointment of parliament, and sometimes without such appointment, when exigencies require. They bear interest from the time when issued, and are taken in by the Bank of England, which promotes their circulation.

2d, Navy Bills. The sums annually granted for the navy have always fallen short of what that service required. To supply that deficiency, the admiralty issues bills in payment of victuals, stores, and the like, which bear interest 6 months after the time issued. The debt of the navy thus contracted is discharged, from time to time, by parliament.

In time of war, the public expenses, since the Revolution, have always been much greater than the annual revenue; and large sums have consequently been borrowed. In time of peace, the revenue exceeds the expence, and part of the public debt has frequently been paid off. But, though there have been more years of peace than of war since the funds were established, the debts contracted during each war have much exceeded the payments during the subsequent peace. This will appear by the following abstract of the progress of the national debt.

| Debt at peace of Ryfwick, 1697 | £21,515,472 | | Debt at the beginning of war 1701 | 16,394,701 | | Discharged during peace 1697 to 1701 | 5,121,071 | | Debt at peace of Utrecht 1714, including value of annuities afterwards subscribed to South Sea stock | 55,282,978 | | Contracted in war 1701 to 1714 | 38,888,277 | | Debt at beginning of war 1740, including 1,000,000l. charged on civil list | 47,954,623 | | Discharged during peace 1714 to 1739 | 7,328,355 | | Debt at peace of Aix-la-Chapelle, 1748 | 79,193,313 | | Contracted during war 1740 to 1748 | 31,238,690 | | Debt at beginning of war 1756 | 73,289,673 | | Paid off during peace 1748 to 1756 | 5,903,640 | | Debt funded at the peace 1763, including 9,839,597l. then owing, which was funded in the subsequent years | 133,957,270 | | Besides this, there was about 6,000,000l. of debt paid off, without ever being funded. | | | Funded debt, 1775 | 125,000,000 | | Paid off during peace 1763 to 1775, besides unfunded debt above mentioned | 8,959,270 | | Funded at the peace 1783 | 211,363,254 |

The following is a state of the national debt at a later period.

| Amount of funded debt on 5th January 1805 | £603,925,792 | | Stock created by loan of 1805 | 38,700,000 | | Transferred for the redemption of the land-tax | 642,625,792 | | Redeemed by the commissioners for managing the sinking fund | 113,500,000 | | Leaving as the amount of the national debt on the 31st January 1806 | £507,125,792 |

It is to be observed that nearly 100 millions of the above amount of 507 millions, consist of 4 and 5 per cent. stock; and if this be converted into 3 per cent. stock, it will make the total amount 557 millions; and taking the 3 per cent. stock at 60 per cent. the present average price, the total capital of the debt in money is 334 millions of pounds sterling.

The original provision of the sinking fund, of a million per annum, with the additions that have since been made to it; and the dividends on stock, bought up by the commissioners for managing that fund, amount at this time (1806) to about eight millions per annum. It has been calculated that the future rate of accumulation of the sinking fund, continuing the same as hitherto, namely, Fundament, namely, at 5 per cent. the whole amount of the national debt will be extinguished in 24 years; for the annual income of the commissioners for the management of the sinking fund being eight millions, this will produce by the year

| Year | Sum (L) | |------|---------| | 1810 | 34,480,000 | | 1820 | 156,700,000 | | 1830 | 356,000,000 |

which last sum exceeds the present national debt.