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s. 5. Keepers and their assistants may apprehend offenders they find in the act, and take them before a justice. Ibid c. 15. R. distress, and for want of distress, commitment for six months, or till paid, with costs, J 1. W. 1. A. half to the King, half to the informer. Ibid s. 11.

Borning furze, fern, &c. on any forest or chase without consent of the owner, keeper, &c. P. 40s. to 5l. R. distress, or in default, commitment from one to three months. J. 1. W. 1. A. half to the informer, half to the poor. 28 George II. c. 19.

Unlawfully entering into any ground, (enclosed or not,) and hunting or killing rabbits. P. treble damages to the party aggrieved and costs, or commitment for three months, and till he find sureties for his good behaviour. J. 1. W. 1. 22, 23, Charles II. c 25, s. 4

Killing or taking house-dove or pigeon, P. 208 or commitment from one to three calendar months, or till paid. R. J. 1. W. 1. A. to the prosecutor, 2 George

III. c. 29.

Driving, or taking by nets, tunnels, &c. any water-fowl in the moulting season, P. 58. for each fowl, and nets to be seized and destroyed. R. distress, and in default, commitment from fourteen days to one month. J. 1. W. 1. A. half to the informer, half to the poor. 9 Anne, c. 25. s. 4.

Game, are deer, hares, pheasants, partridges, moor game, and, by the act now passing, snipes and woodcocks are made game.

It is not to be inferred that these statutes actually impower qualified persons to hunt or shoot any where. They cannot enter another man's land in pursuit of game without his leave; but at the same time, if he has not warned the sportsman against coming upon his land, he will not recover more than 40s. costs in an action of trespass.

geons, wild ducks, wild geese, wild fowls, at any time but in June, July, August, and September.

GAMING, laws of These are founded on the doctrine of chances. See CHANCE.

M. de Moivre, in a treatise "De Mensura Sortis," has computed the variety of chances in several cases that occur in gaming, the laws of which may be understood by what follows:

Suppose the number of cases in which an event may happen, and the number of cases wherein it may not happen, both sides have the degree of probability, which is to each other asp

to q

If two gamesters, A and B, engage on this footing, that, if the cases p happen, A shall win; but if q happen, B shall win, and the stake be a; the chance of A

will be, and that of B

a

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p+q p+q sequently, if they sell the expectancies, they should have that for them respectively.

If A and B play with a single die, on this condition, that, if A throw two or more aces at eight throws, he shall win; otherwise B shall win; what is the ratio of their chances? Since there is but one case wherein an ace may turn up, and five wherein it may not, let a = 1, and b 5. And again, since there are eight throws of the die, let n = 8; and you will have a ・Tn — bn—n a b — 1, to bn + na bn-1: that is, the chance of A will be to that of B. as 663,991 to 10,156,525, or nearly as 2 to 3

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A and B are engaged at single quoits, and, after playing some time, A wants 4 of being up, and B 6; but B is so much the better gamester, that his chance against A upon a single throw would be as 3 to 2; what is the ratio of their chances? Since A wants 4, and B 6. the game will be ended at nine throws; there

Sporting seasons. The time for sporting, in the day, is from one hour before raise a+b to the ninth power, and it

fore sun rising, until one hour after sun setting. 10 George III. c. 19. For bustards, the sporting is from December 1, to March 1. For grouse, or red grouse, from August 11, to December 10. Hares may be killed all the year, under the restrictions in 10 George III. c 19. Heathfowl, or black-game, from August 20, to December 20 Partridges, from September 1, to February 12. Pheasants,

from October 1, to February 1. Wid

will be a99a8 b + 36 a7 b b+84 a6 b3+ 126 as b4+126 a4 b5, to 84 a3 b6+36 a a ò* +6 a b+b call a 3, and 6 2, and you will have the ratio of chances in numbers, viz. 1,759,077 to 194,048.

A and B play at single quoits, and A is the best gamester, so that he can give B 2 in 3; what is the ratio of their chances at a single throw? Suppose the chances as z to 1, and raise z + 1 to its cube, which will be 23 + 3 22 + 3 z

+1. Now since A could give B 2 out of 3, A might undertake to win three rows running; and, consequently, the chances in this case will be as z3 to 3 + 3 z+1. Hence, z3 = =32+ 3 z+1; or, 2 z3 = z3 + 3 z2 + 3 z +1. And, therefore, z 2 = z + 1;

and, consequently, z =

chances therefore, are

respectively.

1

32-1

1 2-1'

The

fore, the odds of losing both wagers is 47 to 8.

This way of reasoning is applicable to the happening or failing of any events that may fall under consideration. Thus, if I would know what the probability is of missing an ace four times together with a die, this I consider as the failing of four different events. Now the proba

bility of missing the first is, the seand 1, cond is also, the third, and the fourth; therefore the probability of missing it four times together is & XX which being subtract671 for

625 = 1296

Again, suppose I have two wagers depending, in the first of which I have 3 to 2 the best of the lay, and in the second, = 7 to 4, what is the probability I win both wagers?

1. The probability of winning the first is 3, that is, the number of chances I 35 have to win divided by the number of all the chances: the probability of winning the second is therefore, multiplying these two fractions together, the product will be, which is the probability of winning both wagers. Now, this fraction being subtracted from 1, the remainder is which is the probability I do not win both wagers: therefore the odds against

me are 34 to 21.

2. If I would know what the probability is of winning the first, and losing the second, I argue thus: the probability of winning the first is 3, the probability of losing the second is 4: therefore, multiplying by, the product will be the probability of my winning the first, and losing the second; which being subtracted from 1, there will remain which is the probability I do not win the first, and at the same time lose the second.

3. If I would know what the probability is of winning the second, and at the same time losing the first, I say thus: the probability of winning the second is 7; the probability of losing the first is ; therefore, multiplying these two fractions together, the product is the probability I win the second, and also lose the first.

4. If I would know what the probability is of losing both wagers, I say, the probability of losing the first is, and the probability of losing the second ; therefore, the probability of losing them both is; which being subtracted from 1, there remains ; there

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ed from 1, there will remain 1296

the probability of throwing it once or oftener in four times; therefore the odds of throwing an ace in four times, is 671 to 625.

But if the flinging of an ace was undertaken in three times, the probability of missing it three times would be &

125

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which being subtracted from 1, there will remain 91 for the probability of throwing it once or oftener in three times; therefore the odds against throwing it in three times are 125 to 91. Again, suppose we would

know the probability of throwing an ace

= 125

once in four times, and no more: since time is, and of missing it the other the probability of throwing it the first three times is it follows that the probability of throwing it the first time, and missing it the other three successive times, is × × × 1296 but because it is possible to hit it every throw as well as the first, it follows, that the probability of throwing it once in four throws, and missing the other three, 4 X 125 500 is ; which being sub1296 1296 tracted from 1, there will remain 796 for the probability of throwing it once, and no more, in four times: therefore, if one undertake to throw an ace once, and no more, in four times, he has 500 to 796 the worst of the lay, or 5 to 8 very

near.

=

7296

Suppose two events are such, that one of them has twice as many chances to come up as the other, what is the probability that the event, which has the greater number of chances to come up, does not happen twice before the other happens once, which is the case of flinging 7 with two dice before 4 once? Since the number of chances are as 2 to 1, the

probability of the first happening before the second is 2, but the probability of its happening twice before it, is but Xor; therefore it is 5 to 4 seven does not come up twice before four

once.

But if it were demanded what must be the proportion of the facilities of the coming up of two events, to make that which has the most chances come up twice, before the other comes up once: The answer is 12 to 5 very nearly; whence it follows, that the probability of throwing the first before the second is, and the probability of throwing it twice is 12, × 124, or therefore the probability of not doing it is 145: therefore the odds against it are, as 145 to 144, which comes very near an equality.

Suppose there is a heap of thirteen cards of one colour, and another heap of thirteen cards of another colour, what is the probability, that, taking one card at a venture out of each heap, I shall take out the two aces?

The probability of taking the ace out of the first heap is, the probability of taking the ace out of the second heap is therefore the probability of taking out both aces is × 13 – 183 which being subtracted from I, there will remain 168: therefore the odds against me 109 are 168 to 1.

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In cases where the events depend on one another, the manner of arguing is somewhat altered. Thus, suppose that out of one single heap of thirteen cards of one colour, I should undertake to take out first the ace; and, secondly, the two: though the probability of taking out the ace be, and the probability of taking out the two be likewise; yet the ace being supposed as taken out already, there will remain only twelve cards in the heap, which will make the probability of taking out the two to be ; therefore the probability of taking out the ace, and then the two, will be

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In this last question the two events

have a dependence on each other, which consists in this, that one of the events be ing supposed as having happened, the probability of the other's happening is thereby altered. But the case is not so in the two heaps of cards.

If the events in question be n in number, and be such as have the same number a of chances by which they may hap pen, and likewise the same number b of chances by which they may fail, raise a+b to the power n. And if A and B play together, on condition that if either one or more of the events in question happen, A shall win, and B lose, the probabili

ty of A's winning will be a+bbn

that of B's winning will be

a+b

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n

; and

for

bn a+b) when a + b is actually raised to the power n, the only term in which a does not occur is the last b n; therefore all the terms but the last are favourable to A.

Thus, if n = 3, raising a + b to the cube a3 + 3 a b + 3 a b2 + b3, all the terms but b3 will be favourable to A; and therefore the probability of A's a 3 + 3 a' b+3ab winning will be a+613

or

; and the probability of B's

a+b)3 — b3 a+b3 winning will be

But if A and B

63 a+b3 play on condition that, if either two or more of the events in question happen, A shall win; but in case one only happen, or none, B shall win; the probability of A's a+bnna fn−1 bni

winning will be

n+bn

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for the only two terms in which a a does not occur are the two last, viz. n a bn-l and bn. See Simpson's "Nature and Laws of Chance." We shall now add a table that may be useful to persons not skilled in mathematics, and which is applicable to many subjects:

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TABLE,

Showing the Odds of Winning in any Game, when the number of Games wanting does not exceed Six, and the Skill of the Contenders is equal.

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tracted from unity gives the chances of A: thus,

a9+9, a3 b+35, a7 b + 84, a b3 + 126, as b++ 126, a4 b5 + 84, a3 ̧b + 36, a2 br + 9, a b8 + 69.

519 +27 × 518 + 324 × 517,

The above proportions are found by the binomial theorem in a very easy way. Suppose the games wanting 1 and 5, raise a+b to the fifth power, being the number of games which must determine the bet. a=b in this case, as the skill is equal: as+5, a+ b + 19, a3 b2 + 10, a2 b3 +5, a b+ + 65, the first five coefficients are the chances of him who has 1 game 57 × 25+27.5+324 to get, viz. 15+ 10+ 10+ 5 = 31, and the other, viz. 1, the chance of him who has five to get.

Suppose the games wanting are 2 and 5, then a6+6, a§ b + 15, a+ b2 + 20, a3 b3 +15, a2 b+ + 6, a bs + bo, the chances for him wanting two are 1+ 6+15+ 20+15=57; but for him wanting 5, are 6+1=7 according to table 57:7.

Suppose the games wanting 4 and 6, then a9+9, as b+36, a7 b2 + 84, a b3 + 126, as b+ + 126, a4 b5 + 84, a3 b6 + 36, a4 b7 +9, a b+b9; therefore for him wanting 4 games, 1+9 +36 +84 + 126+126 382, and to him wanting 6 are 84 +36 + 9+ 1 = 130: the odds are 382: 130 according to table.

=

When the skill is not equal, or when the chances for winning are not equal: as, 1. If A and B play together, and A wants 1 game of being up, and B wants 2; but the chances whereby. B may win a game are double to the number of chances whereby A may win the same. Here the number of games are two. And

a = 1 and b 2..
··· a2 + 2 a b + b will
give the probability of each. A=1+
4 = 5 and B = 4 or the probabilities are
A: B:: 5 : 4.

2. A wants 3 games of being up, B 7; the proportion of chances 3 to 5, what is the proportion of chances to win the set? here the number of games will be 9, a = 36 = 5, therefore raise a + b)9 and the three last terms by a + b9 will express the chances of B, which subVOL. V.

B =

819

9 8

37812500
134217728

GAMMONING, among seamen, denotes several turns of rope taken round the bowsprit, and reeved through holes in knees of the head, for the greater security of the bowsprit.

GAMMUT, GAM, GAMMA, or GAMMAUT, in music, a scale, whereon we learn to sound the musical notes, ut, re, mi, fa, sol, la, in their several orders and dispositions.

GANG, in sea affairs, a select number of a ship's crew appointed on any particular service, and commanded by an officer suitable to the occasion.

GANG board, is a plank with several steps nailed to it, for the convenience of walking into or out of a boat upon the shore, where the water is not deep enough to float the boat close to the landing place.

GANG way, a narrow platform, or range of planks, laid horizontally along the upper part of a ship's side, from the quarter-deck to the forecastle, and is peculiar to ships that are deep waisted, for the convenience of walking more expeditiously fore and aft than by descending into the waist: it is fenced on the outside by iron stanchions, and ropes or rails, and in vessels of war with a netting, in which part of the hammocks are stowed. In merchantmen, it is frequently called the gang-board. The same term is applied to that of a ship's side,

M m

both within and without, by which persons enter and depart; it is provided with steps nailed upon the ship's-side, nearly as low as the surface of the water, and sometimes furnished with a railed accommodation ladder.

GANTLOPE, in sea affairs, commonly pronounced gantlet, is a race which a criminal is sentenced to run in a vessel of war for felony, or some other heinous offence. The whole ship's crew is disposed in two rows, standing face to face on both sides the deck, each person being furnished with a small twisted cord, having two or three knots in it; the delinquent is then stripped naked above the waist, and obliged to pass forward between the two rows a certain number of times, rarely exceeding three, during which every person is enjoined to give him stripes as he runs along: this is call. ed "running the gantlet," and is seldom inflicted but for crimes which excite general antipathy among the seamen.

GAOL, gaols cannot now be erected by any less authority than an act of parliament. All prisons and goals belong to the King, although a subject may have the custody, or keeping of them. The justices of the peace at their general quarter-sessions, or the major part of them, not less than seven, upon presentment made by the grand jury at the assizes, of the insufficiency, inconveniency, or want of repair of the gaol, may contract for the building, repairing, or enlarging it, &c. or for erecting any new gaol within any distance not exceeding two miles from the scite, and in that case for selling the old gaol and its scite, the contractors giving security to the clerk of the peace for the performance of the contract. 24 George III. c. 54. The expenses to be paid out of, and in certain cases money may be raised by mortgage upon, the county-rate.

As there are several persons confined in the county and city gaols, under sentence, and orders made by one or more justices at their sessions or otherwise, upon conviction in a summary way, without the intervention of a jury; it is by 24 George III. c. 56, enacted, that any judge of assize, or two justices, within whose jurisdiction such gaol is situate, may remove such persons to any house of correction within the same jurisdiction, there to be confined, and to remain in execution of such sentence or order.

For the relief of prisoners in gaols, justices of the peace, in sessions, have power to tax every parish in the county,

not exceeding 6s. and 8d. per week, le viable by constables, and distributed by collectors, &c. 12 Charles II. c. 29. But it is observed by Lord Coke, that the gaoler cannot refuse the prisoner victuals, for he ought not to suffer him to die for want of sustenance. If any subject of this realm shall be committed to any prison, for any criminal, or supposed criminal matter, he shall not be removed from thence, unless it be by habeas cor pus, or some other legal writ; or where he is removed from one prison or place to another, within the same county, in order to his trial or discharge; or in case of sudden fire, or infection, or other necessity: on pain that the person signing any warrant for such removal, and he who executes the same, shall forfeit to the party grieved, 100% for the first offence, and 2007. for the second. Justices at sessions make regulations for the gaols of the county, and there are statutes forbidding the selling of spirits, or secretly conveying them into gaols.

GAOL delivery, by the law of the land, that men might not be long detained in prison, but might receive full and speedy justice, commissions of gaol delivery are issued out, directed to two of the judges, and the clerk of assize, associated; by virtue of which commission, they have power to try every prisoner in the gaol, committed for any offence whatsoever. This is one of the commissions by which the judges sit at every assize.

It is a frequent question, what can be given in evidence by the defendant upon this plea, and the difficulty is to know, when the matter of defence may be urged upon the general issue, or must be specially pleaded upon the record. In many cases, for the protection of justices, constables, excise-officers, &c. they are, by act of parliament, enabled to plead the general issue, and give the special matter for their justification under the act in evidence.

GARBOARD strake, the plank next the keel of a ship, one edge of which is run into the rabbit made in the upper edge of the keel on each side.

GARCINA, in botany, so named in honour of Laurent Garcin, M. D. F. R. S. a genus of the Dodecandria Monogynia class and order. Natural order of Bicornes, Linnæus. Guttiferæ, Jussieu. Essential character: calyx four-leaved, inferior; petals four; berry eight-seeded, crowned with the peltate stigma. There are three species.

GARDANT, or GUARDANT, in heral

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