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 , that is the number of chances I 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 subtract ed 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, the probability of losing the second is 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; 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 #; therefore, 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 probability of missing the first is, the second is also, the third , and the fourth; therefore the probability of missing it four times together is & ××=; which being subtracted from 1, there will remain 2 for the proba

bility 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 έ × ×=

which being subtracted from 1, there will remain 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 once in four times, and no more: since the probability of throwing it the first time is, and of missing it the other three times is XX, it follows that the probability of throwing it the first time, and missing it the other three successive times, is x X X =; 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 4 X 125 500 three, is = which being sub1296 1296 tracted from 1, there will remain 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.

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 }, but the probability of its happening twice before it, is but

or; 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 fol. lows, that the probability of throwing the first before the second is, and the proba bility of throwing it twice is x, or 1; therefore the probability of not doing it is

therefore the odds against it are, as 1-15 to 144, which comes very near an equality.

Suppose there is a heap of thirteen cards of one colour, and another heap of thir teen 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, which being subtracted from 1, there will remain : therefore the odds against me are 168 to 1.

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 ×

In this last question the two events have a dependence on each other, which consists in this, that one of the events being 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 happen, and likewise the same number b of chances by which they may fail, raise ub to the

3

ог

Thus, if n=3, raising a+b to the cube a3 + 3 a2 b + 3 a b2+ b3, all the terms but b3 will be favourable to A; and therefore the probability of A's winning will be a2+3a2b+3a h2 a+b2-bs ; and a+b a+u3 the probability of B's winning will be b3 But if A and B play on cona + a dition, 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 winning will be at "nab — 1 br

1

; for the only two

*`n + b) · terms in which a a does not occur, are the two last, viz. nab-1 and b ". 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:

then a +6, a' b+15, aa b2 + 20, a3 b3 + 15, a2 b2 +6, a bs+b, 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, a3 b + 36, a2 b2 + 84, að b3 +126, a3 ba+126, aa b3 +84, a3 b6 +36, a b'+9, a b+b; 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.

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 merchant-men it is frequently called the gang-board. The same term is applied to that part of a ship's

=

5 x 25 +27.5 + 324 37812500 ล 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.

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 accomodation ladder.

GANTLOPE, in sea affairs, commonly pronounced gantlet, is a race which a cri minal 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 called "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 gaols 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 expences 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, leviable 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 corpus, 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, 100l. for the first offence, and 2001. 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.

GARCINIA, 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 heraldry, denotes any beast full faced, and looking right forward.

GARDEN. We must divide this article under four heads; viz. the flower, or pleasure garden, the kitchen garden, the nursery, and the forcing department. Of these we shall treat distinctly under the head of GARDening.

In this place it is proper to state, that a garden should have a favourable aspect, gently declining towards the south-west, and should be enclosed by a substantial wall, high to the north and to the east, but rather low towards the south and west: the former will preserve the plants from the chilling winds proceeding from those quarters, the latter will allow the genial breezes from the favourable points to circulate freely throughout the enclosure, while the sun will not be debarred during the cooler months, especially from visiting the interior in general. In the height of summer, as the sun rises and sets to the northward, the southern borders of the garden will be screened during the heat of the day, but will during the early and late hours of its stay above the horizon, receive sufficient warmth without being scorched. Hence the south side, generally speaking, affords a shady border.

The soil of a garden should be deep, rich, and clean: without such qualities the produce will be inferior, while the labour and expense will be enhanced in exact ratio with the defect. Nor can a garden be too abundantly supplied with water; the absence of which, in adequate proportion, will render every effort towards perfection totally unavailing.

It is of the utmost importance that the whole garden should have a free access of air, and that the subsoil should be wholesome and sound. The great exhaustion occasioned by constant cropping, demands liberal supplies of rich manure, that the

soil should be kept in excellent heart. Nor should such parts as are intended for the production of vegetables be crowded with trees, or bushes. We should advise in the strongest manner, that such trees, &c. as spread their roots widely, be interdicted altogether, and that such as may be considered as really indispensable be set out at ample distances, and not allowed to overshadow the beds.

It is possible, however, to have the soil of a garden made too rich, that is, for the production of vegetables in general, many of which require an open free soil, not too highly dressed. Carrots, parsnips, and even turnips may be injured by over-richness; while onions, mushrooms, asparagus, &c. delight in such parts as are manured even to a degree of rottenness.

The directions given under the head Gardening will furnish ample instruction on this subject; and will give, in a concise form, the leading features of the art, in such manner as may prove useful to, and be easily retained in memory by, those who may not be provided with publications treating abstractedly on that subject.

GARDENIA, in botany, so named in honour of Alexander Garden, M. D. of Charlestown, in Carolina, a genus of the Pentandria Monogynia class and order. Natural order of Contorta. Rubiacea, Jussieu. Essential character: corolla onepetalled, contorted or twisted; stigma lobed berry inferior, two to four celled, many-seeded. There are fifteen species.

GARDENING being a science of the utmost importance to the community at large, is followed by many persons with considerable advantage to themselves. Indeed what is called market-gardening is a medium between private horticulture and that part of farming which relates to the production of green crops. We shall in this confine ourselves to horticulture as suited to ornament, and to the management of grounds cultivated with the view to family supply. The following list of fruits is usually resorted to, when forming a garden. Apples in all their varieties, pears ditto, plumbs ditto, peaches ditto, apricots ditto, nectarines ditto, cherries ditto, figs ditto, grapes ditto, mulberries ditto, medlars, quinces, walnuts, chesnuts, filberds, gooseberries, currants, raspberries, strawberries. The vegetable department usually consists of the following: asparagus, artichokes, ditto Jerusalem, beans, peas, kidney-beans, running ditto, turnips, cauli

flowers, cabbages, brocoli, coleworts, sea kale, cucumbers, onions, leeks, radishes, lettuces, celery, endive, spinach, beet, parsley, fennel, cardoons, cress, mustard, chevril, potatoes, carrots, parsnips, melons, mushrooms, and love-apples; with capsicums, hyssop, marjoram, sage, mint, thyme, balm, lavender, rosemary, basil, clary, borage, and penny-royal, for pot-herbs, &c.

The flower tribe are as follow: First class, or tender annuals: amaranthus of sorts, stiamonium, egg-plant, balsams, iceplant, sensitive plant, humble plant, scarlet convolvolus, snake-melon, and martynia.

Second class, or less tender annuals. African marigold, French ditto, aster of sorts, chrysanthemum, sweet sultan, Indian pink, palma-christi, tobacco, love-apple, gourds, persicaria, Indian corn, mignonette, convolvolus, capsicum, basil, lennia, stocks, tree-amaranthus, carmacorus, Chinese hollyhock.

The third class or hardy annuals. Adonis, larkspur, lupin, sun-flower, lavatera, convolvulus major, starry-scabius, hawkweed, carthamus, nasturtium, Tangier-pea, honey-wort, nigella, catch-fly,lychnis, navelwort, Virginia stock, pansies, snail-plant, cyanus, xeranthemum, garden marigold, purple ragwort, dracocephalum, bastard fumitory, amythysten.

The hardy biennial and perennial flowers are these: Aster, Tripolian, dog's bane, arum, asclepius, astragalus, alysson, bachelor's button, borage, ragged-robin, campanula, Canterbury-bells, caltha, cassia, carnations, pinks, sweet-william, wall flowers, stock July flowers, French honey-suckle, tree primrose, lichnidea, cyanus, lichnis, rose campion, hepatica, linaria, bee larkspur, fraxinella, gentiana, fox-glove, globularia, cyclamen, chelone, gold-locks, lily of the valley, Solomon's seal, filapendula, columbines, ibalictrum, pulsatilla orebus, vesovian, golden rod, valerian, rudbekia, pulmonaria, monarda, jacea, ephemeron, primrose, polyanthus, auricula, violet, London pride, day-lily, aconite, hellebore, geranium, daisies, ranunculus, peony, silphium, iris, cardinal, rocket, scabius, eringo, angelica, asphodel, ononis, lupins, eupetorium, balm of Gilead, moth mullien, snap-dragon, and Tradescantia.

The bulbous and tuberous kinds are, amaryllis, crocus-vernus, snow-drop, ornithogalum, erithronium, muscaria, fritillaria, crown imperials, tulip, gladiolus, anemone, ranunculus, pancratium moly, fumaria-bulbosa, Narcissus, jonquil, lily, squill, asphodel, tu