pamphlets which we have seen on the other side of the subject. The following passage appears to place the argument in the strongest point of view. « On the contrary, we shall find those countries the poorest, who are most dependent upon their agriculture, as in China, and other nations; the policy or prejudices of whose government, has imitated that of ancient Egypt, and many States of old time, and in a great measure secluded its subjects from a free intercourse with their neighbours ; from these principles, too, it is that a system which represents the produce of land as the sole source of the revenue and wealth of every country, has never been adopted by any nation, and has only existed, as before mentioned, in the speculations of the French economists. The true wealth of every nation consists in rendering its labour, and its capital as productive as possible; the profit which remains, after deducting the necessary subsistence of the labourers being the actual revenue of the country: this revenue, therefore, may be increased in various ways; as by machinery, which not requiring to be subsisted, can do the work of men at almost comparatively clear profit; by increasing the number of labourers, according to the increase of capital; or by rendering less expensive the price which is given for their means of subsistence. Subsistence being the deduction from profit, it is consequently of the first importance that it should be procured as cheap as possible. The first principles of political economy accordingly teach us to buy food where it is most readily, and at the lowest price to be had : “ If a foreign country” (says Dr. Smith *) “can supply us with a commodity cheaper than we ourselves can make it, better buy it of them with some part of the produce of our own industry, employed in a way in which we. have some advantage;" it is thus only that the general good of the State is consulted, and its labour and capital made most productive." P. 18. Having lately entered so fully into the question, we shall not at present oppose our sentiments to the author's assertions, but shall content ourselves with giving bim full credit for his ingenuity and research, though generally applied, in our opinion at least, to the weakest side of the question. .... .... Art. XXIII. Bosman's Balance for weighing a Corn Law.. .. Underwood. . 1815. It is sonte relief to our minds after having so long dwelt upon a serious and sober view of this inportant question, to enliven i « * See Smith's Wealth of Nations, Vol. IIp. 192.3%.*. them them with a lighter and more pleasing view of the subject. Not that we approve of trifling upon a question of such moment, but ridentem dicere verum quid vetat? Much sound sense may be conveyed under a light and elegant garb; nor is the dignity of discussion violated by its approximation in a less serious form to those, for whose stomachs sober argument, like Epsom salts, may prove too cold. Sound sense and ingenuity are the characteristics of this little pamphlet, which, while it ainuses the fancy, cannot fail of informing the mind. The following extract will give the reader an idea of its style and manner, and will prove no bad answer to the extract which we gave from the publication above : “ But the family of Bosman had, from its earliest rise, been distinguished for its high spirit and independence of character. How could it be consistent with these, to make themselves totally dependent for their daily bread upon foreigners, whose policy and interest it was to distress them; and who could at any time, if their own lands were suffered to run to ruin, starve them into compliance with their demands ? But there was another and a more important consideration, which influenced the councils of the wise men of Bosland. Where were the poor people to find money to buy even cheap bread from foreigners, when there was no farm at home to employ them, and pay them for their labour? Farmer John could no longer grow Corn, if the farmers of Monkey Island could sell it cheaper than he could sow it; his children, his clansmen, and his labourers, therefore, would be thrown out of employ, and must come upon the common stock for a bare subsistence; and if the land cannot support them, Master Mercat and his clansmen must: for starving outright is quite opposed to the prejudices of the Boslanders ! . “Now, let us suppose (placing ourselves, my worthy reader, in the situation of these good people of Bosland) the whole annual revenue of the island to be, according to their mode of calculation, three thousand marks--one thousand arising out of the land under. the care of Farmer John, two thousand out of the results of trade, manufacture, &c. under the supervision of Master Mercat. “ The thousand marks of Farmer John spring out of the land, renewing every year, as from a mine, as I have before said; and, if all the trade of the island were annihilated, still this would annually renew and accumulate. Policy (perhaps a better term might be provided) dictates the suppression of this branch of revenue. This mine is stopped, and the thousand marks are withdrawn from the common stock. Butthe policy, which bids this cause to operate, would by no means proscribe the use of food. This therefore is to be purchased abroad-let us suppose at half the price for which, under other circumstances, it would have been purchasable at home. · We will take the same average quantity, and calculate the price of this iin. portation portation at five hundred marks. As Farmer John is a bankronts and, together with his family, is probably in the poor-house, he cannot contribute towards this purchase, although out of the common stock he must be fed. Master Mercat, therefore, and his clansmen, 'must make the advance as well as they can; and as Corn is to be imported, free of duty, they must not look for large returns. “ He may indeed send a few cloths and candlestioks, or crockery in barter ; but this must depend upon the foreign folle, on the other side of the water, who may perhaps in time, be able to furnish their persons and their houses with their own hands, after a little intercourse with the island. At all events, with money or money's worth, Corn must be purchased, and we will suppose, for one year, at five hundred marks.” P. 15. MISCELLANIES. NT. XVIV: The Doctrine of Chances, or the Theory of Gaming By 7. Itvuse. Svo.' pp. 550. 155. Lackington. 1814. The title of this book alarmed us at first from the facility of core ription which it freld forth upon a subject, the practice of which is alremiy far too well understood. We were, however, constterably relieved from our apprehensions, by finding a collection of well written treatises, not so much upon the practice as upon the theory of goming, accompanied by calculations, which are 1ur leyond the powers of an uncultivated mind to comprehend: Hi there are no gamesters, except those who can read and un. derstand these treatises, the number of victims to this destructive passion will be diminished in no small degree; and we are of oumion that those who have mind sufficient-tv acquaint themselves with all the principles liere laid down, will be too deeply. convinced of the instability of chance, to trust their property to its disposal. To those who are fond of a calın investigation upon this intricate subject, we can strongly recommend this volume; the author appears to have studied his subject with labour, and to have explained it with perspicuity and success. The following observations upon the Lottery are new, and apo pear to be calculated upon just principles. . * It is the opinion of most persons unacquainted with mathe matical calculations, that as every scheme (however formed) must contain prizes equat in amount to 10l. per ticket, the variation of the scheme does not vary the disadvantage of the purchaser, if he pays the saine price for a ticket; but, such an opinion is very era roneous, for if the price of a ticket be 19 guineas, the scheme may be so varied as to cause the purcbaser to adventure from the ratio of lesø than 2 to 1, to 399 to 1 (and even greater than this) against himself, as will appear by the following schemes. ** Suppose a lottery of 10000 tickets, of Tol, each, the whole value of the prizes is 100,000l.; let there be only one prize of 100,0001., and 9999 blanks. A gives 191. 195. for a ticket; if he wins, he gains 999801. 1s, but the chances are 9999 to 1 against his winning, or 10000 expresses his probability. Now, according to the rule in the introduction, the value of every expectation is found, by multiplying the sum expected by the probability of obtaining it; and, this universally applies, for it is the same as dividing the sum expected into as many parts as there are chances, and giving to A as many of those parts as he possesses chances. Now, as A posesses but I chance in 10000, to gain 999801. 16., the ten-thou. sandth part of this sum (which being more than 91. 193. Il{d. 1 may be called 101.) is A's value, expressed in * 999801. ls. 9999 = 101.; and the value of his risk is expressed in x 191. 195., which sa nearly approaches to the whole sum (not being one halfpenny less), that in this case, of a lottery with only 1 prize. A plays in the ratio of nearly 19 guineas to 10l., against himself, as he exchanges a value 19 guineas for a value 101, Now, suppose as many prizes as blanks, or 5000 prices of 201, each, and 5000 blanks; here, it will be a toss up whether A gets a prize or a blank; if he gets a prize, he wins 1 shilling ! if a blank, he loses 399 shillings ! this must be self-evident; and however the scheme may be varied, so will the ratio of the purchaser's disadvantage of adventure between these two extremes ; indeed, it is possible to form a scheme, by making the prizes only a small fraction above the purchase-money, so that the ratio of disadvantage to the pura chaser of a ticket will be several thousands to l. . “ Many persons have deceived themselves in lottery calculations, by supposing a lottery of only 4 tickets with 1 prize, and that their reasoning on this would apply to a lottery of 20000 tickets witli 5000 prizes. As far as a single ticket, the conclusions are the same in both cases; but, it must be considered, that events in lotteries are dependent, that is, the chances for the happening or the failing of a second event depend on the happening or the failing of the first, the whole stock or chances becoming less each time, like drawing from a pack of cards. In 20000 tickets, 3 or 4 form too insignificant a part to require notice, but in only 4 tickets, one taken away reduces the stoek - leaving only 8 tickets ; therefore, although in cases where the odds to 1 are repeated two or three thousand times, they may be considered as independent events (like the throwing a die, in which all the chances are preserved for the hundredth throw the saine as for the first); yet, in a few VOL. 111. MARCH, 1815. few tickets, the events so much depend on each other, that they must be differently considered; as will evidently appear in the two following simple cases, of 4 tickets with 1 prize, and twice the number, or 8 tickets with 2 prizes; the ratio of 3 blanks to I prize being the same in each. Now, if the 4 tickets were put into a hat, 3 of them marked B, and 1 marked P, there would be 3 chances to • 1 in favour of drawing a B the first trial, the probability being ; this being done, for the second trial there are only 3 tickets remaining, 1 of which is the prize, and the probability of drawing & B is now only, which 2 probabilities multiplied together, are 2 equal to oro; showing a perfect equality of chances, whether the prize falls to the 2 tickets taken, or to an equal number not taken; and, let it also be considered, in this case, the prize must fall either to the 2 tickets taken, or to an equal number; and only 1 prize can be taken. Now, suppose a lottery of 8 tickets with 2 prizes; here, the probability of drawing a blank, is 30 , and the probability of drawing a second is, making or (instead of equality of chances) 30 to 26 against getting a prize with 2 tickets; and the law of combinations gives the same result; 8.7 56 00 for, î.2= Zor y or 28 combinations with 8 things, if taken 2 and 2 (see combinations under Cards); but, this is with and without 6.5 30 the prizes; the blanks being 6, make = 5, or 15 combinations, and which are without the prizes; therefore, there can be only the difference, or 13 combinations with the prizes, and 16 to 13 is in the same ratio as the above 30 to 26. In the first case. the prize must fall either to the 2 tickets taken, or to an equal nume ber; but, in this case, a prize may or may not fall either to the 2 : tickets taken or to an equal number; for the probability of missing .6.5.4.3 360 . a prize in 4 tickets 18 6 .5= 1680' w i in favour of getting a prize with 4 tickets, but not an absolute certainty; and also, it is possible in this case, to get 2 prizes with 2.1 2 2 tickets, the odds being = 5 or 27 to 1 against it; but, in the first case, this is impossible. Sufficient has been shown to prove that the cases are not strictly parallel, and that the reasoning . on one will not apply to the other, except in the instance of a single ticket." P. 218. AaT. |