LOT 



LOT 



«f cliances above written one ftep farther, we fhall find that 

 the probability of taking no prize in feven tickets is 0.47S28, 

 which fubtraifled from unit leaves a remainder 0.52172, 

 which (hews the odds of taking one prize or more in fcven 

 tickets to be 52172 1047828. 



Prob. VII. 



With the fame data, to find the value of the chance of a 

 prize, liippollng each ticket to be 10/., and that after the 

 lottery is drawn, 7/. ics. be returned to the blanks. There 

 being 90000 blanks, to each of which is returned 7/, 10s. 

 the total value of the blanks is 675,000/. and confequently 

 the total value of the benefits is 325,000/. which being di- 

 vided by loooo, the number of benefits, gives a quotient 

 32.'. lor. and, therefore, one might for the.fum of 32/. ics. 

 be en'itled to have a benefit certain, taken at random out of 

 the whole number of benefits: the purchafer of a chance 

 has, therefore, one chance in ten for the fum of 32/. lox. 

 and nine chances in ten for lofing his money ; from whence 

 it follows, that the value of his chance is the tenth part of 

 32/. lor. viz. 3/. 5j. And confequently the purchafer of a 

 chance, by giving the feller 3/. 5^., is intitled to the chance 

 of a benefit, and ought not to return any thing to the 

 feller, although he fliould ha"e a prize f for the feller hav- 

 ing 3/, 5j. iure, and nine chances in ten for 7/. loj. the 

 value of whidi chance is 61. 15J. it follows that he has his 

 10/. p. 



Pkob. VIII. 



In the fame kind of lottery, let A engage to furnifh B 

 ■with a chance, on condition that whenever the ticket on 

 which the chance depends (hsil happen to be drawn, whe- 

 ther it proves a blank or prize, A fhall furnifli B with 

 a new chance, and fo on, as often as there is occafion, 

 till the whole is drawn ; it is propofcd to find what con- 

 fideration B ought to give A before the lottery begins 

 to be drawn, for the chance or chances of one or more 

 prizes, admitting that the lottery will be forty days in 

 drawing. 



Let the abfolute value of a chance, or 3/. 5^-., be called 

 s. Firft A, who is the feller, ought to confidtr, that on 

 the firll day he furnifhes necclfdrily a chance whofe value 

 is s. 



2dly. That on the fecond day, he does rot neceffarily 

 furnidi a chance, but conditionally, viz. if it fo happen that 

 the ticket on which the chance depends fhonld be drawn on 

 the firll day ; but the probability of its being drawn on the 

 firft day is jU ; and therefore he ought to take ^'„ s for the 

 confideration of ihe fecond day. 



.3dly. That in the fame manner he does not necefTarilv 

 furnilTi a chance on the third day, but conditionally, in cafe 

 the only ticket depending (for there, can be but one) fhould 

 happen to be drawn on the fecond ; of which the probabi- 

 lity being -rV,- by reafon of the remaining 39 days from the 

 lecond indufive to the laft, it follows, that the value of that 

 chance is ,-j-. 



4thly. And for the fame reafon the value of the next 

 is ■j'j.f, &c. the purchafer ought, therefore, to give the 



feller 1 + ^'^ + ^'^ + ^'^ + J^ + i x s, 



or I + 4: -1- i -i- i + ,i -I- I + s's X J. 



The fum of ihefe forty terms, being 4.2785 nearly, multi- 

 phed by s or 3-25, will give a produft 13-9. Hiewing that 

 the purchafer ought to give the feller about 13/ iSs. 



From what has been faid it appears, that the value of the 

 chance s for one llngle day that fhall be fixed upon is the 



value of that chance divided by the number of days inter- 

 cepted between that day inclufivc and the number of days 

 remaining to the end of the lottery ; which, however, mufl 

 be underllood with this rcflriSion, that the day fixed upon 

 muft be chofen before the lottery begins j cr if it be done oi» 

 any other day, the ftate of the lottery muft be known, and 

 a new calculation made accordingly for the value of /. De 

 Moivre's Doctrine of Chances, 1 756. See alfo the article 

 Chances. 



Lottery is alfo the name of a well-known game at 

 cards. 



LOTTI, Antonio, of Venice, in Biography, principal 

 organift of St. Mark, and afterwards macltro di cappella of 

 the fame Cdthedral, was one of the greatell men of his pro- 

 felTion. The celebrated Haffe, his difciple and intimate 

 friend, and the beft able to judge of his abilities, thought 

 that none of the great mafters ever united in their works fo 

 great a fhare of exprefTion and fcieuce. In his co.-npofi- 

 tions, he combined with the learning of the old fchool all 

 the grace, rich harmony, and brilliancy of the new. He 

 was the hero of Haffe, who never fpoke of him but with 

 rapture. " What expreflion" (he ufed to fay), " what va- 

 riety, were in that exprefTion, and what truth in the ideas !"' 

 How pleafing it was to hear a man at his time of life, of a 

 merit and reputation above all envy, fpeak with fuch enthu- 

 fiafm of a great mafter. Lotti was long at the head of the 

 Venetian fchool. His ecclefiaftical compofitions were only 

 ufed at St. Mark's on great and folemn occafions. They are 

 truly fublime. The kind of pathos in his ftyle elevates the 

 foul, and e\pre(fes all the grandeur and reverence of devo- 

 tion. (Ellais fur la Muf. torn, iii.) This animated and 

 feeling character of Lotti does not feem to come from an 

 author v.'ho in general fpeaks of the Italians with contempt, 

 and of Ramcau as the only mufician who ever knew h.ir- 

 mony and how to ufe it. We can, however, anfwer for the 

 truth of the above charafter. For though we have never 

 heard or feen any of his dramatic mufic, yet, in 1770, we 

 heard at Venice, in the church of San Giovanni e Paulo, on 

 a day that the doge went in proceffion to that church, a mafs 

 by Lotti, in four parts, without any other inftrument than 

 the organ, which was fo well fung and accompanied, that 

 we do not remember ever to have received more pleafure 

 from choral mufic ; all was corretl, clear, and diftinft ; no 

 confufion or unneceffary notes ; it was' even capable of ex- 

 prefTion, particularly one of the movements into which the 

 performers entered fo well as to render it affecting even to 

 tears. The organift, very judicioufly, fuffered the voices 

 to ^e heard in ail their purity, with which our attention was 

 fo occupied, that we frequently forgot that they were ac- 

 companied. This kind of mufic, a cappella, though exploded 

 as unfit for theatrical purpofes, muft be allowed to have its 

 merit. Lotti was the difciple of Legrenzi, the model of 

 Haife, one of the mafters of Marcello, Galuppi, and Pef- 

 cetti. His name is chiefly known in England by the dif- 

 pute in the Academy of Ancient Mufic, at the Crown and 

 Anchor, in 1732, concerning a madrigal which Bononcini 

 was accufed of having fto'en from him. See BoNOSxixi. 



Lotti compofed for the Venetian theatres, between the 

 years 1698 and 1717, fifteen operas. His cantatas furnifh 

 fpecimens of recitative that do honour to his fenfibility. 

 He was opera compofer at the court of Drefden when the 

 Santa Stelli, his wife, performed the part of firft woman 

 then, in 1 7 1 8 ; and in 1720 he returned to Venice, where he 

 was living in 1733. 



LOTUL, in Geography, a town of Bengal ; 1 6 miles W. 

 of Torea. 



LOTUS, in Botany, a name which has been more va- 

 3Hz riouUy 



