1 86 Alatkemalical Corrifpondaiee. 



of ammoniac and ice dlfengages from the volatile oils part of their aroma ; renders their 

 colour more inteiife, thickens them, produces concretions in the oils of turpentine and 

 lemon, and feparates from the latter an amber-coloured fluid, which appears to pofTefs 

 faline properties; and ladly, that the aftion of the cold from water, with the concurrence 

 of the air on the volatile oil of peppermint, afforded a cryftalline matter difpofed in filky 

 needles, which various experiments prove to be a peculiar fait; whence it maybe con- 

 cluded, that the needles of camphor, which arc faid to have been found in the diftilled water 

 of peppermint, are of the nature of this fait. 



[To be concluded in the next Number.'] 



MATHEMATICAL CORRESPONDENCE. 



Question III. Anfioircd byJ.F R. 



JL-<ET A, B, C and D, be the players in the order of feniority. Then, the lad card boing 

 a trump, there will, when D begins^o deal, be 1 2 trumps out of 5 1 cards, to be diftributed 



among them. The chance that A's firft card is not a trump, will, therefore, be — . This 



having happened, the chance that the next card will not be a trump, will become — ,and the 



>° 



next — . Then A's chance that his firft card will be one, will, of courfe, be — or — ; which 

 49 48 4 



having happened, A's chance of failure becomes—, and fo on. By proceeding in this 



47 

 way, we find the whole value of I^s chance for all the trumps = 



39- 3 ■ 57- 3 • .^5- ^3_3 ■jj_^.j^ ^ — ^ which, by ftriking out common multipliers, 



3 4 1 



becomes = — ; ■ : fo tjjat the odds againft it are 



17.10.7.47.46.5.43.7.41 158753389900 '' 



51. 50. 49. 47.46- ^5. 43 &c, 



becomes 



17.10.7.4 



158753389899 to I. 



The fame. Anfivered by IF. T. of Bath. 

 SUPPOSING a pack of cards to be properly fhuffled, and the bottom card to be after- 

 wards turned up, and confequently known ; it is required, in the firift fenfe of the queftion, 

 to find the probability that every fourth card, dealt off from the top, fliall be of the fame 

 fuit with the trump card which is expofed. But as the chance for fome one of the trumps 

 lying in the 4th, 8th, 12th, &c. place, is evidently the fame as for its lying in any other 

 place ; it amounts fo the fame thing as to determine the probability of a perfon's drawing 

 the 12 remaining trumps, one by one, at random, in 12 trials. To effeft this, it is ne- 

 cefTary to 6bferve, that as there are now 51 cards in all, and only 12 in his favour, the 



probability of his drawing one of the trumps, the firft trial, is — ; and if this be fuppofed 



10 be done, and the card taken away, there will now remain 50 cards in the pack, and 



only 1 1 in his favour ; whence the probability of his fucceeding the next trial is — . In like 



50 



