230 LIGHT SCIENCE FOR LEISURE HOURS. 



to give a fair chance of a fortunate drawing or of many 

 such drawings, the lottery-keeper would win more on 

 such ventures than on any others, despite the enormous 

 sums he would have to pay in prizes. It is probable 

 that many risked their sous and francs in the hope of 

 winning a fortune on a quine determine ; for unques- 

 tionably millions must have ventured on what to the 

 uninitiated must appear scarcely less venturesome 

 than the quine determine as respects the improbability 

 of success viz., the quine simple and the quaterne 

 simple. Success in the former of these required that 

 the five numbers drawn should be the five selected by the 

 speculator, but in any order success in the second required 

 that among the five numbers should be four selected 

 by the speculator. On the average of an immense 

 number of drawings in these ventures respectively, one 

 venture in 43,949,268 would be successful among simple 

 quines, and one in 704,880 among simple quaternes. 

 Now, many speculators won in France on the latter 

 venture, and even simple quine has several times been 

 won. On one occasion it so happened that one and 

 the same drawing lost the lottery-keepers on both 

 these ventures. A speculator had selected the numbers 

 8, 13, 16, 46, and 64, and another had selected for the 

 same drawing 8, 16, 46, and 64. The numbers actually 

 drawn were 8, 46, 16, 64, and 13. Fortunately for 

 the bank, the stakes were very small in the former 

 case Id. and in the latter 2d. The speculators won 

 only 131,350f. and 20,852f. respectively. At their 

 proper mathematical value in relation to the stake 

 the prizes would have been 2,746,829f. and 176,220f. 



