8 



ar-atom, there are then seven cases of agreement with the hypothesis 

 of parallelism, eight disagreements, and nine remaining doubtful. 

 If the ring forms on the ^-carbon there are then ten cases of agree- 

 ment and ten of disagreement and four in doubt. If the ring forms 

 on the ^-carbon there result six agreements, twelve disagreements, 

 and six doubtful. But it has been seen that if the ring forms on the 

 ^-carbon there are twenty-four agreements, no disagreements, and 

 none in doubt. As the chances that an event which can happen in 

 two equally probable ways will happen in exactly the same way 

 twenty-four times out of twenty-four trials is only one in seventeen 

 million, it seems certain that the lactonic ring in these monobasic 

 sugar lactones forms on the ^-carbon atom. 



[Cir. 49] 



o 



