88 
PHILOSOPHICAL SOCIETY OF WASHINGTON. 
Mr. Doolittle, proceeding on the hypothesis that the problem 
is indeterminate, gave an infinite series of possible values for the 
respective probabilities. But he thought the problem should be 
understood as determinate, and assigned as the proper value for 
the third probability. 
Mr, Hill expressed the opinion that the probability for a 
rotten and wormy apple is the proper value, but gave a solution of 
the problem by means of double integrals which brought out a dif¬ 
ferent result. 
Messrs. Curtis, Elliott, and Farquhar gave different solutions 
leading to Jy for the third probability. 
Mr. Farquhar objected to the result i as involving the absurdity 
that if one-fourth are wormy the probability of the combination is 
exactly the same for all values of the rotten between i and f ; and 
also further objected to calling a probability “indeterminate” be¬ 
cause it was not a certainty. 
Mr. Martin gave a brief history of the problem, which appeared 
originally in his Mathematical Visitor,* and of which he gave three 
solutions leading to i for the third probability. He stated that the 
correctness of his solution depended on the correctness of the view 
that all possible values of any one of the probabilities are equally 
probable. 
The subject was further discussed by Messrs. Gilbert, Christie, 
and Woodward. 
Mr. Hill also read a letter from Prof A. Hall relating to the 
problem. 
The discussion was closed with some remarks by the Chairman 
on the language of the problem and its proper interpretation. 
* The Mathematical Visitor; edited and published by A. Martin. 4°. 
Erie, Pa. 1881. Yol. 1, No. 4, January, 1880, p. 115, problem 180; solu¬ 
tions pp. 180-181. 
