602 
PHILOSOPHICAL SOCIETY OF WASHINGTON. 
Mr. M. H. Doolittle discussed A Problem in Probabilities, 
which may be stated as follows : Two persons, A and B, agree in 
their testimony concerning the occurrence of an event. The 
veracity of A is known, of B unknown. What is the probability 
that the event did occur when the testimony is affirmative ? Mr. 
Doolittle considered the answer to this question concurred in by 
several mathematicians, whom he cited, erroneous. He indicated 
the error which led to the erroneous answer and gave the steps 
of the reasoning involved in what he thought the correct solution 
of the problem. In brief, the veracities of A and B being denoted 
by p and x respectively, the probability sought, if a;.were known, 
would be 
px + (1 —_p)(l — x)' 
But x being unknown, though confined within the limits 0 and 
+1, the correct answer according to Mr. Doolittle is the ratio of 
the average values of the numerator and denominator of this 
fraction, or p; while the erroneous answer is the average value 
of the fraction, or 
During the discussion which followed Mr. A. S. Christie 
presided. 
Mr. Artemas Martin read a brief paper maintaining the cor¬ 
rectness of the expression last given above and gave a demon¬ 
stration leading thereto. 
48th Meeting. December 26, 1888. 
The Chairman presided. 
Present, seventeen members and guests. 
Minutes of the 47th meeting read and approved. 
Mr. R. S. Woodward presented a Statement of the Mathemati¬ 
cal Theory of the Stratum of no Strain and its Application to 
the Earth. The object of this communication was to explain the 
