MATHEMATICAL SECTION. 127 
involving either the prediction or occurrence of A may be excluded 
and B and C separately investigated. Suppose it thus ascertained 
that great skill has been shown in discriminating between A and 
Not A, and little or none in discriminating between B and C. No 
single numerical expression can properly comprehend these heter- 
ogeneous. results. 
Mr. Curtis showed that some of the results given by Mr. Doo- 
little could be independently deduced by another method. 
Mr. GrLBeErT noted as a defect in the formula proposed by Prof. ° 
Peirce, that it did not duly discourage positive predictions of rare 
events; and, while gratified with Mr. Doolittle’s discussion of the 
subject, he expressed a disappointment that no satisfactory decision 
as to the treatment of cases of three or more alternatives had been 
reached by him. 
After some further discussion, a communication by Mr. M. 
BAKER was called, but postponed, on motion of Mr. H. FarquyHar, 
to allow time for the consideration of & testimonial to a late asso- 
ciate, Mr. ALVORD. 
Mr. E. B. Exxiorr read the following tribute, prepared by Mr. 
Baker and himself: 
MEMORIAL. 
The Mathematical Section of the Philosophical Society of Wash- 
ington, having suffered the loss by death, on October 16th, 1884, of 
General BENJAMIN ALVORD, one of its founders and active workers, 
desires to place on record this testimonial to his worth and to the 
loss to this Section and to science by his death. 
Of his worth, one of America’s greatest mathematicians has said 
that he was a scientist of “real originality who had actually ex- 
tended the boundaries of science.” 
The bent of General Alvord’s mind and studies was early 
directed towards a purely geometrical solution of the general prob- 
lem of tangencies, and his reward, which it is our pleasure to 
chronicle, was success. 
Of his mathematical publications, the following is submitted as 
a provisionally complete list : 
