582 
PHILOSOPHICAL SOCIETY OF WASHINGTON. 
39th Meeting, March 7, 1888. 
In the absence of the Chairman of the Section, Mr. W. B. 
Taylor was called to the chair and presided during this meet¬ 
ing. 
There were present eleven members and guests. 
The minutes of the 38th meeting were read and approved. 
v 
Mr. C. H. Kummell presented a communication entitled Re¬ 
marks on Some Recent Discussions of Target-Shooting. The 
recent discussions to which he referred are those of J. Bertrand, 
published in the Comptes Rendus, Nos. 3, 4, 6, and 8 of vol. cvi, 
1888, and those of Mr. E. L. De Forest, published in the Trans¬ 
actions of the Connecticut Academy, vol. vn, 1885. These 
authors reject Poisson’s hypothesis that the departure of a shot 
from the center of the target is the resultant simply of the inde¬ 
pendent errors of alignment in azimuth and altitude, and main¬ 
tain that the law of arrangement of shots in any target can only 
be determined by examining the target itself. 
Mr. Kummell referred to his own investigations on target¬ 
shooting, published in the Bulletin of the Philosophical Society 
for 1883, vol. vi, p. 138, which proceed from Poisson’s hypothesis, 
and affirmed the correctness of his published views and results. 
Mr. Kummell gave also a solution of the problem of con¬ 
ditioned maxima or minima from a new point of view. 
This solution consisted in the introduction of certain factors 
or correlates in a manner similar to that followed in the treat¬ 
ment of conditioned observations in least squares, by which the 
problem is changed in form to that of unconditioned maxima 
and minima. 
Mr. G. K. Gilbert proposed a new problem relative to the 
estimation of skill in making predictions. He stated that 
Messrs. Finley and Doolittle and himself had considered in their 
investigations only absolute success and failure. Some weight, 
he thought, should be attributed to a near approach to success, 
or there ought to be considered degrees of success and failure. 
In short, the problem he hoped some of the mathematicians of 
the Section would solve is, “ What is the proper mathematical 
expression for a close miss ? ” 
