PROCEEDINGS. 
597 
right angle being equally distributed in the semi-circumference, or each set 
of legs being equally distributed in a right angle having the hypotenuse 
for one of its sides. 
In the second class there is no locus of equal distribution, and the 
variable whose average value is required is a function of an equicrescent 
variable which moves while it grows. For illustration, let it be required 
to determine the average area of a right triangle with a given hypotenuse 
and one of the legs equicrescent. 
In the published works on the subject nearly all, if not all, the problems 
belong to the first class, and the locus of equal distribution is frequently a 
given constant. When only one such constant is mentioned it has not 
always been thought necessary to state that this constant is the locus of 
equal distribution. 
If it be required to determine the average area of a right triangle having 
a given hypotenuse, with no other conditions given, the problem is con¬ 
fessedly obscure; but the solution best conforming to any system of inter¬ 
pretation is that which makes the altitude divide the hypotenuse into 
equicrescent segments. 
44th Meeting. May 30, 1888. 
In the absence of the Chairman, Mr. H. H. Bates presided. 
Present, fourteen members. 
The minutes’ of the 43d meeting were read and approved. 
On motion of Mr. W. B. Taylor the following resolutions 
were adopted: 
Whereas we have learned of the sudden death of our esteemed fellow- 
member E. B. Elliott, which occurred on last Thursday, May 24th ; and 
whereas Mr. Elliott has been one of the most earnest and faithful mem¬ 
bers of this Section, presiding over the meeting which organized it, attend¬ 
ing almost every session, contributing frequently to its proceedings, and 
always appreciatively following the discussions of others: 
Be it resolved by the Mathematical Section of the Philosophical Society of 
Washington, at a session held May 30th, 1888, That w'e, the members of the 
Section, feel it to be our duty to unite in a warm expression of our high 
appreciation of the intellectual and social qualities of our departed friend, 
of our strong admiration of the courtesy and fidelity manifested by him in 
all his relations with others, and of our deep grief at the loss we realize in 
having no longer the pleasure and the benefit of his familiar presence 
among us. 
Be it resolved, That the Secretary of the Mathematical Section be requested 
to present a copy of this minute of its proceedings to his relatives, with 
