708 
tain assumptions deduced theoretically. 
The second was then derived theoretically 
and was found to satisfy the data. 
An abstract of No. 13 was read by the 
Secretary. It follows the theory of pertur- 
bations in the problems of mechanics in the 
order of its historical development from 
Lagrange to Lie with a view to the final 
presentation of the theory in its just position 
as one phase of Lie’s theory of contact- 
transformations. 
No. 14 was presented by the Secretary. 
It gave a bibliography of the Pythagorean 
proposition, followed by a general solution 
of the equation 2 + 7’ = 2’, and concluded 
with an extensive numerical table of the 
sides of rational right-angled triangles. 
No. 15 expressed in terms of the tabu- 
lated HK and F functions a number of in- 
tegrals, many of which had apparently 
never been completely worked out. 
No. 16 showed how to express the effect 
of a small difference in the equatorial mo- 
ments of inertia of the earth on the period 
of revolution of the instantaneous axis of 
rotation around the axis of figure. A re- 
markable value is obtained for the average 
angular velocity of that revolution, and a 
formula is deduced for the difference in 
the equatorial moments essential to explain 
the discrepancy between the observed and 
computed value of the Eulerian cycle. 
No. 17 considered the case of no applied 
forces, or that in which there is conserva- 
tion of moment of momentum. The prob- 
lem is of practical interest in its applica- 
tion to the question of variation of latitudes 
on the earth. Several new theorems with 
respect to the motions of the mass were 
derived. 
No. 18 obtained some general properties 
of a class of functions of which the spher- 
ical harmonies are special cases. 
No. 19 described the present annoying 
state of the subject-matter of notation and 
coordinate systems, and advocated the 
SCIENCE. 
[N. S. Vou. VI. No. 151. 
adoption of certain standards. It is ex- 
pected that this question will be further 
discussed at the Boston meeting with a 
view to obtaining a consensus on symbols 
and fundamental conventions. 
No. 20 called attention to a certain quad- 
rilateral whose properties throw new light 
on the theory of the Pascal lines of a hex- 
agon inscribed in a conic. 
In presenting No. 21 Professor Green- 
hill gave stereoscopic views of certain in- 
teresting curves in space and pointed out 
the bearing of some of them on certain 
parts of the theory of elliptic functions. 
The section is also indebted to Professor 
Greenhill for interesting contributions to 
the discussions on many of the other 
papers. 
The officers elected for the Boston meet- 
ing are Professors E. EH. Barnard, of Yerkes 
Observatory, and Alexander Ziwet, of the 
University of Michigan. 
JamrEs McManon. 
SINGULAR STRESS-STRAIN RELATIONS OF 
INDIA RUBBER. 
THE curious and unaccountable behavior 
of India rubber in thermodynamic trans- 
formation of energy under load has long been 
familiar ; itis, perhaps,even more generally 
known that it exhibits a peculiar relation 
of elongation to load when approaching its 
limit of tenacity, but I am not aware that 
this later phenomenon has ever been ex- 
hibited by formal test or by graphie repre- 
sentation of the results of such tests. It is 
a matter of common observation that, when 
this substance is subjected to a pull of 
steadily increasing intensity, its resistance 
increases as does that of any elastic and 
ductile material; but that, at the end, in- 
stead of suddenly losing power of resistance, 
or even snapping without observable de- 
erease of load, its resistance for a time ~ 
rapidly and largely increases up to the point 
