632 
NOTICE OF SCIENTIFIC MEMOIR 
The definitions of uniformity (absolute and relative) may be simpli- 
fied by omitting "3. nin and replacing 'a^J by 'an. This form 
of definition is suggested directly by (4); the more complicated form 
(5) with its redundant existential feature nin serves however to suggest 
the definitions of semiuniformity (absolute and relative), and relative 
semiuniformity proves to be of importance in the applications. 
1 M. Frechet, Sur quelques points du calcul fonctionnel, Palermo, Rend. Circ. mat., 22, 1-74 
(1906). 
2 E. H. Moore, Introduction to a Form of General Analysis, 1-150, The New Haven Mathe- 
matical Colloquium, Yale Univ. Press, 1910. Cf. also, E. H. Moore, On a Form of General 
Analysis with Application to Linear Differential and Integral Equations, Atti IV Cong. Inter. 
Mat. (Roma, 1908), 2, 98-114 (1909). 
3 E. H. Moore, On the Foundations of the Theory of Linear Integral Equations, Bull. 
Amer. Math. Soc, Ser. 2, 18, 334-362,(1912). On the Fundamental Functional Operation of a 
General Theory of Linear Integral Equations, Proc. Fifth Inter. Congr. Math. (Cambridge, 
Aug., 1912) 1, 230-255 (1913). 
NOTICE OF SCIENTIFIC MEMOIR 
The Variations and Ecological Distribution of the Snails of the Genus To. By 
Chaeles C. Adams, New York State College of Forestry, Syracuse, N. Y. 
Second Memoir of Volume 12 of the Memoirs of the National Academy 
of Sciences, Washington, 1915. 1-184 p., 64 pi. 
lo is a large gilled snail which lives only in the Tennessee River system. 
It is extremely variable, shows a remarkable distribution in the streams and in 
this it appears to be related to the physical history of the drainage. Through- 
out this Memoir emphasis is placed upon relating the changes of the animals 
to the changes in the environment. The general natural history of the 
snails is briefly summarized, the local races are described and the locahties 
from which the collections studied were secured is given in detail. The shells 
were grouped in convenient classes for descriptive purposes. The diameter 
of the shell, its degree of globosity, and the degree of development of the 
spines were determined quantitatively. These qualities are discussed by 
streams and drainage systems. In the parallel flowing Powell, Clinch and 
(North Fork) Holston rivers, the shells are smooth or with low spines in the 
headwaters, and down stream have longer spines. This condition is quite 
remarkable and no previous detailed investigation has been made of a prob- 
lem of this character. 
The development or evolution of the gross environment is discussed. The 
author states "It is considered that a knowledge of the development and 
structure of the environment is as essential a part of the problem as is the 
development and structure of the animals themselves." An outline history 
of the Tennessee drainage is given. In the past this family of shells was 
thought to have originated in the Northwest (Laramie) but the author sug- 
gests an alternative hypothesis, that they originated in the southeast. 
