282 The Ametncan Geologist. November, i897 
diminishing or scarcely expanding, senile stage was not at- 
tained. In several hundred specimens from the Beloit forma- 
tion and the lower Galena formation, the greater number are 
mere apices in size, many are half grown and none appear to 
be senile. From the Hudson strata at liichmond, Indiana, I 
have collected few small specimens but man}' mature and sen- 
ile ones. In the Macjuoketa (Hudson) stage of Minnesota are 
few small, many mature, and few senile individuals. But their 
growth is alike in other respects. 
The rate of expansion from the apex is variable in anv one 
individual and hence also in many as compared to each other. 
The curvature likewise varies from strongly curved to straight, 
gentle curvature being tlie average. (See ligs. 1 and 2, pi. XVI.) 
They have rarely even a reverse or again a sjiiral ciirvature. 
It has been asserted by Winchell and Schuchert that the ear- 
liest representatives (S. profnndum) are less curved than their 
successors [8. cornicaluin) but nevertheless one sees that the 
curvature is variable in all to the same degVee. Thus, too, the 
rate of expansion from the apex is alike inconstant in SiV\y 
group of them. Ulrich's S. breve is indeed extreme!}- obtuse 
and straight, but one finds every gradation to the extreme op- 
posite of it. 8. apertum Billings may well be considered the 
same kind of "species" as 8. breve, being distinguished like 
it only by a supposed dilference in external form. 
The transverse section is nearly circular. Not rarely, how- 
ever, the cardinal or convex side is sub-angular, and even lat- 
eral angles appear, these being rarely not accompanied by the 
anterior one. All are developed mainly on the rapidly expand- 
ing, strongest curved part of the corallum and each coincides 
with a primary septum. Several small specimens from Rich- 
mond, Indiana (*9. rusticum) show the anterior keel strongly 
developed, and are not distinguishable therefore from Billings' 
proposed species 8. angiihitnm, of which he tells us but little, 
however. Examples of the same age (/S'. rusticum) \n Minn- 
esota show the angularity best and oftenest, but earlier ones 
[8. cornicidum, 8. profundum.) have developed the same in a 
few individuals. 8. robustum Whiteaves shows this feature 
too. 
Winchell and Schuchert have discovered (op. cit.) that the 
8. cornicidum and 8. profundum specimens were often at- 
