JUNE 7, 1901. ] 
torially lucid as to the meaning of the terms 
involved. 
Let A, B, C, be the principal axes of inertia 
and ©, ®, 3, the angular velocities of the rigid 
body around them. All this is kinematic. 
Let A’, B’, C’, be the positions of these axes 
a unit of time later. Lay off the angular mo- 
menta, A®,, Bo, Cw; along these axes in order, 
as shown. Then will 4A’, BB’, CC’, be the 
corresponding per second changes of angular 
momentum. 
Resolve each of these into components paral- 
lel to the original axes, and bring those belong- 
ing to the same axis together, viz., 
— Bo,0., — Co, —Aa;-0», 
+p Coo3-05, + Ao) -0, + Bo,-a), 
remembering that as each axis rotates about the 
other two, the component displacements per 
second will be 
OP CE net ken Uc ERR 
Add to the component changes of momentum 
found, the direct per second changes of angular 
momentum around the respective axes, viz., 
+ Ao, + Bos, + Cis. 
Let L, M, N, be the torques around the three 
axes in order, and equate these to the total per 
second change of angular momentum corre- 
sponding to the same axes. In other words, 
after adding each of the three columns, 
L = Ao,—(B—C)o,0,, 
M— Bo,—( C—A)a,0,, 
N= Co,—(A—B)o,,. 
C. BARUS. 
ON A CRINOIDAL HORIZON IN THE UPPER 
CARBONIFEROUS. 
For more than half a century the Lower Car- 
boniferous limestones of the Mississippi valley. 
have been justly celebrated for their enormous 
wealth of crinoidal remains. On this account, 
they have become widely designated as Encri- 
nital limestones, a title which has long since 
assumed a distinctive value. 
The crinoidal element in the faunas of the 
Lower Carboniferous has been further empha- 
sized by the apparent extreme paucity or entire 
absence of crinoid remains in all other parts of 
the Carboniferous section of the region. The 
SCLENCE. 
915 
few species described were few in number, from 
widely separated localities and from very frag- 
mentary material. 
Unusual interest was, therefore, aroused a 
few years ago by the discovery, in the Upper 
Carboniferous rocks of the Missouri river, of a 
formation so rich in fossil crinoids as to merit 
the title Encrinital as appropriately as any ter- 
rane of the Lower Carboniferous. Species were 
not only new and numerous, but individuals 
occurred in the utmost profusion, their stems 
and long, slender, beautifully pinnulated arms 
intertwining as intricately as the richest of flow- 
ing arabesques. Moreover, the state of preser- 
vation was wondrously perfect. From a mor- 
phological standpoint the discovery was one of 
the most important ever made. 
The geological position of this rich crinoid 
fauna is a short distance above what is called 
the Lower Coal Measures. It is in the terrane 
now known as the Thayer shales, the base of 
which is a stratigraphic level not much over 
600 feet above the Lower Carboniferous lime- 
stones. The Thayer shales are in the lower 
part of the Missourian series. They are dark. 
blue in color, and lithologically are indistin- 
guishable from the Crawfordsville Shales of 
Indiana, which have been so prolific in crinoids 
in fine state of preservation. 
The biological peculiarities of the crinoids 
from the Thayer shales as compared with those 
of the nearest forms from the Lower Carbonif- 
erous are noteworthy features. For two faunas 
so closely connected in space the differences are 
so profound when apposed to the resemblances 
as to be almost inexplicable. 
But a satisfactory solution of the remarkable 
problem has been lately supplied from a source 
other than the biotic. The recently worked- 
out stratigraphy of the region throws light upon 
it in an unsuspected manner. The actual posi- 
tion of the Thayer shales, instead of being re 
moved only 600 feet from the Lower Carbonif- 
erous limestones, are, stratigraphically, thou- 
sands of feet away. 
While the lower coal measures have long 
been known to rest unconformably upon the 
underlying rocks, the stratigraphic break has 
been regarded as merely local in nature. Of 
late, the real significance of this hiatus has been 
