W. M. Fontaine—Primordial Strata of Virginia. 361 
y can enter into the development, we have, calling R, the 
value of R at the origin, 
1/d? (R, 2 a(R? 
RI=Ry?45(— oe ot + Nie ‘) 
1 /d*(R,?) d*(Ry?) ,., d4(R,?) 
Piaf de® — daz? dy? sed ak dy* y')+ 0 
When the vibrating body is very small the first two terms will 
suffice: hence we have 
ee ee) PUo*) +e 
Ma ano sin y cosy f” Pigind. 
in which 7 is the length of the bar. If S is the density of the 
“e 
body (weight of a unit of volume), I=" “and n becomes 
n=— | ~(“Ee me oo) 
AM 2y\. de? dy? jf’ 
hee ah d?(R,?) 
in which, however, it is to be noted that — dy? 
negative and so the sign of the term containing it will be posi- 
tive in the actual development. 
This equation is independent of the dimensions of the body, 
and hence we conclude that when the body is small and very 
long as compared with its other dimensions, the number of vi- 
brations which it will make ina given field is dependent merel 
on its coefficent of magnetization and on its density ; a result 
first given by Sir Wm. Thomson, in the paper referred to. I 
have given it once more and put it in its present form merely 
to call attention to the facility with which x can be obtained 
from it when we have measured R in different parts of the field 
by known methods. This could be done by means of a rotating 
evil as used by Verdet, or my magnetic proof plane which I 
will soon describe, combined with my method of using the earth 
inductor. This will give the best method that I know of for 
obtaining x for diamagnetic or weak paramagnetic substances. 
Troy, Jan. 15, 1875. 
is essentially 
Art. XXXIX.—On the Primordial Strata of Virginia; by WM. 
M. FonTaAINE. 
My investigations in the strata of the Primordial period in 
Virginia were confined to the immediate vicinity of the Blue 
Ridge, near Harper’s Ferry, Rockfish Gap, Balcony Falls, and 
the Peaks of Otter. They extended to the rocks of the Cal- 
