378 Solution of Biquadratic Equations. 
About four inches above the coal in which the animal was found, 
numbers of muscle-shells in a fossil state lie scattered in a loose 
grey earth. 
At a considerably higher level, and in an alluvial soil, near this 
town, a mass of these shells is found at twelve yards from the sur- 
face, imbedded in a stratum of black limestone about twelve 
inches thick, which takes a good polish. This bed or band of 
fossil muscles is found in all the coal mines in this neighbour- 
hood, but generally connected with iron ore. 
Mr. Scholes mentioned auother circumstance worthy of reeord, 
which occurred some years ago under his own eye at the Stanley 
colliery two miles NE of this town. In sinking a pit to the depth 
of 86 yards, they came to a bed of coal 2 feet 6 inches thick, be- 
neath which, in their further progress, they found what they 
supposed to be a petrified tree, or rather plant, having no branches, 
standing upright, but rather inclining to the east. It was six 
inches diameter at the top; but as they sunk down, it increased 
to twelve inches, and at the depth of 42 feet seemed to branch out * 
roots to another bed of coal six feet thick. The body was a 
grey sandstone, coated round with a black carbonized matter 
one-tenth of an inch, supposed to be its bark. 
Before concluding, I will take this opportunity of communi- 
cating to you another remarkable phenomenon in some measure 
connected with this at Stanley colliery, which is on the NW side 
of the river Calder. On the SE side of this river, and nearly 
in a parallel line, there is a hill about 200 feet above the level of 
the river. It consists of an argillaceous sandstone, and a few feet 
from the surface there are strong appearances of its having once 
been on fire. For many years a quarry has been worked there 
for procuring materials for the repair of the roads, for which pur- 
pose this burnt stone is well adapted. In this quarry many gi- 
gantic fossil plants have been found standing upright, as well as 
casts and impressions of vegetables unknown to these climates 
lying horizontally. Many specimens of these fossil reliquiz are 
in the possession of Mr. Parkinson, Hoxton Square ; of Mr. Wat- 
son, of Bakewell, Derbyshire ; and I believe in the collection of 
the Geological Society. I am, Sir, 
Your constant reader, 
To Mr. Tilloch. W.S. 
SOLUTION OF BIQUADRATIC EQUATIONS. 
The following solution of the Biquadratic is founded upon Des 
Cartes’s method of multiplying together two quadratic factors 
with indeterminate coefficients. A modification of his assamp- 
tion presents us with two new and simple formulz of solution, 
and places the true principle of his method in a clear light. 
By 
