148 
( 1 J 1 )=H,+H 3 +H 3 +H 1 +H 5 , 
( 1 J 2 )=Hf+HI+H!+H!+HI, 
( l J 3 )=H;+H;+H!+HH-HI, 
( 1 J 4 )=H*+H*+H*+Ht+Hf, 
( 1 J 5 )=H5+H=+H^+H;+H?, 
With these data we can form the quintic whose roots are 
Hj H 2 H 3 H 4 and H 5 . Its coefficients will be given irrational 
functions of the coefficients of G=0 formed from the definite five 
(iL), in which every radical will have a determined sign. 
Solving this quintic, and substituting its five roots (H 4 ), (H 2 ), 
&c., for Hj H 2 H 3 H 4 , H g in our expression for # 0 , we have the 
algebraical solution of the general sextic G=0 : and every one of 
% 0 x x x 2 x 3 x± x 5 is definitely given by the proper reading of the 
cube roots of unity. 
By a like process can every algebraic equation be solved, the nth. 
degree after the ( n — l)th. 
“ Description of a Dolerite at Gleaston, in Low Furness/' 
by E. W. Binney, F.R.S., F.G.S. 
During the last 30 years the tract of land known as the 
Hundred of Low Furness has been investigated and 
described by several geologists. It was one of the earliest 
fields investigated by the venerable Sedgwick, who has left 
us a most valuable memoir of his labours in that district. 
Since then, Mr. Jopling, myself, and Sir It. I. Murchison, 
and Professor Harkness have published descriptions of the 
silurian mountain limestone and permian formations of the 
country. Miss E. Hodgson has also given us information 
as to the drift deposits overlying the paloeozoic strata. 
Still, notwithstanding what has been done, it may confidently 
be asserted that the peninsula comprising the southern 
part of tbe Hundred of Low Furness has yet to be care- 
fully examined before its geology can be said to be 
thoroughly known. 
None of the above-named persons appear to have been 
aware of the occurrence of any trap dykes in this district, 
