of Edinburgh, Session 1866-67. 
121 
Table of Weights. 
6 oz. 6 drs. 3 oz. 
6 oz. 3 drs. 2 oz. 2 drs. 
3 oz. 3 drs. 1 oz. 7 drs. 
On section they are seen to be perfectly homogeneous, presenting 
the same uniform structure throughout, showing that the nodules 
on the external surface are produced by some external agency act- 
ing on the surface of the stone. They are probably formed in the 
same way as the fairy stones, viz., by the dropping of water con- 
taining the matter of which they are composed ; but must be of 
great age, as the cutting in which they were found is about one 
hundred yards from the bed of a river. The following are the 
geological characters of this part of Cumberland in which they 
occurred. It is situated on the New Red Sandstone, but at Coathill 
and Newbiggin gypsum is found lying in red argillaceous marl 
between two strata of sandstone, and at Wreay is the commencement 
of the whinstone dyke which extends from that place to Renwick. 
4. Note on Professor Tait’s “ Quaternion Path” to Deter- 
minants of the Third Order. By the Rev. Hugh Martin, 
M.A. Communicated by Professor Kelland. 
I have read with much interest Professor T ait’s “ Note on Deter- 
minants of the Third Order ” in the Proceedings of this Session 
(pp. 59-61), and admire the method of discovering new proper- 
ties of Determinants. I am not sure, however, that the properties, 
when discovered, are more difficult of proof by Determinant 
methods, and I venture to submit the following as simple and 
elementary 
The first property, namely, 
x + *1 y + 2/1 * + z i 
= 2 
x y z 
*1 + X 2 Vl + V -2 *1 + *2 
x i yi 
x . 2 + x y* + y z-2 + z 
X 2 y-i z -i 
is true under greater generality, and the Determinant proof is the 
same as for the special case. 
VOL. VI. 
Q 
