386 
in which, if we put zz + jy + kz in place of 7, we obtain the 
expression given by Dr. Boole. 
As regards the functions F,, F,, F;, involved in the ex- 
pression f+ jF,+kF;, proposed by Dr. Graves as a complete 
solution of the equation 
EV VV 
ces art aa 
(p. 221), he desired it to be understood that he had not in- 
tended to claim for them such an independence upon imagi- 
naries as Dr. Boole supposed him to assert. When developed 
in the form of series, they involve indeed*no square roots of 
negative unity; but analytically they owe their origin to 
imaginaries of this kind. 
Mr. Charles Haliday read a Paper on the Scandinavian 
Antiquities of Dublin. 
The following letter from Mr. Francis M. Jennings was 
read :— 
** Gibraltar, May 22, 1856. 
«¢ My pear Sir,—I have made up, ready to send either by 
post or private hand, an earring of silver used by the Soos 
men, at a place about 60 miles south of the city of Morocco. 
Also, a brooch of silver, such as are used by the Bedouins of 
Morocco at present; you will see it has been worn. The first 
I got out of the man’s ear; the other from a trader. I keep du- 
plicates, for fear of their being lost ; they are for the Academy, 
if they think them worth accepting. I have got a few other 
things also, including a necklace; but I think the brooch is 
the most curious, as its resemblance is so great to the Irish 
ones. Lalso got off the right arm, from above the elbow, 
(where it is worn) what would be called a piece of ring-money 
