386 
in which, if we put zx + 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, +k, proposed by Dr. Graves asa complete 
solution of the equation 
aV ay, 0 
dx dp de” 
(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 Pane on the Scandinavian 
Antiquities of Dublin. 
The following letter from Mr. Francis M. Jennings was 
read :— 
“‘Gibraltar, May 22, 1856. 
«¢ My pear Sir,—lI 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. I also got off the right arm, from above the elbow, 
(where it is worn) what would be called a piece of ring-money 
