375 
Monpbay, JUNE 9TH, 1856. 
JAMES HENTHORN TODD, D.D., Presipenrt, 
in the Chair. 
Dominick M‘Caustanp, Rebert M‘Dermott, M.B., Rev. 
James M‘Ivor, and Sir Colman M. O’Loghlen, Bart., were 
elected Members of the Academy. 
Rey. Charles Graves, D. D., read a letter from Dr. Boole, 
on the solution of the equation of continuity of an incom- 
pressible fluid. 
“ Queen’s College, Cork, 
“5th May, 1856. 
«* My pear Graves,—Your memoirs on the application 
of the method of Quaternions to the solution of the partial 
differential equation, 
dui du du 
ie + ay + aa 7 0, 
have called to my mind some researches upon which I was 
engaged many years ago, and which establish what I con- 
ceive to be the general theory of such applications, and throw 
some light upon the question of the probable value of the re- 
sults obtained. I will communicate to you the fundamental 
theorem to which my investigations led, and explain its ap- 
plication to the particular case which you consider. But I 
wish you to understand that this application was not contem- 
plated by me at the time the theorem was discovered. 
‘* First, however, I will observe that your method ex- 
pressly consists in interpreting the forms 
er PahPs) f(y, zZ), et UPa**Pa) f(y, 2), 
d 
where D, stands for —, and D, for ae originally sug- 
d Zz 
gested by Mr. Carmichael, but by him erroneously inter- 
VOL. VI. 2N 
