. 
216 
Colman in the Irish character, with the word bochz [poor] 
written under it in Ogham. I doubt whether this tombstone 
is still to be found. My information respecting it is derived 
from Dr. Petrie, who furnished me with a drawing of the mo- 
nument made by him several years ago. Since then many of 
the monuments have been broken, buried, or removed to other 
churchyards in the neighbourhood.” 
Rey. Robert Carmichael, F.'T.C. D., read a Paper on La- 
place’s Equation and the Calculus of Quaternions. 
‘‘ Early in the year 1852 it accidentally suggested itself 
that the celebrated Equation of Laplace’s Functions, which 
had hitherto, for all practical purposes, baffled the powers of 
ordinary analysis, might possibly be solved with simplicity, and 
in a form admitting of useful application, by the new method 
of analysis discovered by Sir William Hamilton. The results 
of the investigation thus set on foot were published in the 
‘ Cambridge and Dublin Mathematical Journal,’ February, 
1852. 
*< To one starting with the simpler equation, 
D.U+ Di U=0, 
the solution of which was known to be 
U=@ (a+ ty) + ¥ (a-y), 
where i?=-1, it seemed probable that the solution of the 
higher equation, 
D.V+ Di V+ DiV =0, 
should be susceptible of deduction by the employment of two 
imaginaries 7 and j, governed by the laws 
P=-1, fa=-l,. G=-ji 
The integral thus deduced appeared to be 
V=0 (a+iz, ytjz)t ¥ (w-iz, y—J): 
Unable to interpret this form, and impressed with the convic- 
tion that, to render the solution, iftrue, of any value, such in- 
