PROCEEDINGS 
Or 
THE ROYAL IRISH ACADEMY. 
1844-45, No. 50. 
January 27, 1845. 
SIR Wm. R. HAMILTON, LL.D., President, in the 
Chair. 
The Correspondence (see Appendix, No. 1.) was read 
from the Minutes of Council. 
The Rev. Charles Graves read the continuation of his 
paper on Algebraic Triplets. 
The triplet x + yw +z, or (a, y, 2), being employed to 
represent the right line drawn from the origin to the point 
whose rectangular coordinates in space are x, y, and z, it be- 
comes a matter of interest to determine the position of the 
right line which represents the product of two such triplets. 
For this purpose it will be convenient to lay down some defi- 
nitions. 
1. The symmetric axis is the right line drawn from the 
origin, so as to make equal angles with the three positive por- 
tions of the axes of coordinates. 
2. The symmetric plane is a plane passing through the 
_ origin, and perpendicular to the symmetric axis. 
3. The modular plane is the plane containing the axis of 
x and the symmetric axis. 
4. The radius, r, of the triplet («, y, z) is the right line 
drawn from the origin to the point a, y, z. 
VOL. III. F 
