William Rowan Hamilton. 299 
s two memoirs can only 
be compared with that effected at an earlier epoch by the publi- 
‘ worth, but because they are less within the scope of our Society ; 
to the length of the other line; 4 : 
2. The angle through which the one line must be conceived 
to be turned in order that it may coincide with the diree- 
tion of the other; ‘ : 
e plane in which the two lines lie. __ ; 
And inasmuch as the determination of this plane involves 
two elements, viz: Ist, its inclination to some fixe or known 
plane, and 2d, an element which is analogous to the longitude of 
a planet’s node, it follows that four* elements or symbols are re- 
* The shove is in fact one of Hamilton’s many illustrations of the meaning of a 
quarternion, Analytically speaking, a quarternion is an e of the form 
w+ie+tjy+tkz, where i,j,k are imaginary roots of 4/ —1, differing from the eal 
