( 487 ) 
(ab)? = 2 (ax, ao — 47)» 
united by the relation found above. 
Whilst (ab) =0 points to the coinciding of the two lines indi- 
cated by a? = 0, aa disappears when those lines are at right angles. 
If ce is the tangent of the angle formed by the two lines, their 
angular coefficients satisfy the relation 
or 
4 (aso agg — a?) + C° (azo + 209) = 9, 
or 
2 (ab)? + ctaa by = 0, 
or at last 
(c? + 2) (ab)? + ec? a2 = 0. 
So the invariant a, disappears when ¢? = — 2. 
4. By the interpretation of the substitution zy = 0 or 
Y 2 Yg = MF — 4 
follows immediately that the covariant 
(ax)? 
disappears for two lines which are at right angles to the lines 
representing a?. 
The covariant 
(av) az 
changes only its sign by the substitution «, = 0. 
So (az) az = 0 represents two orthogonal lines. 
Indeed the sum of the coefficients of «? and #3 is equal to zero. 
If aj, = 0, so that the lines of a? lie symmetrically with respect 
to the axes of coordinates, we have 
(az) ax = (499 — %2) #1 22: 
This proves that the covariant (a)az furnishes the bisectors of 
the angles of the lines a? = 90, 
