( 130 ) 
we deduce that the nodal envelopes have tangents which pass through 
the angles of the triangle, if either w‚,, or wy, or wy, Ur are 
equal to zero. The tangent contains the angle representing the third 
component, if w.,—O; that representing the second component if 
u, =O; and that for the first component if wy, = tr 
The conditions that a tangent of the envelope is parallel to one 
of the sides of the triangle may be deduced from the values of 7,— 7, 
and y,—y,- So from «,—7r,=0 follows the condition that the 
tangent is parallel to the side of the first and the third components. 
This condition has the following form: 
1 
U. op 
Ys PAB helene, | 
= , P 
== a, ef | 
ll 
Now ahs = tana, where a represents the angle enclosed between 
— WV 
1 
the radius vector drawn from the second component, and the A- 
axis. As « must be less than 45°, we get for the condition for the | 
existence of points where the tangent is parallel to the Y-axis: | 
We 
el 
tan A= 
A 
ef nh re | 
and u, < u, if both are positive. 
The condition that the tangent is parallel to the N-axis may be 
derived from y,—y,-—= 9 and has the following form: 
/ 
“ ure | eee 
cs e 1 
Dy 
oo, — tan 8, where 3 represents the angle, enclosed between 
a a 
the radius vector drawn from the third component, and the Y-axis, 
we may write this condition as follows: 
As 
et tes Og a 
tan B=—, 
2 
e 01 nn 
and w'‚, >> wy, if both are positive. 
The condition that the tangent is parallel to the hypothenuse may 
be derived from: 
Orte eae 
Lt ‘ 
2 1 
