( 1038 ) 
n soy as 
cot dy =D) Ya = IO Moree a V eos? 6 — sin? V becomes 
>0, cot2y< 0 i. e. —o; the angle 2y in accordance with the 
figure must, be taken in the 4 quadrant: 24, = 0°, y= O°. 
Tv 
For 5 >v>0 and cot2y <0 consequently 2, lies in the 4 
ad a 
quadrant, and y,, in so far as one takes the value 5 > Yu > — = 
d 
likewise in the 4*® quadrant. In the 1s' octant consequently is always 
Sega The same holds good for the octants HII, VI and 
VIL, where the denominator of the formula (2) is likewise > 0. 
To the value ya (v‚o) in the first oetant correspond identical values 
with (« +), 6 in the IIrd, (w—y),— ov in the VI, and (2r—v), 
—o in the VIII octant. Where the product sin 2u sina < 0 
(cf. (2)), consequently, in the IIrd, IV, Vt and VII™ oetant becomes 
Or jy et To ya(y,7) in the Ist oetant correspond identical values 
with a contrary sign with vy, —o in the V", (w—g), o in the IIrd, 
(qe), =o in the Vil hand (Ame 0 Anat re IV‘ oetant. In the 
same way as has been done above for the octants I, III, VI, and VIII 
one can determine the ratio between the sign of cot 2y and the 
value of ya. The following ‘result is obtained: if the a-axis stands 
perpendicular to the projection-planes, then lies 
in the octants I, HI, VI, VIII 
with cot 2y > 0, 2ya in the 3'¢ quadrant 
cot 2y <9, 2ya in the 4% quadrant 
> (42) 
in the octants If, 1V5-Vy Vil 
with cot Jy > 0, 2ya in the Ist quadrant 
cot 2y <9, 2yq in the 2rd quadrant 
In this way the orientation of the velocity-ellipse can be found 
with certainty. 
To find the angle which, in a discretionary section, the long ellipse- 
axis forms with the trace of a discretionary plane V’, we return to 
fig. 1. The plane WV, the pole of which is given by the coordinates 
u— ~ILM, v= —~ Ms, is cut by S according to the line EO, 
forming with OH an angle HOH=h. Now we found that 
cos 6 cot a +- sin 6 sin (U—¥) 
ool) = - 
| cos (e= 7) 
