2 ) A 
VIG (ee ol ee gee + 2 cos? ed ; ten 0) | 4 
sn? (vp) NN Ae 4 —A,, 
T 4 
Y= ——_——— _ , d= e+ , wp =ilogd; 
23 
cos — 
2 
2 ) A 
VAD ws le es ane eee se ion 9 
7 sn* (v) 2 VA, sn I 
t 
ve, d= ew = ilog d. 
Wro - 
2 
When point (zy) describes the conic, the variable » will describe 
a certain curve in its complex plane. This curve we shall investigate 
in the five cases mentioned above whilst at the same time we shall 
indicate how the functions &, & and J bear themselves during that 
motion. 
Case II. Point O lies in the domain of the conjugate hyperbola; 
the diameter through O does not intersect the curve, i.e. the points 
T, and 7, are imaginary. On the contrary the points R,, R,,S,, 8, 
are all real. 
| | 
II {in Sj” on oR in Ri on R1S2”® | 
| | | ins”) 
in S2” |on Ss” Ra \inRo\ on R2S,” 
sl 0 purely imag. 2iK' 2iK’+ real 2KH2iK 2K+p.imag 2K real 0 
t| oo pos. real | 0 |pos.imag.| © pos. real 0 | pos.imag.| oo 
| z | pos. imag. +5 pos.imag-| oo | neg. imag. —5 neg. imag.| oo 
I\ w | neg. imag. o | neg. real (460 pos. imag. | co | pos. real | oe) 
Here the curves are sketched which are described by rv and J in 
their respective complex planes. 
The points where / turns its direction of motion are arrived 
at by putting /=0. We then find the values of / corresponding 
tothe ‘roots. of .7=0; these are n= 0543 =e 
| 1+à 
BA a == 18 te Den LE =, 
