\ 
452 
ON THE DETERMINATION OF THE 
[476 
Article Nos. 95 to 98. Planogram No. 3, the Orbit-pole at one of the points A. 
95. When the orbit-pole is at one of the points A, the orbit-plane passes through 
one of the rays, and as there is no longer on this ray any determinate point of 
intersection, the orbit (as was seen) becomes indeterminate. Thus consider the point 
A for which 6 = 270°, c=60°: we have 
Fig. 9. 
1 
S 
and consequently the formula gives 
x x : yi : 1 = 0 : 0 : 0 , 
x' : y' : 1 = -IV3-V3 : 3 : -1V3-V3, 
x' : y' : 1 = -IV3-V3 : - 3 : -1^3-V3, 
0 : 0 
and, moreover, x = — x', y = — y\ From the formula the value of x x or x x is given as 
g, but the true value is obviously x x = l\ the value of y x is actually indeterminate. 
The formulae give the values of (x 2 , y 2 ), (x 3> y 3 ), viz. the system is 
y x = ind. 
2 - 
V2= -j=, whence r 2 = r 3 = , 
2