( 14 ) 
this as vertical plane of projection; the position b has now been 
indicated by two arbitrary projections. Through A we bring the 
plane N x x a, through B the plane JX 2 ±b; the line of intersection 
(NiNt) is conjugate to AB. Let us construct the transversal of (N’ l N' i ) 
and AB normal to the horizontal plane and let us bring the plane E x 
through C and that transversal. The line of intersection Y of the 
plane E x with the plane E 2 , made parallel to AB and {N X N^ runs 
parallel to the principal axis of the focal system, at the same time 
axis of the motion. 
4. We shall deduce out of Y the real position of the principal 
axis and to that end we choose fig. 2 1 ), upon which L ABC together 
with the line of intersection have been transferred. We put a plane 
By x Y and we project on it the points A, B, C with the directions 
of velocity a and b of A and B. In the figure these are represented 
revolved into the vertical plane by A„, B n , C n , a n , b n . Let us erect 
out of A r „ B n the normals on a n , b n ; these intersect each other in 
the pole P n of the motion projected on JST r The pole P„ is also a 
revolved point of the principal axis; from this follow easily the 
projections X', X" of these. 
On N y we now also project A „; in the figure A n A ni is the revolved 
projection of AA 0 ; as the pole P n is known we can construct 
the revolved projections of BB 0 and CC 0 on N y ; from this follows 
length and direction of the components BB r and CC r in the planes 
normal to the axis X; the components //X, AA t , BB t , CC t which 
must be equal to each other, are now also easy to find. 
5. Although when arranging this construction we have only 
spoken of the lines a and b and the horizontal plane we can 
generalize the supposition by assuming that a and b are the tangents 
of the points A and B of the curves described by two fixed points 
of the spacial system and that the horizontal plane is the tangential 
p ane to C of a curved surface described by a third fixed point. 
Furthermore may be observed that when only the velocity of point 
nee s constructing it is sufficient to construct the direction Y , the 
position of the axis X not being necessary. 
,Ii' e tW0 , fl?ures separated from each other are derived from a single M re 
at Delft 00 3 argC SCa ^ e ^ G. Ferguson, assistant at the Technical University 
