631 
lie perpendicularly above the centres of rotation Piro ine en IN 
P Ivo „Vo On & straight line through A’,,, determined by the point Ze 
8 i 
lying © above B. 
L 00 
As on introduction of the other moments of transition Mc=y 
meterton there appear points B, defined by B, B=y. B, B, it is 
Oy 00 Oy 00 01 
evident, that the centres of rotation mentioned, undergo vertical 
displacements, which are proportional to these moments. 
Especially at the introduction of Mc = y metreton the 
; 4 : : 
segment P'_1vo Vo P IV, iy will be equal to y times the segment 
Ua / 
P x!V9 xVo P „IVi Vr: 
On account of the law of superposition, on which the whole 
problem is founded, the descent C C of the point C will increase 
5) cal 
in direct ratio to the value y of the moment of transition Mc. 
The distance of the point C" to the point C can therefore be 
y 0 
put equal to: 
y .(C" C—C C). 
ott oil a) onl 
The lines (EAN aie C") connect therefore corresponding points 
x Vy 3 e 
of two similar series of points; they pass through one point. 
As VI, .VI, can be linearly expressed in C" C and P’ rv, ‚v‚, 
ay 0 ¥ 8 
P’ iv Vix the series of points .VI, is also similar to the series 
yx 
C, so that the lines .VIy, ‚VII, too have a fixed centre of rotation 
P ‚vj But then also the sides VII VIII and VIII D have 
„VI VII sy) Ly y y 
fixed centres of rotation P vu ‚VII and P* vil ‚VIT 
The series of points „D is therefore similar to the series C", C, 
y LY 
P’ tv, „v‚--- which in their turn are similar to the series ,D, for 
yxy J 
which holds good: 
yD oD=y XD oD. 
Hence the series of points D and D are also similar. Their 
double point D at finite distance is the extreme point of the 
link-polygon in question for the beam on four points of support. 
Now that this double point is known, the construction of the 
whole link-polygon no longer presents any difficulty. 
