626 
point of intersection of the sides „IV „V with this straight line is a 
fixed point, the point of intersection of the sides „V „VI with the 
same straight line must also be invariable. 
Consequently all the sides of the link-polygon Ay’ I, Ix HI, 
BIV «V xVIxC rotate round a fixed point. 
The series of points xC is therefore similar to the series of points 
A's. But also the series of points „C is similar to this latter series. 
For this reason also the series of points „C and ,C are similar. 
6. The double point C of these series at finite distance gives the real 
situation of the third point of support C of the beam, as it can on 
the one hand be considered as the point 0 through which the beam 
must pass on introduction of the moment of transition M/z belonging 
to C by reason of the construction of the elastic link-polygon, 
and on the other hand may be considered as the point C, which is 
found by the direct determination of the descents in consequence of 
the given charge and the moment of transition just mentioned. 
When once this point C has been determined by the help of the 
proportion ; 5 
C OC 
the required link-polygon can be dew completely, as C VIV 
must pass through P’ IW Ns VIV through JE Ry ig LY OU through 
Jes „Iv, IIL Il A’ through the point of intersection B of VIV and 
lg and finally II I through the point A (lying at a distance a 
above A’), 
The magnitude of the required moment of transition Mp is deter- 
mined by the segment BB". 
7. Although in the preceding paragraphs the beam on three 
elastic supporting points has been fully discussed, we shall before 
proceeding to the beam on four points of support, make mention of 
one more theorem bearing upon the situations, considered in a hori- 
zontal sense, of the centres of rotation veri Ill TPA ABS Jr „Iv, 
LEIP AS IY Ve 
It has already been pointed out in §5, that the situation of P4’ z 
x 
A’ A! 
is determined by the ratio. which is independent of the charge 
GX 
J5) 15 
Om: 
of the beam. 
