Mathematics. “Graphical Determination of the Moments of Transition 
of an Elastically Supported, Statically Indeterminate Beam’’. IL. 
By Prof. C. B. Biezeno. (Communicated by Prof. J. CARDINAAL). 
(Communicated at the meeting of December 29, 1917). 
12. In quite the same way as it has been attempted in § 8 to 
prepare a transition from the case of three points of support to that 
of four, it might now be tried to use the construction just found 
for the treatment of the beam on five points of support, by cutting 
it above its last point of support but one and charging it there by 
a moment of 0,1,2,... metretons. We are, however, arrested by 
two difficulties. In the first place the amount of drawing required 
becomes so extensive, that it is impossible to avoid mistakes. In 
the second place, however, an obstacle arises which has not yet 
been able to manifest itself in the case of the beam on three or 
four points of support. 
When the beam has been cut above the fourth point of support, 
it is among others necessary to construct a link-polygon for the left- 
hand part on four points of support after applying a moment of 
transition of one metreton above the last point of support. 
In the construction, however, of this link-polygon the beam on 
four points of support is again cut above the third point of support. 
Consequently this will be charged besides by the given forces acting 
Ì 
on ABC, by a force of, ton, directed upward and originating from 
the introduced unit couple Mp. 
Of course a similar thing happened in the case of the beam on 
four points of support above the second point of support. But there 
UL : 
the ascent 7 of the second point of support, due to the extra force, 
was known, because the remaining lefthand part of the beam was 
only supported at two points. Here the ascent of the third point of 
support is not known, as the unaltered lefthand part of the beam 
is itself statically indeterminate. 
And although it would of course be possible by the aid of $$ 3—7 
to determine the ascent which the righthand end of the beam ABC 
supported at three points, would be subject to in consequence of a 
