67 
ences the situation of the point C. According to § 15 this point 
0 
a Dees. 
rises by an amount C C=-—~y,, in consequence of which the line 
00 He a 
. . 4 
6) as which in absence of Mp contained the centres of rotation 
of the ‘tides VI VII and VII VIII, must be replaced by the line 
ie 4 Now the point Q,"" of en line is already determined as 
a 
the Becton of lg,” with the side VIII VII, so that P,', through 
which VII VI must pass, can be found as the intersection of Q," Q," 
with /p,. 
After VII VI we can draw VI V through C", V VI being again 
determined by the known segment which VI. V and V IV must 
cut from lp. 
Now V IV determines again on /g," a point Q,"" through which 
the line A’, Q,” can be drawn, which intersects /p, in the point 
P,’ of the side IV III. The completion of the link-polygon does not 
present any difficulties. 
" wm 
18. It appears from the preceding considerations, as was indeed 
already noted in § 2, that with the beam on five points of support 
the subject mentioned in the title of this paper has been treated 
generally, save for the restrictions made, that the fieldlengths of the 
beam as well as the coefficients of stiffness of the elastic supports 
are supposed to be equal. 
These restrictions, however, do not affect the general soundness 
of the construction. 
If for instance the fieldlengths AB and BC (fig. 1) were unequal, 
the sides II III and IV V would indeed not meet on /g, but at 
any rate on a perpendicular dividing the distance dr /rv into pieces 
which are inversely proportional to the fieldlengths AB and BC. 
Neither is the inequality of the coefficients of stiffness of the 
springs essential. If e.g. for the beam ABC with the fieldlengths 
AB=L, and BC=L, the coefficients of stiffness of the springs 
are a, 8, y, the extra descents of the springs which appear when 
the beam is cut above B in consequence of the introduction of a 
moment of transition of 1 metreton, will be oa te —+ 
sf 
; eee ft , | 
instead of EE oS = This alters indeed the values of the 
segments A’, A’, BB, ,C,C, but not essentially the construction 
0 1 
itself. 
5* 
