63 
immediately known, as the point A remains in its place and AB 
remains straight. *) 
145. If the end B is charged by a moment of 1 metreton, the point 
A rises by an amount AA;y, while the point B descends by an 
amount 55. As the sides A17 3,,, and 3, B must cut a segment 
iM 1M 
of known length from /, the former, hence also the latter, is known. 
B 
Consequently the angle of inclination (7,) and the descent (y,) at 
B can also for this charge be found in a very simple way. 
15a. We can now proceed to the treatment of the beam ABC 
charged at its extremity C by 1 ton. 
If the beam is cut above B, the point C descends by an amount 
CC=u. The beam AB remains uncharged. The construction of 
017 
the elastic link-polygon furnishes therefore the straight line ALC; 
the point C coincides with C. 
017 
If then a moment of transition of 1 metreton is introduced at B, 
{ 
the point C rises by an amount C C= so that C is known. 
0,17 it by Cis i LP 
No more does the construction of C by the aid of the elastic 
i We 
link-polygon give rise to difficulties. The introduction of the moment 
of 1 metreton above B will cause the point of support B to des- 
= 1 
eend by an amount B B=y, + —y,, while the side III] B assu- 
re Ey Va? 
mes an angle of inclination Dy -+ ma 
The side III, B IV‚r (indicated in fig. 30 by the line P, B) 
tives gn 
can therefore be drawn, hence, also the side ,IV,7,C, since this side 
17 
together with III, ‚IV‚r must cut a segment of known length 
from /p. 
It is clear that the sides IIL, xIVi7 belonging to the different 
moments of transition J/g—.w metretons, pass through one fixed 
point P, on AB, because the descents of the point B as well as 
x 17" 
the angles of inclination of the side ,III, „IV‚r increase in propor- 
1) The angles of inclination 9 are replaced in the usual way by their tangents. 
These tangents are read in fig. 34 on perpendiculars drawn at distance one to 
the right of the different points of support. 
