65 
~C are known, can immediately be determined as well as the corre- 
01M 
sponding point C”. 
1M 
The side .1Viy.Vl;,, must lie along the line joining this point to 
Q’,, so that the point .VI,y, can be constructed. Then .VI,y C can 
. 4M 
be drawn, by means of which y, and p,‚ are found. 
16. In quite the same way as Yar Var Par P, have been determined 
out of y,, 41, Pr, p, also Yar Yor Par Py CAN be bond out of y, ya, Par Py 
and in general 4, Uns Pn Pn Out of ys, Une Mii TR 
Any new quadruple of unknowns belonging to a following point 
of support, requires the drawing after a fixed precept of only six 
lines. 
Although for completeness’ sake the construction of the point C 
AM 
has been discussed, it will not be necessary to execute it in reality. 
For the theorem of Maxwerr teaches that y,=y,, so that C is 
LM 
directly determined. 
17. By the aid of the quantities y, p, y and gp, to be found accord- 
ing to the §§ 14 and 15, the construction of the elastic link-polygon 
of the arbitrarily charged beam can now be executed in the way 
as has been indicated in fig. 35 for a beam on 5 points of support. 
The charge is again applied in the middle of the fields, and 
amounts for the successive fields resp. to 3, 1'/,, 1'/, and 3 tons. 
First the descents A A, B B, CC... of the points of support are 
00 000 09 
determined which appear when the beam is cut above all the points 
of support. 
Then the point C is determined over which the beam ABC con- 
sidered as a al must pass. 
_ This point is determined exclusively by the aid of the link-polygon 
A’, C conjugating the point ie to the point C. For we can omit 
000 000 
the construction of the for aie: gon A’... B...C because itis only 
01 10 10 
used to determine two points C and C the situation of which gives 
100 100 
the ratio of the pieces into which the distance C C is divided by 
00 000 
the point in question C. This ratio, however, is already fixed in 
‚0 
5 
Proceedings Royal Acad. Amsterdam. Vol. XXIII. 
