654 PROCEEDINGS OF SECTION H. 
The extension of the method to more complex cases is 
comparatively easy. Let us suppose the bracket or canti- 
lever in Fig. 1 extended by another triangle or panel as in 
Fig 3, and stressed to the same degree as before. Then, in 
Fig. 4, the part shown in full lines is identical with Fig. 2. 
OB. represents in magnitude and direction to the enlarged 
scale the movement of B. To find that of D we proceed as 
follows:—Draw OD , to represent the movement of D due 
to the shortening of DC, OD , its movement in the direction 
BO due to the motion of B from O to B,, being the resolved 
part in that direction of the motion OB,, and D,D, the 
motion in the same direction due to the elongation of BD. 
Then, drawing the perpendiculars D,D,and D,D,, we 
find D, and OD, is the total motion of D and D, D,, the 
deflection of the cantilever. D,D ,of course ought to be an 
are of a circle of 200 feet radius, and D.D,one of 140 feet 
radius, but the difference between them and the perpen- 
dicular is imperceptible under the conditions of ordinary 
draughtsmanship. 
The extension of the system from catilevere to ordinary 
trusses supported at the ends presents but little difficulty. 
It is merely necessary to treat each as a pair of cantilevers, 
regard the central point as fixed, and finding how much 
the ends move upward relative to it. This will give the 
deflection, which can then be compared with the actual 
measured deflection of the structure under its test load. 
The subjoined example will illustrate this, and the various 
steps are indicated by the lettering. C is taken as the 
reference point or origin. 
In this diagram— ‘ 
CD, =upward motion of D due to shortening of CD 
CB, = motion of B due to motion CD, 
BB ditto lengthening of BD 
CBs. = ditto shortening of BC 
CB, = resultant motion of B 
CE, =notion of £ due to lengthening of HD 
CPs ditto upward motion of B 
Eski — ditto shortening of BE 
CH, = resultant motion of H 
CA, -=‘motion of A due to motion CH, 
A, A® — ditto lengthening of A 
CA, ar - ditto shortening of AC’ 
CA, , = resultant motion of A 
A.A, = Deflection of centre of truss when loaded to a 
scale 10 times full size. 
