72 
Proceedings of the Poyal Society of Edinburgh. [Sess. 
and the inclined portions of the influence lines are not necessary in 
such cases. 
In the case dealt with, the several maximum positive shears are 
om v on v om 2 , om 3 , and om 4 , of which om. is the greatest; while the 
maximum negative shears are on 2 , on z , and on 4 , the last being numerically 
the greatest. 
By dividing the span into a number of equal parts, say ten, and the 
four parallel-sided figures into an equal number of parts, the greatest 
positive and negative shears for each of the several points in the beam 
may be determined by inspection. From these a diagram of maximum 
shears (fig. 4) can be drawn. In practice, the maxima values can be 
obtained by means of tracing paper. 
To save confusion, only one of the four diagrams has been so divided. 
It is to be observed that the ordinates of the figures — 1 to 10 — are 
numbered in the reverse direction to the points on the beam. 
The diagrams, figs. 3 and 4, have been drawn to scale for the case where 
W 4 = 2, W 2 = 7, W 3 = 3, and W 4 = 9 tons; p = 3, q = 4*5 and r = 6 feet. A 
scale of shearing force is attached to the diagram in fig. 4. 
{Issued separately May 9 , 1921 .) 
