70 
Proceedings of the Royal Society of Edinburgh. [Sess. 
Consider now the general case, where the load length exceeds the span 
(fig. 2). The “ control line <x6 4 is drawn exactly as has been described, 
where b 1 a 1 = W 4 , b 2 a 2 = W 2 , b z a 3 — W 3 , and b^a^ — W 4 , and the horizontal 
distances between these lines are equal to the respective spacings of the 
loads. The “ moment ” line aa^ which forms the base line of the influence 
line, is constructed in the manner already explained. The vertical ordinates 
between these two lines give the values of the reactions R as the loads 
move from the position where W 4 is at A until W 4 reaches B. 
The ordinate under A has two values, differing by W r according as W 4 
is just to the left, or just to the right, of B. 
Considering the point X on the beam, distant x to the left of B. When 
W 4 is immediately to the left of X (and the other loads are in corresponding 
positions), the positive shear at B is eqttal to the reaction m x o, where m 1 is 
distant x to the right of A. The shearing force is considered positive when 
the portion of the beam to the right of X tends to move upwards relatively 
to the portion on the left of X, and vice versa. 
Immediately the loads move so that W 4 is between X and B, the positive 
shear at X — R — W 4 , R varying as the loads proceed to the right. When 
W 4 has moved a distance p to the right of X, W 2 comes over X, and the 
