32 Hoskins—Maximum Stresses in Bridge Members. 
the strict sense of the word, but are in reality distributed over 
short distances along the track. In the actual case, therefore, 
the value of w does not become infinite, and the results of the 
above discussion are applicable. 
Even in the ideal case of true concentrated loads, such a 
series of loads may be regarded as the limiting case of a dis¬ 
tributed series, the distribution being gradually varied in any 
desired manner; and the results of the foregoing discussion, with 
slight modification in the form of their expression, may be shown 
to apply to this case also. 
When the loads are concentrated, it is usually necessary that 
a load should be at one of the four points A, B, C, D , in order 
that equation (7) may be satisfied; and in applying the equation 
such a load must be regarded as divided between the adjacent 
portions of the truss in some arbitrary manner. This state¬ 
ment applies both to the ideal case of true concentrated loads, 
and to the case of train loads as actually applied to bridges. 
We shall now consider, in the several special cases, how to 
determine the greatest among the possible maximum values of 
the stress in any member, and also how tp apply the general 
condition already deduced for distinguishing whether any 
given position of the loads corresponds to a maximum or a min¬ 
imum value of the stress. 
6. Application to Member of Loaded Chord .—Before applying 
equation (7), it is well to compare the effects of equal loads 
placed in different positions. Taking the case shown in Fig. 2, 
it is easily seen that a load on any part of the truss produces 
tension in II K. Also the effect of a load between A and C is 
greater the nearer it is to (7; and the effect of a load between 
D and B is greater the nearer it is to D. To determine the 
relative effects of loads in different positions between C and B, 
we may compare the effects of equal loads in the extreme posi¬ 
tions, C and D. By putting x=z J rl l — n x in equation (2) or (4), 
we find the tension due to a load P at C is 
PI2 d i nl ) 
it 
And by putting x = z + l x + n 2 in equation (3) or (4) we find 
the tension due to a load P at D is 
