Mathematical Discussion. 
29 
and the above equation may be written 
Putting ^ — 0, we get 
h h 
'2 
which agrees with equation (1) stated at the outset. 
The discussion has thus far referred to the case shown in 
Pig. 2. Other cases will now be considered. 
Case in tohich n x or n 2 is negative .—Considering still a member 
of the chord to which the loads are applied, a possible (though 
unusual) case is that in which the member corresponding to 
H F f in Fig. 2 is so inclined that F falls to the left of 6C (This 
case is not shown in any of the figures.) This makes n x nega¬ 
tive; and an examination of the reasoning by which equations 
(2), (3) and (4) were deduced shows that these equations are cor¬ 
rect for the present case, if regard be had for the sign of n x . 
Also, in equation (5), the limits of the definite integrals are 
correct, if n x be given its proper sign. 
If F falls to the right of D, n 2 is negative, but the results are 
still applicable. 
As a special case, F may fall at C or D, making either n x or 
n 2 zero. 
Deck truss .—If the moving load is supported at the upper 
chord, and H K is a member of that chord, the above reasoning 
may be repeated, the loads and re-actions being regarded as re¬ 
versed in direction. The result will be the same, except that 
H K will be in compression instead of tension. 
Case of Member of Unloaded Chord. 
If H K is a member of that chord at which the live loads are 
not carried, let M N (Fig. 4) be a section cutting II K and two 
other members so as to divide the truss into two parts, and let 
