Mathematical Discussion. 
88 
Pit (l2 ^ 2 ) 
Ft * 
The former of these values will be the greater if 
1% (^1 n l) ^ ll (J» n z) 
that is if 
lpl 2 l» 
The latter will be greater if 
li n 2 ^> ^2^1* 
Hence with a given series of concentrated loads, we see that, 
as a general principle, the whole truss should be loaded, and the 
heaviest loads should be brought as near as possible to C or to 
H, according as l x n 2 is greater or less* than l 2 n x . We have 
then to find some position of the moving loads which, while 
satisfying this general principle as nearly as possible, exactly 
satisfies equation (7). 
As a limiting case, n x = 0 (in which case l x n 2 is necessarily 
greater than l 2 n x ) or n 2 — 0 (which makes l x n 2 < l 2 n x ). 
Also it is possible (though unsual) that n x is negative (making 
l x n 2 > l 2 n j) or n 2 negative (making l x n 2 < l 2 n x ). 
7. Application to Unloaded Chord. —If R K (Fig. 4) is a mem¬ 
ber of the chord not carrying moving loads, we have necessarily 
either n x = 0 and n 2 = n, or n x == n and n 2 = 0. In either case 
the reasoning of the preceding case applies without change. 
In this case and in the preceding, the condition (7) may be ex¬ 
pressed in words thus: 
Assume the whole load on C D to be divided between C and D in 
the ratio of C F to F D; then the total loads on A F and F B are to 
* The limiting case between these two is that in which l 1 n 2 =l 2 n 1 , or 
h _ n x 
F 2 
That is, if the point F divides C D and A B in the same ratio, the effect 
of a load upon the stress in question is the same at whatever point be¬ 
tween C and D it be placed. 
Let A be a point between C and D so located that 
CI_ X D 
AX X B' 
Then if F is between C and A, a load will have a greater effect if 
brought nearer to C; while if F is between A and D , the effect will be 
greater the nearer the load is to D. 
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