BEAM OF RECTAXGULAIt CROS8-SECTIOX UNDER ANY SYSTEM OF LOAD. 145 
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- T7-/'d 
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- W6 
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its limiting value with very great 
We see therelore that the stretch reaches 
rapidity. At a distance from the point of application of the load equal to about U 
times the greatest breadth 26 of the bar the error in the stretch is only 3/1000. In 
fact the stretch begins to get near its limiting value at a much earlier stage than 
this, the error being less than 10 per cent, at a distance from the load of about half 
the greatest breadth. 
W^e find therefore that in this case also the distrihutton ol the load becomes 
practically indifferent as soon as we come to distances from the load which are of the 
same order of magnitude as the greatest dimension of the cross-section. As a 
practical rule, when accurate measurements are to be taken, it will be advisable 
to keep always a length varying from 1 to U times this greatest dimension between 
the points wheie the stress-system is applied and those at which measurements 
are taken. 
PAliT V. 
Solutions in Finite Terms : Special Application to the Case of a Beam 
Carrying a Uniform Load. 
§ 39. Solutions in Finite Terms. 
If in (21)-(25) of pp. 70, 71 we write 
X ^ wnf (A' - *®") j 
. . . (109) 
VOL. CCI.—A. 
u 
