104 THE STRUT PROBLEM. 
The Smith-Euler analysis as modified by the author 
e 
gives =cos 6, see later equation (18) .......... (16) 
a Le 
By expanding both series the error of (16) is only 
‘2% when vO@='l. In Engineering practice v@ is rarely 
greater than ‘Ol. 
The results just stated for exact solutions show that. 
the assumptions of a cosine curve, and of Q as a_ unit. 
maximum load have very small errors which are quite 
negligible in Engineering Design. 
Granting an essential eccentricity ‘e,’ as argued above,. 
and using equations (5) and (8) the Author deduced the 
following result :— 
l l p 
In (5) when x= — then y=e and -=4/-— from (8) 
is I’ q 
pz 
*,e@ =(a--e) cos y— — |. .2cne eee (17) 
q 2 
pa 
or-(a-Fe)=e sec! 4/s— 222 See (18). 
q 2 
Consequently curves may be plotted* showing (a+e) 
or maximum deflection in terms of ‘e’ as the load P varies ; 
when P=Qthe deflection is infinite (see Plate V). Curves 
have been plotted usually with abscissa ranging from 
q 
O to 1, showing all variations of stress as the load varies,. 
and thus the actual meaning and accuracy of various. 
formulae are clearly shown. 
The many tables and curves of the author of which 
some examples are shown*, should allow of experimental 
results being properly interpreted, and probably a formula. 
evolved, showing how ‘e’ varies with the dimensions 
end construction of practical columns: if this were known 
authoritatively the theory of design of columns might 
become as satisfactory as that of a simple beam. 
*See diagrams appended. Plates V and VI. 
