96 THE STRUT PROBLEM. 
The differential equation of equilibrium 
d?y 
The solution of this equation is a cosine curve 
1% 
$6. VB COB KR oe oes oe corel ae (2): 
oo 
and it has been proved that Q can have only one value, viz. 
m2 KI 
QS ee ba Use Venda Boe (3) 
]2 
which will be called the ‘ Euler Value’ or ‘Q’ of the 
COlMMD 9) ie bc ele ee es 2 + eines (5a) 
The results (2) and (3) were deduced a century and 
a-half ago by Euler; the derivation of the Euler results 
appears in almost any book on infinitesimal calculus, or 
on the theory of structures, yet it is with their meaning and 
interpretation that this paper deals, because the author 
thinks that neither has been fully nor correctly understood. 
Mathematicians and Engineers using the results (2) 
and (3) of Euler gave various explanations of their meaning, 
such as :— 
(a) the column is in ‘ neutral’ or ‘ unstable ’ equilibrium, 
(6) a deflection occurs under one load only, and is 
then indeterminable, 
(c) it is true only for long thin columns, 
(d) the Euler load always causes collapse, 
(e) and many others. 
To make clear the proposed explanation, it will be 
necessary to examine a modified case, shown in Fig. (2), 
that is, instead of the load being central it is applied with 
an eccentricity ‘e,’ the differential equation is then 
