9S THE STRUT PROBLEM. 
would not acknowledge any practical meaning* of result 
(3) or the ‘German Rule,’ as he called it, though admitting 
the accuracy of the mathematics. He deduced l’ of (6) 
72 EI 
as ,/——~ but saw no practical application in his result.f 
P . 
Apparently he did not realise that he was virtually repeating 
Euler’s analysis. 
Smith’s work was somewhat neglected by subsequent. 
writers; in many Engineering text-books it is not 
mentioned,t but, later, equation (7) has been quoted as 
‘Professor Smith’s Formula,’§ but often under a special 
heading of eccentrically loaded columns. 
The author|| (who at the time did not know of Smith’s 
work) put the solution of the differential equation in the 
form shown in (5) and (6) and using (6) has proceeded as 
follows :— 
z?KL Qi? Q 
since P=——-=—— ..]' =1/—.l 
‘hes l? r 
eae (8) 
Q P q 
or if gq =— and p =— then l’=,/—. 
A A p 
that is to say, every column bends as if it has a ‘ virtual 
length,’ according to the load applied, provided Q is 
assumed a constant. He adopted lst (with Smith) the view 
that there is an ‘essential eccentricity’ of loading small 
or large according to practical conditions of making and 
adjustment; 2nd, that absolutely central loading is a 
mathematical conception only, but (in disagreement with 
Smith) the ‘ Euler Value ’ ‘ Q’ has a very practical applica- 
tion, as will be shown below. 
*See Footnotes, pages 101 and 102 ; also pp. 36,37, “Column Analysis 
and Design.” 
See pp. 35, 36, 37 of paper by author, ““ Column Analysis and Design.” 
{Vide Morly “Theory of Structures,” who solves the differential 
equation (4) and apparently was not aware of Smith’s work. 
§Jamieson “‘ Applied Mechanics.” 
||Vide Proc. Inst. C.E., Vol. 204, paper No. 4207. 
