BY R. W. H. HAWKEN. 105 
When this variation is known, possibly formulae 
eliminating intermediate computation based on ‘e’ may 
be evolved: this at present those of (12) and (13) attempt 
to do, but they are not sufficiently rational. 
The method of the author seems to bring into touch, 
and reconcile, the various deductions made for columns 
thus :— 
Taking as the basis the pin ended column of length / 
m2 KI 
it has an Euler value Q=—— —..... nee cece eee (19) 
/2 
All practical columns bend with a virtual length 
Q 
l'= »1/— 1 where P is the load applied .............. (20) 
Aig 
The extreme cases are for ideal conditions.* 
(a) Fixed at both ends then P=4Q and virtual length 
Q l 
Ba af = Ses Abs, DISTANT BAL. (21) 
4Q 2 
(6) Fixed at one end and free at the other then P=— 
4 
Q 
and virtual length l’=./— /=21_ ........ (22) 
Q/4 
Between these extreme cases every column bends with 
a virtual length according to the partial fixing and the 
amount of load. 
In Engineering Practice judgment will have to be 
exercised in deciding on the amount of fixing or otherwise 
to be allowed for. 
* “The deflection of a column with fixed ends does not depend on 
the eccentricity of loading. Extra strain is brought on the fixed ends, 
but not on the column itself.” (Extract from Prof. Chapman’s corres- 
pondence with the author). 
