BY R. W. H. HAWKEN. 103 
This view is confirmed by the solution of (14) using 
elliptic functions by R. W. Burgess,* he shows that each 
central load is accompanied by a definite deflection, and, 
as was to be expected, that the cosine curve is quite 
dy 
inaccurate when the slope (:) becomes appreciable. 
dx 
Keeping to the assumption of Q as a unit basis for all 
loads for the column and putting H for the actual central 
load, some figures of Burgesst have been put into the form 
of Table I. 
TaBLe I. 
wp Corresponding values of 
Values of -;/— for | In the Author’s Deflection 
2q | notation. a/l, i.e. ————— 
pin-jointed columns. | Length 
1.57080 er — GO) 0.0000 
1.57092 H=1.00014 Q 0.0111 
1.58284 H—1O1@ 0.1097 
The figures of Table I. show that for any deflection 
to take place the load must be somewhat greater than Q, 
Q 
but when the load is —— greater than Q, the deflection 
7500 
is 1% of the length, an amount beyond that usually allow- 
able in Engineering practice, so that the error in assuming 
Q as the unit maximum load is less than 1 in 10,000 ; yet 
Q is not necessarily a load causing collapse, nor is there 
instability even for a central load. 
Professor Chapman, of Adelaide University, has 
deduced by exact analysis for eccentric load 
e a+e pz 
that =cen (6, v6) where v=—— and 6 = 1/- —- 
ate l q 2 
ae. pis 
and thus v@= /—— :...(15) 
l q 2 
*Physical Review, March, 1917. 
tThe table has been prepared by the author in the way shewn from 
figures kindly supplied by Professor Chapman, of Adelaide University. 
See Proc. Roy. Soc. South Australia, Vol. xlii, 1918. 
