216 
MR. L. N. G. FILON ON THE ELASTIC EQUILIBRIUM OF 
This agrees with the figures shown by Bach in his ‘ Elasticitat und Festigkeit ’ 
(figs. 2 and 3, Par. 11) of the distorted sliapes of such cylinders. There are, 
however, in the possession of Professor Karl Pearson, at University College, 
London, specimens of iron which have been strongly compressed, so that the strain 
has been large and permanent and the meridian section of the distorted curved 
surface is an obviously wavy curve, with tivo maxima, one on either side of the mid¬ 
section. With regard to the apparent disagreement here between theo]yand practice, 
I would observe tliat these specimens have been subjected to enormous stresses, for 
which the equations of elasticity certainly do not apply, and probably are not even 
an approximation; in the second place, the specimens I have seen are longer, 
compared with their diameter, than the cylinder of the present numerical example, 
so that it is easy to see why the conclusions above need not apply to these specimens. 
§ 25. Apparent Young's Modulus and Poissons Ratio. 
AVe find that the total shortening of the bar 
(IIG) 
where 
, [(% + 1)» + + 1)1 - t’ (2r + 1) 
L_J M 
Hence the apparent Young’s modulus Ey' = Qc/( 
Now if a be small, i.e., if the bar l)e very long 
and 
retaining only terms of 4th order, 
where v is the greatest integral value for which a = vnajC makes the above approxi¬ 
mation sufficient. 
