18 THE ROYAL SOCIETY OF CANADA 
Each of the above values for the q’s, except that for tin, was de- 
termined by Wertheim by a statical method; in the case of tin the 
value of q was determined from transverse vibrations. 
In the paper referred to Wertheim gives results for Young’s modu- 
lus for the various metals by methods involving (1) direct elongation, 
(2) transverse vibrations, and (3) longitudinal vibrations. The agree- 
ment between the values obtained for the same metal by direct elonga- 
tion and by vibration differ in some cases by as much as 20%. 
Regarding these results Lord Kelvin wrote:—“It will be seen that 
Young’s moduli obtained by Wertheim by vibrations, longitudinal or 
transverse, are generally in excess of those which he found by static exten- 
sion ; but the differences are enormously greater than those due to heating 
and cooling effects of elongation and contraction and are certainly to 
be reckoned as errors of observation. It is probable that his modulus 
determinations by static elongation are minutely accurate; the dis- 
crepancies of those found by vibrations are probably due to imperfec- 
tion of the arrangements for carrying out the vibrational method.” * 
A glance at the published tables of the elastic constants of various 
substances would suffice to show the utter uselessness of trying to test 
the formula showing the relation between q and q’ for any substance 
by any method except finding directly q and q’ for the same specimen. 
of a given material. The purpose of the experiment described below 
was to find these two Young’s moduli for a given specimen by direct 
methods in order to get the value of the ratio q:q’. The adiabatic 
Young’s modulus was found by determining the velocity of sound in a 
brass rod by means of Kundt’s well known dust-tube method and 
applying the formula:—V — \ > The static method used was that 
based on the observation of the bending produced in the rod when it 
was supported on two knife-edges and a weight was applied to the 
middle of the bar. 
1. Determination of the Adiabatic Young’s Modulus. 
The Kundt method is so well known as to need no description here. 
The air and powder in the closed tube were carefully dried by blowing 
a slow current of air through a tube containing phosphorus pentoxide 
and afterwards through the dust tube. The distances between the 
1st and 7th, 2nd and 8th, ete., dust heaps were measured by means of 
a microscope which was placed so as to view also a standard yard placed 
just below the tube. The microscope was provided with a scale and 
3 Loc. cit. 
