450 M. G. Wertheim on the Cubical Compressibility 
But without going so far as this, and without comparing 
bodies chemically different, if we attribute to a body one of the 
species of homogeneousness imagined by M. de Saint-Venant, as 
for instance cylindrical or spherical homogeneousness, or any 
other, we ought at least to be able thus to explain the results of 
the various experiments to which these bodies may be submitted. 
It would, for example, be easy to invent a molecular arrange- 
ment such that a cylindrical piezometer would possess a cubical 
compressibility conformable to that given by the ancient theory ; 
but it would be necessary to show also that this cylinder, when 
subjected to longitudinal traction, would exhibit the elongation, 
and at the same time the transverse contraction, which is shown 
by experiment, that its resistance to torsion might be determined 
beforehand, &c. 
As long as this demonstration has not even been attempted, 
all discussion on these hypotheses is necessarily futile. 
Lastly, M. Kirchhoff has just published an important memoir 
on this point, which it will be necessary for me to examine with 
the degree of attention due to the name of the author and the 
interest of the subject. Instead of indulging in mere conjectures, 
M. Kirchhoff has devised the following experiment :—A weight 
applied to the end of a lever produces simultaneously the flexion 
and torsion of a homogeneous cylinder ; these two displacements 
are measured exactly by means of an ingenious application of 
Gauss’s method; and their ratio, which is independent of the 
modulus of elasticity and the radius of the cylinder, gives by 
known formule the required relation between the elongation and 
transverse contraction. 
This method is lable to numerous objections. It would be 
difficult to imagine one more indirect and consequently more 
subject to error: the coefficient of the change of volume is deter- 
mined by two distortions, which are themselves unaccompanied 
by any change of volume whatever; this at least is what is — 
assumed in order to establish the formule, though it is not 
rigorously true ; the experiment may be considered as the flexion 
of a cylinder which has been rendered non-homogeneous by tor- 
sion, or the torsion of a cylinder rendered heterogeneous by 
flexion ; and the ordinary formule for torsion and flexion, which 
are inexact in themselves (as I think I have sufficiently shown in 
the case of the former, and as I shall hereafter endeavour to 
prove of the latter), become still less trustworthy in the present 
case. 
M. Kirchhoff’s apparatus is one of great delicacy, and. does 
not seem as if it could possess sufficient stability for researches 
of this nature ; the small dimensions of the cylinders subjected 
to experiment (less than 3 millims. in diameter, and only 145 
