8 REPORT—1868. 
“ These words define, as precisely asif they had been written for the express 
urpose, the aims of the present proposal. It is for this powerful and enlightened 
Bo y to consider whether such an investigation of the subject shall be instituted 
as may serve to direct and impel public opinion in a channel which the educated 
classes of Englishmen seem now disposed to enter—insisting on the value and the 
comparatively backward condition of physical research, and indicating the means 
best fitted to place at man’s disposal, systematically and promptly, the intellectual 
pee and the material riches which a bounteous Providence has created for 
is use. 
MatHeEemarics. 
A historical Note on Lagrange’s Theorem. By W. Barrett Davis. 
On a new Correction to be applied to observations made with Hadley’s Sextant. 
By T. Doxson. 
Résumé of Experiments on Rigidity. By Professor J. D. Everurt, D.C.L. 
After pointing out the relations which connect Young’s modulus of elasticity, 
simple rigidity, resistance to cubic compression, and the ratio of lateral contrac- 
tion to longitudinal extension, in isotropic substances, which relations are such that 
if any two of these coefficients are given the other two can be inferred, the author 
proceeded to describe the method by which he had determined experimentally the 
values of the two first-mentioned coefficients, and had hence derived the values of 
the other two. The method consisted in applying a given couple to bend and 
twist alternately one and the same portion of a cylindrical rod. The especial object 
of investigation was the coefficient called ‘ Poisson’s ratio,” that is to say, the ratio 
which the lateral contraction of a rod bears to its longitudinal extension when it is 
forcibly lengthened within the limits of elasticity, which ratio was erroneously sup- 
posed by Poisson to have the constant value + for all substances. 
In order to determine the value of this coefficient for any particular isotropic 
substance, it was only necessary to compare the amounts of bending and twisting 
aeened in a given portion of a cylindrical rod by couples of equal moment. 
et T denote the amount of twisting, F the amount of bending, and o Poisson’s 
: TT 
ratio, then c= F- if 
In this way the following values of o had been found for one specimen of each 
of the undermentioned substances :—flint-glass, ‘229; drawn brass, -469; drawn 
steel, ‘310; wrought iron, ‘275; cast iron, ‘267; copper, ‘378. 
Examples of Ocular Demonstration of Geometrical Propositions. 
By Axrravur GEARING. 
The object of this communication was to demonstrate the possibility of any 
given geometrical form or forms being reduced to any other required geometrical 
figure without loss of material, and of equal area to the given number of contained 
counterparts. 
As tests for instrumental measurements and as discipline for the hand of the 
artist, the series suggested exact and interesting exercises in practical geometry, 
and might be used in the economy of adjusting materials. The examples (above 
50 in number) comprise the reduction of regular polygons of any number of sides 
to squares and other figures with the same identical number of counterparts, each 
figure having some special distinction. The whole series could be cut out in paper, 
and a given figure made into another figure, thus constituting by ocular demon- 
stration an additional means of testing great geometrical truths as a pleasing ex- 
perimental exercise. 
