14 
MR. H. TOMLINSON ON THE INFLUENCE OF STRESS 
Discussion of Wertheim’s Experiments on Elasticity." 0 
The values of “ Young’s modulus” obtained by Wertheim by vibrations, longitu¬ 
dinal or transverse, are generally larger than those got by static extension ; and these 
differences are considerably greater than those which would be produced by the heating 
and cooling effects of contraction and elongation. 
Sir W. Thomson sayst that “ it is probable that his (Wertheim’s) moduli, 
determined by static elongation, are minutely accurate ; the discrepancies of those 
found by vibrations are probably due to imperfections of the arrangements for carrying- 
out the vibrational method.” I venture, however, to believe that the main cause of 
the above-mentioned discrepancies is to be found in Wertheim’s mode of proceeding 
when determining the elasticity by static extension. The plan adopted by him was to 
put on a weight, take a reading with the measuring microscope, and, after removing 
the weight, take a second reading, the difference between these two readings being- 
used in determining a value for the modulus. The same operations were repeated 
with greater and greater loads until the wire underwent very considerable permanent 
extension, and was in many cases broken. The mean of all the values thus obtained 
was taken to represent the true one. 
Now, if, after considerable extension had taken place, Wertheim had repeated his 
trials with each of the previous weights, he would have obtained appreciably different 
values, and the general result would have been to give him a greater mean value for 
the elasticity. Moreover, my experiments have shown, as we have seen, that, even if 
all precautions be taken, different loads will give different values for the elasticity. 
The best way of comparing the methods of static extension and longitudinal vibra¬ 
tions would be to determine, first, the elasticity by the former method with small 
loads, and then to use the latter method with the same wire under as nearly as possible 
the same conditions of tension. I hope at some future time to be able to make further 
experiments in this direction; but in some few trials with copper, iron, steel, and 
German-silver I have obtained values for the elasticities by the two methods which 
accord more nearly with each other than those got by Wertheim. 
In order to ascertain whether the influence of rest—which in iron is so marked in 
increasing the value of “ Young’s modulus ” as determined from static extension— 
would be equally or at all apparent when longitudinal vibrations are employed, several 
experiments v'ere made on iron by the latter method, both the syren and Appunn’s 
tonometer being employed for the purpose of counting the number of vibrations. 
Both these instruments gave very consistent results, and could be depended upon 
within at least \ per cent. ; yet no difference could lie detected between the note of 
the wire after recent permanent extension and that after a rest of 24 hours. As it 
was thought that perhaps the act of vibrating the wire might immediately produce the 
* Ann. de Chim. et Phys., tom. xii., 1844. 
f ‘Brit. Encyc.,’ Art.: “Elasticity,” § 77. 
