Stress and Strain on the Properties of Matter. 517 



sured at ten different places equidistant from each other by a gauge 

 graduated to T^th of a millimetre, and capable of measuring by 

 estimation to 10 1 00 th of a millimetre. The accuracy of the gauge had 

 been repeatedly tested on previous occasions, and could be depended 

 upon at least to 1 p^o th of the diameter of the wire : nor would any 

 error of consequence be introduced in the determinations of either the 

 length or mass. 



The following were the results : — 



Number 

 of piece. 



Length, in 

 centimetres. 



Mean 

 diameter in 

 centimetres. 



Mass in 

 grams. 



Densitv at 

 20° C. 



1 



162-5 



0-08736 



1-6910 



1-736 



2 



123-0 



0-08671 



1-2742 



1-754 



3 



1315 



0-08723 



1-3670 



1-740 





0-08710 





1-743 



The probable error in the determination of the density in this way 

 would therefore appear to be - 2 per cent. But values of " Young's 

 modulus " obtained by the method of longitudinal vibrations are apt 

 to be slightly too high in the case of wires in consequence of slight 

 yielding of the supports at either end of the wire.* It was therefore 

 deemed advisable to employ also the static method, and accordingly a 

 pair of wires were suspended and examined in the manner already 

 described in Part I of this memoir, and with the same precautions to 

 avoid error, f " Young's modulus " as thus obtained proved to be 

 424*3 X 10 6 grams per square centimetre. It was impossible, however, 

 in this instance to have any but a comparatively small load perma- 

 nently on the wire, and in such a case the result is apt to bte too low 

 to a slight extent. We may, I think, then, find a very near approach 

 to the true value by taking the mean between the values got by the 

 two methods : this mean is 430 '8 + 1 6 grams per square centimetre, 

 and is, I should say, certainly less than 1 per cent, in error. 



From "Young's modulus" and the simple rigidity the ratio of 

 lateral contraction to longitudinal extension can be calculated ; this 

 ratio would be — 



430-8 xlO 6 _-. 

 2xl72'3xl0 6 ' 



* It might be thought that any kind of yielding would depress the pitch of the 

 •wire, but the mathematical investigations of Lord Eayleigh as given in his " Theory 

 of Sound," vol. i, p. 161, show that with transverse vibrations there would be in 

 the case before us an increase of pitch. Rayleigh's investigations will equally 

 apply, as far as the point in question is concerned, to longitudinal vibrations. 



t Loc. cit., pp. 2-4 inclusive. 



