of the Physical Properties of Iron. 251 



into longitudinal vibrations, so as to produce a musical note, 

 the pitch of this note becomes lower as we raise the temperature 

 even when the wire is heated for the first time.* 



It seems rather strange that the error should have been so 

 long allowed to remain uncorrected ; for it has been known 

 for many years that the pitch of a steel tuning-fork is lowered 

 by small rises of temperature to a greater extent than would 

 follow from mere change of dimensions. Calling the fre- 

 quency of the fork n we havef 



K n s * \ 



n= 2rf m ' W 



where m is an abstract number, 



b is the velocity of sound in steel, 

 I is the length, 



k the radius of gyration of the section about an axis 

 perpendicular to the plane of bending. 

 If D be the thickness of the fork, 



K= D 



We mav therefore obtain § 



* 47TV3* 2 



b= \- ^-n 2) 



From (2) and the value of the coefficient of thermal expan- 

 sion of steel, it follows that if the pitch of the note is lowered 

 by rise of temperature to the extent to which it is known to 

 be, the velocity of sound must be lowered also. Indeed from 

 the coefficient of thermal expansion of steel and from my own 

 determination of the effect of change of temperature on the 

 longitudinal elasticity of steel, I have calculated what would be 

 the lowering of pitch of a certain fork, and find it in sufficient 

 accord with the lowering of pitch as determined by direct 

 experiment. 



Wertheim inferred the increase of velocity of sound in iron 

 and steel from the apparent increase of longitudinal elasticity 

 produced by rise of temperature. From his experiments on 

 the longitudinal elasticity of these metals I have collected the 

 following : — 



TVf-x-i Increase per cent, of elasticity 



lueiai ; between 15° to 20° and 100° C. 



Annealed iron 4*90 



Annealed iron wire 6*91 



Annealed cast steel 2' 79 



Annealed steel wire . . . . . . . 23*20 



Steel tempered blue 5*18 



* The lowering of pitch produced by rise of temperature was shown 

 before the Society. 



t Lord Rayleigh's < Theory of Sound/ vol. i. p. 219. 



