178 C. K. Wead—Intensity of Sound. 
C. Physiological questions; the loudness of sound, etc.; 
something of this must be anticipated under A and B. I have 
found very little in print bearing on A, more will be cited 
under B, while much has been done on the physiological side. 
I. Tur Tunine Fork. 
All bodies of class A are deformed at the outset by a blow 
or otherwise; the potential energy thus acquired may be meas- 
ured with comparative ease in some cases as will be seen; let 
the calculation and measurement of this be the first problem. 
In any elastic body, within the limits for which Hooke’s law 
is true, the potential energy of the distorted body =V=4Wa,: 
where W= the force applied, and a= the distance through 
which the point of application of the force moves. = the 
force when a=1, then (1) W=Pa and (2) V=$Pa?. Since 
practically a fork is very nearly a representative of a bar fixed 
3 
at one end and free at the other (3) a= where /= the 
length of the prong, b= its breadth, d= the thickness, and H= 
Young’s modulus; for steel H=2-14X101?2 in C.G. S. units 
(Everett), and for Kénig’s forks b6=1-4em. and d=0°65 cm. 
approximately; therefore (4) P=2-056x1011+/3= the force in 
ynes, which applied at the end of the prong will bend it 
lem.; and 
(5) V=4Pat= 
1°03 K 1011q@2 
B Ergs. 
It would be more convenient to express V as a function of 
N, the vibration-frequency, than of /; this may be done by Mer- 
cadier’s formula;* here as before d= the thickness in em., /= 
the length of the prong, which I take as the length from the 
upper side of the stem plus half the thickness, and the constant 
is determined so as to satisfy best the observations; the average 
difference between the observed and computed values of N 1s 
a little less than 1 per cent. The Ut, and Sol, are thinner 
than the others and so relatively shorter, and were omitted 1D 
determining the constant; besides Ut, is not uniform 19 
thickness. 
(6) N=82550d+/?. Therefore 
(1) P=16540N%, (8) V =4x16540N4a?. 
For Ut, =128 d. v. 9) V,=$xX 23°94 x 108a*® Ergs. 
For any other fork of this series of harmonics of Ut, if 
represents the number of the harmonic, : 
* Comptes Rendus, Ixxix, 1001, 1069. 
