of Metal Rods with rounded ends. 
265 
The static tests resulted as follows : — 
Steel 
Copper 
Aluminium 
Length of Specimen (inches) . 
16 
18 
18 
Mean diameter (inches) 
•5000 
•4985 
•5090 
Weight (lbs.) 
•883 
M24 
•3562 
Density (lbs. per cub. ft.) ... 
485-7 
553-0 
1684 
E (lbs. per sq. in.) 
29,410,000 
17,220,000 
9,972,000 
. f Bg ^ p er sec.) 
'V p , 
16,750 
12,010 
16,580 
In determining the densities iD the above table, the volume 
of the specimen was taken as the product of its length and mean 
cross-section, thus: — 
w 
9 = 7 ttc / 2 • 
t X — r- 
4 
The values of Young’s Modulus were determined in the usual way 
with Ewing’s Extensometer. Thus if W be the total load, and x 
the extension per unit length, we have : — 
7 tcI 2 
so that the formula 
v = 
v = 
Eg 
reduces to the simple form 
W l 
x iv 
— .g. Hence an error in the mean diameter will not 
affect the final result, and, the quantities l and w being determin- 
able with great accuracy, it follows that the error in v will only be 
half the error in the extensometer observations. 
The value of v, thus obtained, assumes that the waves are 
propagated isothermally, and a small correction will be necessary 
to get the true adiabatic value. If we denote the isothermal and 
adiabatic cases by the suffixes 6 and $ respectively, a process 
precisely analogous to that given in Thomson and Poynting’s Text- 
Book of Physics (Heat, pp. 288 — 9), gives rise to the formula: — 
Eg> 1 
Ea „ or Ea 6 
1 - 
pA p 
VOL. XIV. PT. III. 
18 
