266 
Mr Sears, On the Longitudinal Impact 
where a. is the coefficient of the linear expansion, 6 the tempera- 
ture (absolute), and K p the mechanical equivalent of the specific 
op E 6 
heat at constant pressure. The quantity — jp is very small, and 
we may therefore write : — 
_ V _ i , nr v Jt = l . l a?Ee6 
E e v 6 2 pK p v e 2 pK p 
[It is interesting to compare this result with that of Duhamel*. 
Duhamel takes the case of uniconstant isotropy (Poisson’s ratio = £) 
and gets the relation 
Ea — Ea 
1 - 
7 
E$ 6 
where 7 is the ratio of the specific heats at constant pressure and 
volume. Hence 
E a _ w — 1 Ea 7 — 1 , y ~ 
or 4 =1 + 67 = 1 ■* g - 
= 1 - 
E$ 67 
since 7 is very nearly unity. 
Now we have (Thomson and Poynting, loc. cit.) 
a 2 e e 0 
= 1 + 
a 2 e e 0 
pK p 
pE p 
where a is the coefficient of volume expansion, and e e the modulus 
of volume elasticity. 
Now, a — 3 a and, taking Poisson’s ratio = e g = \E g , so that, 
for this case, 
E<t> _ j 
E, 
crE e 6 1 a 2 e e 0 _ 7 
P K p “ i + 6 pKp - 1 + 6 
J e w 
which agrees with Duhamel’s result.] 
The following figures, with the exception of the first row, are 
taken from Wrapsonand Gee’s Mathematical and Physical Tables. 
Steel 
Copper 
Aluminium 
Ee (lbs. per sq. in.)... 
29-5 x 10 6 
17 x 10 6 
O 
X 
O 
a 
•000011 
•000017 
•000024 
p (c. G.S.) 
7-8 
8-8 
2-6 
K p (c.G.S.) 
•113 x J 
•093 x J 
•21 x J 
J= 4-2 x 10 7 . 
Todkunter and Pearson, Hist, of Elasticity, Vol. 1 . § 889. 
