1540 
dlogu 
— by means of the values 
Og v 
found for a and 6. Let us suppose the metal to be stretched equally in 
all directions, so that there is an infinitely small eubical dilatation 
dlogv. Then we have according to (21) in which expression we 
must put x=y=2z=—4 dlogv, 
du = $(2u + 2a4b) d log v, 
dlogu 2u + 2a+b 
dlogv Ju 
$ 15. We can further calculate 
To calculate from this the coefficient of dilatation, we shall 
suppose that, when the volume is increased, 2 and « change propor- 
tionally to each other. 
The differential coefficient in (17) then becomes 
„ dlog u 
2 : 
d log v 
and the formula itself 
___,dlogu IE 
VU, = 24 -—1]|E. 
: 3 dlog v i 
Treating the coefficient of / as a constant (comp. § 9) we find 
from this for the coefficient of cubical expansion 
1 lox 
== DA eme ie 1 | Aco. 
* dlog v " ; 
If the coefficient of compressibility x is derived from 2 and wu, 
this equation gives the following results: 
Pr | ro 5 | vii a 
dlog tl x Cc o == 
| dlogv calc.” |” Obs: 
| | 
Steel 1 234, die | 0,11 | 18 | 32.105 | 33.105 
y 2 Ss ODI OL fees: 3,6.10—5 | 3,3. 10 
Copper | | 7,7.10—13 | 0,093 89 | 28.105 | 5,1.10—5 
The only inaccuracy in the above calculation of the terms in (41) 
corresponding to transverse vibrations is the application of the 
ordinary formulae of the theory of elasticity to very short waves. 
For the determination of the terms referring to the longitudinal 
vibrations, however, we had to make the assumption that 4 changes 
proportionally to uw. As however the transverse vibrations have a 
greater part in the heat motion than the longitudinal ones we may 
