511 
of Edinburgh, Session 1865 - 66 . 
where M denotes the Young’s modulus of the substance for con- 
stant temperature, s its specific heat (per unit mass, as usual), e 
its longitudinal (linear) expansion per degree of elevation of tem- 
perature, p its density or specific gravity,* and t its actual tempera- 
ture from absolute zero (“ Dynamical Theory of Heat,” Part VI., 
§ 100), that is, temperature centigrade with 274 added. Of course, 
if M is reckoned (“ Thomson and Tait’s Natural Philosophy,” 
§§ 220, 221, 238), in gravitation measure (weight of one gramme, the 
unit of mass), J must be reckoned in gravitation measure (grammes 
weight working through one centimetre), in which case its numeri- 
cal value is 42,400, being Joule’s number (1390), reduced from feet 
to centimetres. Values of surface resistance to gain or loss of heat 
in absolute measure, derived from experiments by the author, are 
used to estimate the etfect of radiation and convection in dissi- 
pating energy in virtue of the thermo-dynamic change of tem- 
perature in a rod executing longitudinal vibrations. The velocity 
of propagation of longitudinal vibrations (as in the transmission of 
sound along a bar) being equal to the velocity acquired by a body 
in falling through a height equal to half the “ length of the 
modulus,”! is, of course, half as much affected as the modulus, by 
changes of temperature. In iron, for instance, the effect of change 
of temperature, when there is no dissipation, is an increase of about 
one-third per cent, on the Young’s modulus, and of about one- 
sixth per cent, on the velocity of sound along a bar. The effect of 
the conduction of heat in diminishing the differences of tempera- 
ture in a rectangular bar executing flexural vibrations, is investi- 
gated from the solution invented by Fourier for expressing periodi- 
cal variations of underground temperature. Its absolute amount 
for bars of iron or copper, of stated dimensions, vibrating in stated 
. . ^ 
periods^ is determined from Forbes’ and Angstrom’s conductivities. 
It is proved that the loss of energy due to this effect at its maximum 
is not by any means insensible, though it is not sufficient to account 
for- the whole loss of energy which the author has found in experi- 
* Which, when the French system (unit bulk of water being of mass unity) 
is followed, mean the same thing 
f The “ length of the modulus ” is M-^p, if M be the modulus in grammes 
weight per square centimetre . — Thomson and Tait's Natural Philosophy, 
I 689 . 
3 X 
VOL. V, 
