THE PLASTICITY OF SOLIDS 237
Since the flow is of the nature of local slippage rather than true
plastic flow, strains accumulate and they remain after the stress
is removed. The result is the same as that observed by Trouton
in pitch, in that the substance tends to creep slowly back toward
its old position of rest during a period of time which in pitch is
comparatively short but may be observed in metals for hours or
even days. The elastic "after effect" has been the subject of
exhaustive investigation by Weber (1835), Warburg (1869),
Kohlrausch (1863-76), Boltzmann (1876), G. Wiedemann (1879),
Pisati (1879), Streintz (1879), Rakkuk (1888), Wiechert (1889)
and others.
Kupffer (1860) was inclined to attribute this partial flow of
the metal to what he would denominate the fluidity of solids
in analogy to the fluidity of liquids. He says, "II paratt que
les molecules des corps solides possedent la propri6t£ non seule-
ment de s'6carter les unes des autres en produisant une resistance
proportioned aux hearts, mais aussi de glisser les unes sur les
autres, sans produire aucune effort. Cette propri6t6 est poss6d6e
a un haut degr6 par les fluides; je le nommerais volontiers la
fluidity des corps solides; le coefficient if/ pourrait £tre appel£
coefficient de fluidity; la mall6abilit6 des metaux parait en d6-
pendre et peut-etre aussi leur duret£." According to the present
views we would say that this partial flow was evidence of low
friction or high mobility.
In harmony with this view, it has been found 'that the logarith-
mic decrement of the amplitude of vibration is low in hard metals
like steel and high in soft metals like lead. The logarithmic
decrement also increases as the temperature is raised but in this
respect iron and steel are exceptional below 100°C according to
Kupffer, Pisati, and Horton (1905). It will be recalled that
sulfur presents a similar exception in the case of liquids.
According to this view, the elastic limit is reached when the
shearing stress is equal to the friction constant, for at this value
of the stress the material begins to yield. But since the deforma-
tion takes place with exceeding slowness at this particular stress,
a wire may be loaded considerably beyond the elastic limit before
the flow becomes appreciable. The yield point naturally depends
to some extent upon the rate with which the load is put on.
Just as Trouton found that a given shearing stress produced a