364 Proceedings of Royal Society of Edinburgh. [sess. 
exterior tending to the attainment of the convergence temperature, 
and on the other hand a compensation for this by the formation or 
fusion of ice, heat being thereby produced or absorbed, and the 
system tending in consequence to its true freezing point. The 
thermometer after a time becomes stationary at an apparent 
freezing point, which lies between the true freezing point and the 
convergence temperature, and may differ from the former by a very 
considerable amount. The divergence between the true and 
apparent freezing points depends on two factors. First, it depends 
on the difference between the true freezing point and the con- 
vergence temperature, and, second, on the rate at which ice is 
formed and dissolved. If the convergence and true equilibrium 
temperatures are identical, the thermometer will evidently give the 
true freezing point. The true freezing point will also be registered 
if the rate of formation or fusion of ice is infinitely great, for then 
the compensation for heat exchange will be instantaneous and 
complete. 
In most of the accurate work hitherto done, attention has been 
paid to the first mode of securing the exact freezing point — that is, 
by suitably tempering the bath in which the apparatus is immersed, 
the convergence temperature has been nearly adjusted to the freez- 
ing point which it is desired to determine. The external bath is in 
such a case at a temperature a little below the true freezing point, 
so that the heat gained from the room through the thermometer, 
stirrer, etc., is lost to the external bath, and so the influence of the 
exterior is on the whole reduced to zero. It must be remembered, 
however, that this mode of external compensation is only theoreti- 
cally perfect if the ivhole environment is at the same temperature, 
i.e ., the freezing point. In actual practice, the external bath is 
below the convergence temperature, whilst the upper parts of the 
thermometer, along which conduction takes place, are above that 
temperature. When the freezing point experiment takes place, 
therefore, although ice on the whole may neither be formed nor 
dissolved, local formation of ice near the external bath, and fusion 
of ice near the thermometer, stirring apparatus, etc., must occur, so 
that constant stirring must be resorted to in order to eliminate to 
some extent this error. The stirring in itself, of course, generates 
heat, and has an appreciable effect on the apparent freezing point, 
