In working with the Method of Variations one must allow for the
occurrence in a series of 'critical points,' at which sudden and
sometimes heterogeneous changes may take place. Every substance exists
at different temperatures in three states, gaseous, liquid, solid; and
when the change takes place, from one state to another, the series of
variations is broken. Water, e.g., follows the general law that
cooling is accompanied by decrease of volume between 212° and 39° F.:
but above 212°, undergoes a sudden expansion in becoming a gas; and
below 39° begins to expand, until at 32° the expansion is considerable
on its becoming solid. This illustrates a common experience that
concomitant variations are most regular in the 'median range,' and are
apt to become irregular at the extremities of the series, where new
conditions begin to operate.
The Canon of Variations, again, deals not with sudden irruptions of a
cause, force or agent, but with some increase or decrease of an agent
already present, and a corresponding increase or decrease of some other
phenomenon--say an increase of tax and a rise of price. But there are
cases in which the energy of a cause is not immediately discharged and
dissipated. Whilst a tax of 6_d._ per lb. on tea raises the price per
lb. by about 6_d._, however long it lasts, the continuous application of
friction to a body may gradually raise its temperature to the point of
combustion; because heat is received faster than it is radiated, and
therefore accumulates. Such cases are treated by Mill under the title of
'progressive effects' (_Logic_: B. III., c. 15): he gives as an example
of it the acceleration of falling bodies. The storage of effects is a
fact of the utmost importance in all departments of nature, and is
especially interesting in Biology and Sociology, where it is met with as
heredity, experience, tradition. Evolution of species of plants and
animals would (so far as we know) be impossible, if the changes (however
caused) that adapt some individuals better than others to the conditions
of life were not inherited by, and accumulated in, their posterity. The
eyes in the peacock's tail are supposed to have reached their present
perfection gradually, through various stages that may be illustrated by
the ocelli in the wings of the Argus pheasant and other genera of
_Phasianidæ_. Similarly the progress of societies would be impossible
without tradition, whereby the improvements made in any generation may
be passed on to the next, and the experience of mankind may be gradually
accumulated in various forms of culture. The earliest remains of culture
are flint implements and weapons; in which we can trace the effect of
tradition in the lives of our remote forefathers, as they slowly through
thousands of years learnt to improve the chipping of flints, until the
first rudely shaped lumps gave place to works of unmistakable design,
and these to the beautiful weapons contemporary with the Bronze Age.
Public-domain text, read in full here on John Shaqi.
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