of a Tax), do not depart widely
from regular curves; and accordingly, assuming the causes at work to
vary continuously during the intervals between points of measurement,
curves may be substituted. In fact, a curve often represents the course
of a phenomenon more truthfully than can be done by a line that zigzags
along the exact measurements; because it is less influenced by temporary
and extraordinary causes that may obscure the operation of those that
are being investigated. On the other hand, the abrupt deviations of a
punctilious zigzag may have their own logical value, as will appear in
the next section.

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 deg. and 39 deg. F.:
but above 212 deg., undergoes a sudden expansion in becoming a gas; and
below 39 deg. begins to expand, until at 32 deg. 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