large tract the rate of growth
may be taken as uniform from year to year. In the case of bacteria growing
under ideal conditions in a culture, _i.e._ with unlimited food supplied,
the increase in the number of bacteria per second is proportional to the
number of bacteria present at the beginning of that second. Any function
in which the rate of change or rate of growth at any instant _t_ is
directly proportional to the value of the function at the instant _t_
obeys what has been termed the 'law of organic growth,' and may be
expressed by the equation,

_y = ce__kt_,

wherein _c_ and _k_ are constants determined by the physical facts
involved, and _e_ is a constant of nature analogous to {~GREEK SMALL LETTER PI~}. The constant _k_
is the proportionality constant and is negative when the quantity in
question decreases; _c_ is commonly positive;

_e_ = 2.178....

"The values of the function of _x, ce__kx__, increase according to the
terms of a geometrical progression as the variable x increases in
arithmetical progression_....

"The most immediate application of a function in which the growth is
proportional to the function itself is to the air. The decrease in the
pressure of the air at the distance _h_ above the earth's surface is
proportional to _h_.

"The expression _P = 760 e__-h/7990_ gives the numerical value of the
pressure in millimeters of mercury for _h_ measured in meters. The
negative exponent indicates that the pressure decreases as _h_ increases.
In inches as units of length of the mercury column, _h_ in feet,

_P = 29.92e__-h/26200_

This is known as Halley's law.

"The growth of bean plants within limited intervals and the growth of
children, again between quite restricted limits, follow approximately the
law of organic growth. Radium in decomposing follows the same law; the
rate of decrease at any instant being proportional to the quantity. In the
case of vibrating bodies, like a pendulum, the rate of decrease of the
amplitude follows this law; similarly in the case of a noise dying down
and in certain electrical phenomena, the rate of decrease is proportional
at any instant to the value of the function at the instant....

"_The Curve of Healing of a Wound._--Closely allied to the formulas
expressing the law of organic growth, _y = e__kt_, and the law of 'organic
decay,' _y = e__-kt_, is a recently discovered law which connects
algebraically by an equation and graphically by a curve, the surfa