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ENVIRONMENTAL CONSEQUENCES in rocky mountain coniferous ...

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O f course, it may be very difficult to isolate the limit<strong>in</strong>g component for each<br />

"dependent" component, so we will treat this problem more generally. We recognize,<br />

or th<strong>in</strong>k we know, that the status of any particular environmental component is a<br />

function of all environmental components and time. Ideally, we would like to con-<br />

struct a function for the state of each component as<br />

where<br />

It seems highly unlikely that we will ever def<strong>in</strong>e such a function, however, for<br />

both mathematical and other reasons. But given that we know the state of an environ-<br />

ment at a particular po<strong>in</strong>t <strong>in</strong> time, t, and given a set of assumptions about the near<br />

future--pr<strong>in</strong>cipal ly with regard to macrocl imate--i t seems considerably more 1 i kely that<br />

we could estimate the rate of change <strong>in</strong> the state of a particular environmental com-<br />

ponent. Expressed formally,<br />

Differentiat<strong>in</strong>g equation 6 with respect to time, t, we obta<strong>in</strong> an expression for<br />

the rate of change of the rate of change, or<br />

d2x df. af. dxl afi dx,<br />

+ i - - 1 -<br />

af, dxi<br />

+...+- -+...<br />

dt2 dt ax, dt " ax2 dt ax dt<br />

i<br />

In a f<strong>in</strong>ite difference format, equation 7 can be written<br />

(5)

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