What factors influence the relative humidity as an airstream flows
over a mountain to create a rainshadow

The wind drives the moist air up over the mountains to a higher and
cooler elevations, the cooler moist air no longer being about to
contain so much moisture, the surplus condencing and fallomg as rain.

myoarin-ga mentioned the decrease in water content as air passes up a
mountain side due to cooling and subsequent rainfall.

Since you mentioned rainshadow, I might also mention that, as the air
descends the opposite side of the mountain, it heats up due to the
increase in pressure as it moves lower; this heating, in turn, results
in a still lower relative humidity.

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"rainshadow

Definition: The dry region on the leeward side of a mountain (the side
sheltered from the wind)."

from

<a href="http://weather.about.com/library/glossary/bldef-rainshadow.htm">http://weather.about.com/library/glossary/bldef-rainshadow.htm</a>
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"Source: USA TODAY research by Brian Brinch; graphic by John Herne

How mountains influence rainfall patterns

As air ascends mountains, such as the Washington Cascades, it is
forced to rise. The rising air cools, condenses, and drops rain on
locations situated on the windward slopes, like Seattle. When the air
descends the back side of the mountain toward Spokane, it is
compressed, warming and drying it out. This sinking, dry air produces
a rain shadow, or area in the lee of a mountain with less rain and
cloudcover."

from

<a href="http://weather.about.com/gi/dynamic/offsite.htm?site=http://www.usatoday.com/weather/tg/wrnshdw/wrnshdw.htm">http://weather.about.com/gi/dynamic/offsite.htm?site=http://www.usatoday.com/weather/tg/wrnshdw/wrnshdw.htm</a>

(I hope that these two links show up properly. I'm still unsure how to
make a web site address show up as a link.)

Thank you both for your information and research. I wish there was
some way I could reward you. You've both been a great help!