OT: shell scripting problem

[linux.whiz at gmail.com]

My brain is fried.  I know there is a simple answer to this but I'm
drawing a blank.  I want to run a script against the contents of a
text file.  The text file is just my users' first name, middle initial
and last name like this:

John A Smith
Mary P James
Sally R Jones
Fred Q Davis

What I want to do is for each user in this file, run a script.  I
tried to do this:

for i in `cat textfile`; do
  myscript.sh $i
done

I expect this to run like this:

myscript.sh John A Smith
myscript.sh Mary P James
myscript.sh Sally R Jones
myscript.sh Fred Q Davis

Instead it runs like this:

myscript.sh John
myscript.sh A
myscript.sh Smith
...
etc.

How do I get this script to run correctly?

Thanks!
LW