Splitting up a large text file with 'seek relative'

[Hugh Senior]

I need to split large (1 Gig) log files for a client into more managable 
chunks. The routine works fine, then (apparently) starts to slow down. I 
suspect that I have not implemented 'seek' correctly, and that the file is 
being read from zero each time, but would appreciate anyone's insights into 
optimizing this utility...

Given tFilepath, write out 1Mb files sequentially numbered...
  put the hilite of btn "Binary" into isBinary
  if isBinary then open file tFilePath for binary read
  else open file tFilePath for text read
  set the numberFormat to "####"
  seek to 0 in file tFilePath
  repeat
    set the cursor to busy
    add 1 to n
    seek relative 0 in file tFilePath
    read from file tFilePath for 1000000
    put the result="eof" into isEOF
    if (it="") then exit repeat
    if isBinary then put it into URL("binfile:"& tDir&"/" &n& ".txt")
    else put it into URL("file:"& tDir&"/" &n& ".txt")
    if (isEOF OR the result <>"") then exit repeat
  end repeat
  close file tFilePath

Many appreciations in advance.

/H