How would I count the lines of a text file situated on a server?

I know that if the file is on my pc I just do this:

Code:
        Dim lines As String() = IO.File.ReadAllLines("C:\mytextfile.txt")
        msgbox("The text file has " & lines.Length & " lines.")
But what about if the file is on a server such as "http://www.mywebsite.com/mytextfile.txt"?

If try to download the file in memory and read it, it works fine:

Code:
Dim textfilet As String = client.DownloadString("http://www.mywebsite.com/mytextfile.txt")
            MsgBox(textfile)
But I just cannot find a way to count its lines.

Thank you in advance,

Andrea