Read dynamic textstream step by step

Question

Hello forum, I want to display the input of a logfile in a textbox. The difficulty is that the logfile grows and the content of the textbox should also display the new entries in realtime. I do not want to read the whole content of the logfile and display it in the textbox. What I am looking for is to read the stream till "readline = null" and then try to read every x seconds from that position on. Does anyone know if that is possible? Thanks in advance, MG