Read from last point

Hi again,

first thanks for all your suggestions. This forum it is very useful.
I have a question. Is it possible to read from the last line a file was closed. For example, imagine that i've got a file with a LOT of timestamps :

1467387616.868717770
1467387616.874189609
1467387616.888759180
1467387616.894188020
1467387616.908742591
1467387616.914199431
(..)

and i need to read it in block of 70 lines each time, BUT since the file is updating quite fast i need to return to read it form the last (awk?) command without missing any line.

i don't know if i render the idea or if it's possible. Maybe i need a program instead.

Thanks!
Kind Regards

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