Before phdtree.org existed, I used this paper as a primary source for the following lineage:

10. Joseph John Thomson (Nobel Prize winner, 1906), 1856-1940
 9. Lord Ernest Rutherford (Nobel Prize winner, 1908), 1871-1937
 8. Sir Ralph Fowler, 1889-1944
 7. Paul Dirac (Nobel Prize winner, 1933), 1902-1984
 6. Sir Fred Hoyle, 1915-2001
 5. Leon Mestel
 4. Donald Lynden-Bell
 3. Simon White
 2. Dennis Zaritsky
 1. Dennis W. Just!

But now with phdtree.org expanding the "branches", I've copied over some of their result, while expanding it further. Note that some of the linkages aren't formal advisor-to-student, but rather "notable pupils".

Dennis W. Just
Dennis Zaritsky
Simon D.M. White
Donald Lynden-Bell
Leon Mestel
Fred Hoyle --> Maurice H.L. Pryce, Paul Dirac, Rudolf Ernst Peierls
     (at which point it splits)
Branch 1: Pryce --> John von Neumann, Wolfgang Pauli --> Arnold Sommerfeld
Branch 2: Dirac --> Ralph Fowler --> Archibald Hill
Branch 3: Peierls --> Werner Heisenberg --> David Hilbert, Niels Bohr, Max Born
     (at which point there's another major split)
Branch 4 Hilbert --> Ferdinand von Lindemann --> Felix Christian Klein, Rudolf Friedrich Alfred Clebsch
Branch 5: Bohr --> Ernest Rutherford --> J.J. Thomson
Branch 6: Born --> Joseph Larmor, J.J. Thomson, Carl David Tolme Runge
Runge --> Ernst Kummer --> Heinrich Scherk --> Friedrich Bessel --> Carl Friedrich Gauss
     and evidently there's a long branch starting with Joseph Larmor that leads to Isaac Newton and Galileo!
Larmor --> Routh --> Hopkins --> Sedgwick --> Jones --> Postlethwaite --> Whisson --> Taylor --> Smith --> Cotes
Cotes --> Isaac Newton --> Barrow --> Viviani --> Galileo Galilei