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Dave Pelz in his Dave Pelz''s Putting Bible book defines a fall line as line which is in line with the pure downhill direction from the hole as shown in Figure 7.9.9. The 1st photo of pictures (link) shows the two aim lines extended to the fall line. It is seen that they intersect at a single point. H.A. Templeton[1] was the first person to determine that for a flat surface, a single point target located on the fall line results in desirable ball tracks independent of the initial clock position. This represents a significant reduction in the task of sinking the ball in the hole. The task of determining desired both speed and aim line is reduced to determining the desired speed.
His Vector Putting book provides tables for the target points for various green slopes, green speeds, and ball-hole distances. Here’s the basic procedure in establishing the aim points from approximately 10 ft from the hole on the fall line for a particular green slope and green speed. (1) Establish the downhill direction
(2) Stand near the hole near the 3 or 9 o’clock position
(3) Pace off 4 steps (about 10 ft) away for the hole.
Make two putts from this position. The 1st putt is directed at the hole and adjust the speed such that the ball stops approximately 17 inches past the fall line. Take note of the distance below the hole where the crossing occurs. Make the 2nd putt directed to a point at the same distance from the hole only on the high side of the hole.
For comparison with Templeton’s results (see 2nd picture of photos) shows e.g. at 10 ft, and medium fast green, the break is given as 10 inches.
p.s. Don't expect to find Templeton's book in your local library. I borrowed one from the Library of Congress through a request from my local library.
Pictures link:
http://www.facebook.com/photo.php?id...07298&pid=4798
[1] H.A. Templeton, Vector Putting, Vector Golf Inc. 1984