Umm.<p>But the water droplets/sand particles do NOT form a straight line if you accelerate the jug. You have to decelerate the jug with exactly the right timing to form a straight line, not accelerate it. Nor do the beads in the Caltech video form a straight line, despite their dishonest attempt to arbitrarily impose a straight line on beads that are clearly not in a straight line.<p>In the second diagram, which is alleged to be an attempt to plot acceleration due to gravity to the position of an accelerating water jug, the values [0,1,2,4,8] are marked on the x-axis, and [0,-1,-2,-4,-8] on the y-axis. Da Vinci then plots lines from [0,-8] to the points (0,0),(1,0),(2,0),(4,0),(8,0). Doing so doesn't really establish any sort of relationship between accelerating jugs and acceleration due to gravity, even allowing for an incorrect equation of motion for an accelerating object.<p>Da Vinci spent most of his early career trying to sell military technology to potential patrons (largely if not completely unsuccessfully). One of the pieces of technologies he was trying to sell was a process for calculating improved artillery range tables (tables of elevation vs. range). He didn't manage to sell that either.<p>The second diagram is more easily interpreted as a doodle that makes an unsuccessful attempt to scry a relationship between elevation and range for artillery pieces.