Rowbotham is describing movement between points in space in his text and the illustrator from the book company, George Davies, drew lines between the points described.
put the ship in motion, and let the ball be thrown upwards. It will, as in the first instance, partake of the two motions--the upward or vertical, A, C, and the horizontal, A, B, as shown in fig. 47; but because the two motions act conjointly, the ball will take the diagonal direction, A, D. By the time the ball has arrived at D, the ship will have reached the position, 13; and now, as the two forces will have been expended, the ball will begin to fall, by the force of gravity alone, in the vertical direction, D, B, H; but during its fall towards H, the ship will have passed on to the position S, leaving the ball at H, a given distance behind it.
No, clearly he says:
"but because the two motions act conjointly, the ball will take the diagonal direction, A, D." This is why the illustrator drew it that way.
Next he states that the ball's forward motion will come to an abrupt stop at D:
"the ball will begin to fall, by the force of gravity alone, in the vertical direction, D, B, H" and state this is because the:
"two forces will have been expended". What is 'expending' the two forces? The force of gravity is always acting on the ball, the net force that launched it in the first place was done once the ball was in flight and traveling with momentum. What would suddenly reduce it's forward momentum to zero at D? This would and does not happen.
Rowbotham is wrong!Rowbotham is talking about acceleration. The ship is accelerating, and leaves the ball behind. The same happens with the next example.
The same result will be observed on throwing a ball upwards from a railway carriage, when in rapid motion, as shown in the following diagram, fig. 48. While the carriage or tender passes
FIG. 48.
from A to B, the ball thrown upwards, from A towards (2, will reach the position D; but during the time of its fall from D to B, the carriage will have advanced to S, leaving the ball behind at B, as in the case of the ship in the last experiment.
Look at the spacing of the trains. Accelerating. The ball is left behind. True.
The illustrator also made it look like the ball hit the train again, but if you read the text it is clearly conveyed what Rowbotham is describing.
So, the illustrator can't get the other drawings right, but he get's this 'acceleration' (that is never mentioned by Rowbotham), just right perfect - maybe because now his ineptness supports your point? LOL!
Get onto a merry-go-round that is rotating at a 'constant speed' and see if you can throw a ball up straight into the air and get it to fall back into its same position with you.
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If the merry-go-round was in space, and the floor of the merry-go-round was as attractive as the earth would be, I don't see how the ball would behave any differently.
A merry-go-round is not the same situation as throwing something up from the surface of the spherical earth, as you know well enough. However, it would be similar to what would happen on a flat earth (like in your 2nd comment above), and since what happens on a merry-go-round is not what we see when we toss a ball in the air form the surface, the the earth can't be flat, can it?