"A strong cast-iron cannon was placed with the muzzle upwards. The barrel was carefully tested with a plumb line, so that its true vertical direction was secured; and the breech of the gun was firmly embedded in sand up to the touch-hole, against which a piece of slow match was placed. The cannon had been loaded with powder and ball, previous to its position being secured. At a given moment the slow match at D was fired, and the operator retired to a shed. The explosion took place, and the ball was discharged in the direction A, B. In thirty seconds the ball fell back to the earth, from B to C; the point of contact, C, was only 8 inches from the gun, A. This experiment has been many times tried, and several times the ball fell back upon the mouth of the cannon; but the greatest deviation was less than 2 feet, and the average time of absence was 28 seconds; from which it is concluded that the earth on which the gun was placed did not move from its position during the 28 seconds the ball was in the atmosphere. Had there been motion in the direction from west to east, and at the rate of 600 miles per hour (the supposed velocity in the latitude of England), the result would have been as shown in fig. 49. The ball, thrown by the powder in the direction A, C, and acted on at the same moment by the earth's motion in the direction A, B, would take the direction A, D; meanwhile the earth and the cannon would have reached the position B, opposite to D. On the ball beginning to descend, and during the time of its descent, the gun would have passed on to the position S, and the ball would have dropped at B, a consider-able distance behind the point S. As the average time of the ball's absence in the atmosphere was 28 seconds--14 going upwards, and 14 in falling--we have only to multiply the time by the supposed velocity of the earth, and we find that instead of the ball coming down to within a few inches of the muzzle of the gun, it should have fallen behind it a distance of 8400 feet, or more than a mile and a half! Such a result is utterly destructive of the idea of the earth's possible rotation.
The reader is advised not to deceive himself by imagining that the ball would take a parabolic course, like the balls and shells from cannon during a siege or battle. The parabolic curve could only be taken by a ball fired from a cannon inclined more or less from the vertical; when, of course, gravity acting in an angular direction against the force of the gunpowder, the ball would be forced to describe a parabola. But in the experiment just detailed, the gun was fixed in a perfectly vertical direction, so that the ball would be fired in a line the very contrary to the direction of gravity. The force of the powder would drive it directly upwards, and the force of gravity would pull it directly downwards. Hence it could only go up in a right line, and down or back to its starting point; it could not possibly take a path having the slightest degree of curvature. It is therefore demanded that, if the earth has a motion from west to east, a ball, instead of being dropped down a mine, or allowed to fall from the top of a tower, shall be shot upwards into the air, and from the moment of its beginning to descend, the surface of the earth shall turn from under its direction, and it would fall behind, or to the west of its line of descent. On making the most exact experiments, however, no such effect is observed; and, therefore, the conclusion is in every sense unavoidable, that THE EARTH HAS NO MOTION OF ROTATION."
-Earth Not a Globe

According to this, it sounds to me that Rowbotham hasn't heard of inertia. The cannon ball only moved from a few inches to a few feet due to it's inertia gained from the rotating planet as the ball rises the air provides a resistance slowing the balls movement which began equal in both speed and direction of the Earth. If we were to use Rowbotham's ideas of this type in another way, for example, a bus and a lead ball. If the bus were moving down a straight stretch of highway at ,we'll say, 70mph and the lead ball was tossed up into the air within the bus, it would appear to shoot back and put a good sized dent into the back of the bus(or possibly someone's head

), and this would be due to the ball's total lack of inertia according to Rowbotham's expiriment. When infact the ball will simply come back down just very slightly back from where it was due to friction within the air.
Someone give me a reason why his expiriment is considered to be without fault.