“The orange, as it is thrown into the air, is influenced by two forces: the one arising from the progressive motion of the rider, the other from the projectile force imparted to it. These two forces are in the direction of the adjacent sides of a parallelogram, and were it not for the operation of gravity, the body would accordingly describe its diagonal in the same space of time as it would have described one of the sides.[18] The influence of gravity, however, not only deflects it from a right line into a curve, but diminishes its force, so that instead of arriving at the opposite angle of the parallelogram _a_, its greatest altitude will be short of that point; it will then descend through a similar curve; and, since the times of ascent and descent are equal,[19] it will reach the hand of the rider at the very moment he is prepared to receive it; for the orange will have traversed the parabolic curve in the same space of time as the horseman required for passing from one extremity of the curve to the other.” Mr. Seymour having concluded this explanation, much to the satisfaction of the young party, observed that the present occasion was an appropriate one for the introduction of some remarks on the favourite pastime of the HOOP. “It is a classical pastime,” exclaimed the vicar, “and was as common with the Greeks and Romans as it is with boys of the present generation.” “And it has the advantage,” added Mr. Seymour, “of sending the tide of life in healthful currents through the veins.” Tom began to trundle his hoop along the gravel walk. “Stop, stop, my dear boy,” cried his father, “you seem to have forgotten our compact, that every toy should be fairly won before it was played with. Come upon the lawn, and let me ask you some questions relative to the motions of the hoop. Can you make it stand still upon its edge?” “Not readily,” was Tom’s reply. “And yet,” continued Mr. Seymour, “during its progressive motion, it rolls on its edge without any disposition to fall: how happens that?” “It is owing to the centrifugal force, which gives it a motion in the direction of a _tangent_ to the circle, and, consequently, overcomes the force of gravity.” “Your answer is pat,” replied his father: “as long as you give your hoop a certain degree of velocity, the _tangential_, or centrifugal force, overcomes gravity, in the manner you have already witnessed;[20] but, when that is slackened, the hoop will fall on its side; not, however, until it has made several complete revolutions. Now, answer me another question. Why is it so difficult to make the hoop proceed straight forward, without turning to the right or left?” “I suppose it arises from the same cause as that which altered the direction of my marble as it ran along--the inequality of the ground.”