He proceeded to observe, that the force acting in the direction A B would certainly be resolved into two others, viz. one in the direction F B, and another in that of D B; “because,” continued he, “these lines are the adjacent sides of the parallelogram, of which A B is the diagonal; and I well know that whenever a force strikes obliquely, it is thus resolved.”
“That is all very well explained,” replied his father; “pray proceed.”
“Now comes the difficulty,” continued Tom; “for the force D B will of course be destroyed by the wall, and that represented by F B, which is the only one that can remain, would carry the ball to E.”
“It certainly would do so,” answered his father, “if the ball were perfectly devoid of elasticity; but remember that, in consequence of this property, the force D B will be exchanged for one in an opposite direction, B D.”
“I had entirely overlooked the elasticity,” said Tom; “I now see my way clearly, for in that case there must be two forces acting in the directions B D, B E, which will, of course, drive the ball down the diagonal B C.”
“Your demonstration is perfectly correct, my boy; and I think you will now admit that I could not have adduced a more beautiful instance of the composition and resolution of forces; for, in the first place, you resolve the diagonal force into two others, and then you recompound these again to produce another diagonal one.”
“But I think you told us that the angles of incidence and reflection were only equal when the rebounding body was perfectly elastic.”
“Clearly so; the force D B must be exchanged for an equal one B D, or else the angle A B D cannot be equal to the angle D B C; but I will render this fact still farther intelligible by another diagram.
Let B, as in the former case, represent the wall, upon which the imperfectly elastic body impinges in the direction A B.--The force will of course be resolved into two others, viz. into D B and F B; the force D B, however, instead of being replaced by the opposite one B D, will now be represented by the shorter line B G; or that of B H or B I, according to the degree of elasticity. If we, therefore, complete the parallelogram, B C, B K, or B M will be the diagonal path of the body; making, as you perceive, the angle of reflection D B C, greater than that of incidence A B D; and where the body is perfectly inelastic, the force D B will be wholly destroyed, and, the force B E alone surviving, the body will be carried along the line B E. I have now,” continued Mr. Seymour, “explained to you the principal laws which govern those forces by which your ball or marbles are actuated. It is true that in practice you cannot expect the results should accurately coincide with the theory, because, in the first place, you cannot obtain marbles that are of equal density and elasticity, and of true figure; and, in the next, there will be obstacles against which it is impossible to guard. The spinning of the marble will also have a material influence on its motion, as we have already discovered. In the game of billiards, where every obstacle is removed, as far as art can assist, the theory and practice are often strangely discordant. But we have dwelt sufficiently upon the subject; we will, therefore, return to the library, where I intend to exhibit an experiment in farther elucidation of the subject of collision.”