“If we consider this table as a parallelogram, I should say, that the block described the diagonal.”
“Well said, my boy; the ablest mathematician could not have given a more correct answer. The block was actuated by two forces at the same time; and, since it could not move in two directions at once, it moved under the compound force, in a mean or diagonal direction, proportioned to the influence of the joint forces acting upon it. You will, therefore, be pleased to remember, it is a general law, that where a body is actuated by two forces at the same time, whose directions are inclined to each other, at any angle whatever, it will not obey either of them, but move along the diagonal. In determining, therefore, the course which a body will describe under the influence of two such forces, we have nothing more to do than to draw lines which show the direction and quantity of the two forces, and then to complete the parallelogram by parallel lines, and its diagonal will be the path of the body. I have here a diagram which may render the subject more intelligible. Suppose the ball B were, at the same moment, struck by two forces X and Y in the directions B A and B D. It is evident that the ball would not obey either of such forces, but would move along the oblique or diagonal line B C.”
“But,” said Tom, “why have you drawn the line B D so much longer than B A?”
“I am glad you have asked that question. Lines are intended, not only to represent the direction, but the momenta, or quantities of the forces: the line B D is, as you observe, twice as long as B A; it consequently denotes that the force Y acting in the direction B D, is twice as great as the force X acting in the direction B A. Having learned the direction which the body will take when influenced by joint forces of this kind, can you tell me the relative time which it would require for the performance of its diagonal journey?”
Tom hesitated; and Mr. Seymour relieved his embarrassment by informing him, that it would pass along the diagonal in exactly the same space of time that it would have required to traverse either of the sides of the parallelogram, had but one force been applied. Thus, the ball B would reach C in the same time that the force X would have sent it to A, or the force Y to D. “I will endeavour to prove this fact beyond all doubt. It is, I think, evident, that the force which acts in the direction B A can neither accelerate nor retard the approach of the body to the line D C, which is parallel to it; hence it will arrive at C in the same time that it would have done had no motion been communicated to it in the direction B A. In like manner, the motion in the direction B D can neither make the body approach to nor recede from A C; and it therefore follows, that, in consequence of the two motions, the body will be found both in A C and C D, and will therefore be found in C, the point of intersection.”
Louisa seemed to express by her looks the irksomeness of such demonstrations; and which did not pass unobserved.
“This may appear tedious and uninteresting,” said Mr. Seymour, “but the information is absolutely essential to our future progress: if you would reap, you must sow.”
Tom and Louisa both expressed themselves willing to receive whatever instruction their father might consider necessary; and they farther declared, that they understood the demonstration he had just offered them.
