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may render the subject more intelligible. Suppose the ball в were, at the same moment, struck by two forces x and y in the directions BA 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 в 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 BA; 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 would reap, you must sow."

you

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.

"Is it not then evident," proceeded Mr. Seymour, "that the composition of forces must always be attended with loss of power; since the diagonal of a parallelogram can never, under any circumstances, be equal to two of its sides: and is it not also evident that the length of the diagonal must diminish as the angles of the sides increase so that the more acute the angle at which the forces act, the less must be the loss by composition? But I shall be

better able to explain this law by
a diagram. If BA, A C be the
sides of a parallelogram, represent-
ing the direction of two forces, and
A D the diagonal path of the body, is
it not evident that the line A D will c
shorten as the angle B A C diminishes?"

Fig. 5.

B

B

"We see that at once," cried Tom, "from the diagram before us."

"Then we will proceed to another fact connected with the same subject. Look at this

diagram; is not the diagonal A D common to both the parallelograms inscribed about it, viz. of A B C D, and A E F D?"

"To be sure it is."

Fig. 6.

"Then it is equally clear that a body may be made to traverse the same path A D, by any pair of forces represented by the adjacent sides of either of such parallelograms."

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"I request you to keep that fact in your recollection. We will now suspend our studies until to-morrow."

"I approve of your determination," said Mrs. Seymour, who had been an attentive auditor during this lesson; "your birds are, as yet, scarcely fledged, and they will make greater advances by short flights, frequently repeated, than by uninterrupted progression."

CHAP. VII.

THE VICAR'S INTERVIEW WITH MAJOR SNAPWell. -THE RESOLUTION OF FORCES.

ROTATORY

MOTION.THE SLING. THE CENTRIFUGAL AND CENTRIPETAL FORCES.-THEORY OF PROJECTILES.

-A GEOLOGICAL CONVERSATION

MR. SEYMOUR AND THE VICAR.

BETWEEN

OUR readers will remember that Mr. Twaddleton left the party at the lodge, in order to pay his respects to Major Snapwell. As the circumstances developed during their interview are intimately connected with our story, we shall relate, as nearly as we are able, the conversation which took place upon that occasion.

"Mr. Twaddleton," said the major, as he advanced towards the door to meet his visitor, "I feel myself obliged and honoured by your kind attention. As a perfect stranger I could scarcely have expected this civility; but your village, surrounded as it is with all the softer charms of nature, is calculated to impress the

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