right angle. c represents an Obtuse-angled triangle, it having one obtuse angle. An Acute-angled triangle is one in which all the three angles are acute, as represented in figure A."

As you have succeeded so well in your explanation of a triangle, let us see whether you can describe the nature of a circle."

"It is a round line, every part of which is equally distant from the centre."

"And which round line," said Mr. Seymour, "is frequently called the circumference. What is the diameter ?" "A straight line drawn through the centre, and terminating in the circumference on both sides."

"And an arc ?" said Mr. Seymour.

"Any portion of the circumference."

“Now let me ask you, what name is given to a line which joins any two opposite angles of a four-sided figure?"

"The diagonal," promptly answered the boy.

"You are quite right," said Mr. Seymour; and, turning towards the girls, he desired them to remember that term, as they would frequently hear it mentioned during their investigation into the nature of Compound Forces.' "I really think," continued their father, "that Tom is as capable of instructing you in these elementary principles as myself; I shall, therefore, desire you, my dear boy, to conclude this lecture during my absence; remember, that by teaching others we always instruct ourselves: but before I quit you, I will give you a riddle to solve, for I well know that you all delight in an enigma.”

"Indeed do we," said Louisa.

"Pray let us hear it, papa," cried Fanny.

Mr. Seymour then recited the following lines, which he had hastily composed; the point having, no doubt, been suggested on the instant by the remark he had just offered: :

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"Here's a riddle for those who delight in their gold,

Which they p'rhaps may explain, when my story is told;
No treasure's so precious, and yet those who gain me,
Though they give me away, will always retain me!
Indeed, if they wish to increase their rich store,
By giving away they will only add more!
To Fancy's quick eye, in what forms have I risen!
And Poets declare that my birth was in heaven;
To some as a flame, as a stream, or a fountain,
To others I seem as a tower or mountain.
Should these hints not betray me, I only can say,
You do not possess me-I hope that you may."

Why," cried Tom, "what can that be, of which the more we give away, the more we have left ?"

"Ay," added Louisa, "and that we actually increase the store, by giving away a part of it!"

"It is some word, I think," observed Fanny; "do you not remember that mamma asked us what that was, from which we might take away some, and yet that the whole would remain ?"

"To be sure," cried Tom, "I remember it well; it was the word wholesome."

Mr. Seymour here assured them, that the enigma they had just heard did not depend upon any verbal quibble: and that as the object of its introduction was to instruct, rather than to puzzle them, he would explain it, and leave them to extract its moral, and profit by its application.

"It is KNOWLEDGE," said he.

"No treasure's so precious,' " repeated Louisa; "certainly none;' and yet those who gain me, though they give me away, will always retain me ;'-to be sure," added she. "How could I have been so simple as not to have guessed it? We cau certainly impart all the knowledge we possess, and yet not lose any of it ourselves."

"By instructing others," said Mr. Seymour, "we are certain, at the same time, of instructing ourselves, and thus to increase our store of knowledge. Let this truth be impressed upon your memory, and after our conversations, examine each other as to the knowledge you have gained by them; you will thus not only fix the facts more strongly in your recollection, but you will acquire a facility of conversing in philosophical language. I hope you have not forgotten

how forcibly your good friend the vicar urged the importance of avoiding the use of words that did not, at once, enforce their meaning; he told you that philosophical language was purposely invented to embody, by the fewest possible words, the highest amount of ideas; and with his usual love of classical illustration, he likened them to that 'meaning-crowded' word, which Andromache so deeply grieved at not having heard from the lips of the dying Hector.* It is undoubtedly well known that the misuse of a word has even led to a false theory in science; if you ask me for an example, I will remind you of our late discourse regarding the term Vis Inertiæ.'† It is possible that this conviction of the vicar's mind, may have originally led him to that extravagant abhorrence of puns, which so distinguishes him."

* πυκίνον ἔπος, Iliad, lib. 22.

† Page 59.

CHAPTER VII.

COMPOUND FORCES. THE COMPOSITION AND RESOLUTION OF MOTION.ROTATORY MOTION,-THE REVOLVING WATCH-GLASS.-THE SLING.-THE CENTRIFUGAL AND CENTRIPETAL FORCES.-THEORY OF PROJECTILES.THE TRUNDLING OF A MOP.-THE CENTRIFUGAL RAILWAY.-A GEOLOGICAL CONVERSATION BETWEEN MR. SEYMOUR AND THE VICAR, IN WHICH THE LATTER DISPLAYS HIS POWERS OF RIDICULE.

ON the following morning Mr. Seymour proceeded to explain the nature of "COMPOUND FORCES." The young party having assembled as usual, their father commenced his lecture by reminding them that the motion of a body actuated by a single force was always in a right line, and in the direction in which it received the impulse.

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Do you mean to say, papa, that a single force can never make a body move round, or in a crooked direction; if so, how is it that my ball or marble will frequently run along the ground in a curved direction? indeed, I always find it very difficult to make it go straight."

Depend upon it, my dear, whenever the direction of a noving body deviates from a straight line, it has been influenced by some second force."

"Then I suppose that, whenever my marble runs in a curved line, there must be some second force to make it do so."

"Undoubtedly; the inequality of the ground may give it a new direction; which, when combined with the original force which it received from your hand, will fully explain the irregularity of its course. It is to the consideration of such compound motion that I am now desirous of directing your attention: the subject is termed the 'COMPOSITION OF FORCES.' Here is a block of wood, with two strings, as you may perceive, affixed to it: do you take hold of one of these

strings, Louisa; and you, Tom, of the other. That is right. Now place the block at one of the corners or angles of the table and while Tom draws it along one of its sides, do you, Louisa, at the same time, draw it along the other." The children obeyed their father's directions.

"See!" said Mr. Seymour, "the block obeys neither of the strings, but picks out for itself a path which is intermediate. Can you tell me, Tom, the exact direction which it takes?" "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 в were, at the