it evidently must be the opening, and not the length of the lines, that determines the measure of the angle." “Say, rather, the value of the angle, for that is the usual expression: but I perceive you understand me; tell me, therefore, how many degrees are contained in each of the two angles formed by one line falling perpendicularly on another, as in the above figure.” "I perceive that the two angles together are just equal to half the circle ; and since you say the whole circle is divided into 360 degrees, each angle must measure 90 of them, or the two together make up 180.” "You are quite right, and I beg you to remember that an angle of 90 degrees is called a right angle, and that, when one line is perpendicular to another, it will always form, as you have just seen, a right angle on either side." "I now understand," said Louisa, "what is meant by lines being at right angles to each other. But, papa,” continued she, “what are obtuse and acute angles, of which I have so often heard you speak?” Mr Seymour replied, that he could better explain their nature by a drawing, than by any verbal description. "Here," said he, "is an acute angle, a; and here an obtuse one, B; the former, you perceive, is one that contains less than 90 degrees: the latter, one which contains more, and is consequently greater than a right angle." A B Louisa fully comprehended the explanation, and observed that she should remember, whenever an angle measured less than a right angle, that it was acute, and when more, obtuse. "But you have not yet explained to me," she continued, "the meaning of a triangle." "That is a term denoting a figure of three sides and angles. I dare say Tom can describe the several kinds of triangles.” Tom accordingly took the pencil, and drew a set of figures, of which the annexed are faithful copies. A B 66 с "A," said he, "is an Equi-lateral triangle; its three sides being all equal. B is a Rightangled triangle, having one right angle. 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 :— "Here's a riddle for those who delight in their gold, To Fancy's quick eye, in what forms have I risen! "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. 66 "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 can 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 meaningcrowded' 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." * πυκὶνον ἔπος, Iliad, lib. 22. † Page 46. CHAPTER VII. 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. "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 moving 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 sub Y A D B -X ject more intelligible. Suppose the ball в were, at the same moment, struck by two forces, x and y, in the directions в 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 в C." 66 But," said Tom, "why have you drawn the line B D so much longer than BA?" "I am glad that you have asked that question. Lines are intended, not only to represent the direction, but the momenta or quantities of the forces the line в 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 a in the same time that the force x would |