had just before resisted it, rose up on the opposite side and thus deluged poor Rosa." Louisa was quite delighted with this simple and satisfactory application of philosophy, and observed, that she should not herself mind a thorough soaking, if it were afterwards rewarded by a scientific discovery. "I will give you, then, another illustration of the same law of motion," said Mr Seymour, "which, instead of explaining an accident, may, perhaps, have the effect of preventing one. If, while you are sitting quietly on your horse, the animal starts forward, you will be in danger of falling off backward; but if, while you are galloping along it should stop suddenly, you will inevitably be thrown forward over the head of the animal." "I clearly perceive," said Louisa, "that such would be my fate under the circumstances you state." "Now, then, my dear children, since our friend the vicar cannot attend us at present, suppose we retire to the library, where I have an interesting experiment to perform, and a new toy ready for your inspection." In compliance with their father's wishes, the children cheerfully returned to the library, when Mr Seymour presented Louisa with a BANDALORE. Most of our readers are, doubtless, acquainted with this elegant toy; but before we proceed to describe its construction, it may be interesting to learn something of its history. It is of French origin, and in the Memoirs of Mr Thomas Moore we have the following curious notice of it:-"The first instance I can recall of any attempt of mine at regular versicles, was on a certain toy, very fashionable about the year 1789 or 1790, called in French a ‘Bandalore,' or in English a 'Quiz. To such a ridiculous degree did the fancy of this toy pervade at that time all ranks and ages, that in the streets numbers of persons of both sexes were playing it up and down, as they walked along, or as my very doggrel described it 'The ladies, too, when in the STREETS, or walking in the GREEN, And Mr Moore adds, he was informed by Lord Plunket, that the Duke of Wellington (then Captain Wellesley, or Westley?) was in 1790, one of the aides-de-camp of the Lord-Lieutenant, and a member of the Irish House of Commons, and that during the whole time of the sitting of one of its Committees, he was playing with one of these toys, called Quizzes. It consists of two discs of wood, united to each other by a small axis, upon which a piece of string is affixed. When this string is wound round the axis, and the bandalore is suffered to run down from the hand, the end of the string being held by a loop on the fore-finger, its momentum winds up the string again, and thus it will continue for any length of time to descend from, and ascend to, the hand. It affords a good example of the operation of vis inertia, or what may, with equal propriety, be termed the momentum of rotatory motion. Its action may be compared to that of a wheel, which, running down a hill, acquires sufficient momentum to carry it up another. There are several toys which owe their operation to the same principle, of which we may particularize the windmill, whose fliers are pulled round by a string affixed to the axis of the sails. In playing with the bandalore, a certain address is required to prevent the sudden check which the toy would otherwise receive when it arrived at the end of the string, and which would necessarily so destroy its momentum as to prevent its winding itself up again. Mr Seymour then informed his young pupils that he had an experiment to exhibit, which would further illustrate, in a very pleasing manner, the truth of the doctrine of vis inertia. He accordingly inverted a wine-glass, and placed a shilling on its foot; and, having pushed it suddenly along the table, the coin flew off towards the operator, or in a direction opposite to that in which the glass was moving. He then replaced the shilling, and imparted to the glass a less sudden motion; and, when it had acquired sufficient velocity, he checked it, and the coin darted forward, leaving the glass behind it. Louisa, upon witnessing this experiment, observed that she felt satisfied of the correctness of her father's statement, when he told her that, if the horse suddenly started forward, when she was at rest, she would be thrown off behind, and that if it should suddenly stop on the gallop, she would be precipitated over its head. The children arranged themselves around the table, in order to consider several curious toys which Mr Seymour had collected for the purpose of explaining the nature of the Centre of Gravity. 66 But, in the first place," said Mr Seymour, can you tell me, Tom, what is meant by The Centre of Gravity?" "Its central point," answered the boy. "Certainly not; the central point is termed its centre of magnitude, not that of gravity; and it is only when a body is of uniform density, and regular figure, that these centres of magnitude and gravity coincide, or fall in the same spot." "I now remember that the centre of gravity is that point about which all the parts of a body exactly balance each other." 66 Now you are right; it is, in other words, that point in which the whole weight, or gravitating influence of a body is, as it were, condensed or concentrated, and upon which, if the body be freely suspended, it will rest with security; and consequently, as long as this centre is supported, the body can never fall; while, in every other position, it will endeavour to descend to the lowest place at which it can arrive." "Have all bodies, whatever may be their shape, a centre of gravity?" asked Louisa. "Undoubtedly." "And you say that every body will fall if this point is not supported ?" 66 Infallibly. And now, Tom," said Mr Seymour, "can you tell me what is meant by the line of direction?" The young philosopher was unable to answer this question; and his father, therefore, informed him that, if a perpendicular line were drawn from the centre of gravity of a body to the centre of the earth, such a line would be termed the line of direction; along which every body, not supported, endeavours to fall; and he was also informed that if this said line fell within the base of a body, such a body was sure to stand; but never otherwise. Louisa observed that she was not quite sure she understood her father's meaning, and, therefore, begged for further explanation. Fig. 11. Fig. 10, "I will exemplify it, then," replied Mr Seymour, "by a drawing. Fig. 10 represents a load of stones in a cart moving upon the sloping road C D E this load being low down in the cart, в will represent its centre of gravity, and в F its line of direction, which, you perceive, falls much within the supporting or lower wheel, G G; and there cannot, therefore, be any danger of such a cart being overturned; but in fig. 11 the centre of gravity is raised from its former position to н, and H I is now the line of direction; which, fall K ing without the base, or wheel, к, the load will not be supported, and must consequently fall. These figures," added Mr Seymour, "will also explain a fact which you must have frequently observed, that a body is stable or firm in proportion to the breadth of its base; hence the difficulty of sustaining a tall body, like a walking-stick, upon its narrow base; or that of balancing a hoop upon its edge, or a top upon its point; while, on the contrary, it is almost impossible to upset the cone or the pyramid, since, in the latter cases, the line of direction falls within the middle of the base, the centre of gravity of the body being necessarily low." “I suppose,” observed Louisa, "that this is the reason why carriages, when too much loaded, are so apt to upset." 66 Say, when too much loaded on their tops, and you will be right. As you now, I trust, understand this part of the subject, let us proceed a step further: if you take any body with a view to suspend it, is it not evident, that if it be suspended by that point in which the centre of gravity is situated, it must remain at rest in any position indifferently?” "I thought," said Tom, "we had already settled that question." "True, my dear boy; but there is another question of great importance arising out of it, and which you have not yet considered: tell me, should the body be suspended on any other point, in what position it can rest?" "I do not exactly understand the question." "There are," replied his father, "only two positions in which it could rest, either where the centre of gravity is exactly above, or exactly below the point of suspension; so that, in short, this point shall be in the line of direction. Where the point of suspension is Fig. 12, I below the centre of gravity, it is extremely difficult to balance or support a tall body by such a method, because the centre of gravity is always endeavouring to get under the point of support. Look at this diagram, and you will readily comprehend my meaning. K is the centre of gravity of the diamond-shaped figure, which may be supported, or balanced, on a pin passing through it at м, as long as the centre of gravity, K, is immediately over the point of suspension, м; but if that centre is removed in the slightest degree, either to the right or left of its place к, the body will no longer retain its erect position I K м, but it will revolve upon м, and place itself in the situation indicated by the dotted lines beneath the point м, and its centre of gravity will now be removed to N, directly under м, and in the line K L, which, as you well know, is the line of direction. Have I rendered myself intelligible?" "I understand it perfectly," answered Tom, "And do you also, my dear Louisa?" Louisa's answer was equally satisfactory; and Mr Seymour went Fig. 13. B on to state that the information they had now acquired Iwould enable them to ascertain the situation of the centre of gravity of any plane surface which was portable, notwithstanding it might possess the utmost irregularity of shape. "You shall, for example," continued he, "find the centre of gravity in your kite." "I cannot say," observed Tom, "how I should set about it." 66 Well, fetch your kite, and I will explain the method." Tom soon produced it, and the tail having been removed, Mr Seymour proceeded as follows: "I now," said he, "suspend the kite by the loop at its bow, and since it is at rest, we know that the centre of gravity must be exactly below the point of suspension; if, therefore, we draw a perpendicular line from that point, which may be easily done by a plumb-line, with a weight attached to it, such a line will represent the line of direction, (as indicated by A в in fig. 13.)” "It is clear enough," said Tom, "that the centre of gravity must lie in the line A в, but how are we to find in what part of it?" с Fig. 14. "By suspending the kite in another direction," answered Mr Seymour, who then hung it up in the position represented at fig. 14, “and then by drawing another perpendicular from the new point of suspension." "The centre of gravity," said Louisa, "will in that case be in the line c d, as it was before in that of A B." "In both the lines?" exclaimed Tom, with some surprise; "it cannot be in two places." "And therefore," added Mr Seymour, "it must be in that point in which the lines meet and cross each other;" so saying, he marked the spot g with his pencil, and then told his little scholars that he would soon convince them of the accuracy of the principle. He accordingly placed the head of the stick upon the pencil mark, and the kite was found to balance itself with great exactness. 66 Quite true," said Tom, "that point must be the centre of gravity, for all the parts of the kite exactly balance each other about it." "It is really," observed Louisa, " a very simple method of finding the centre of gravity." "It is," said Mr Seymour; "but you must remember that it will only apply to a certain description of bodies: when they are not portable, and will not admit of this kind of examination, their centres of gravity can only be ascertained by experiment or calculation, in which the weight, density, and situation of the respective materials must be taken into the account. Having proceeded thus far, you have next to learn that the centre of gravity is sometimes so situated as not to be within the body, but actually at some distance from it." 66 Why, papa!" exclaimed Tom, "how can that possibly happen?" "You shall hear. The centre of gravity, as you have just said, is that point about which all the parts of a body balance each other; but it may so happen that there is a vacant space at this point. Where, for example, is the centre of gravity of this ring? Must it not be in the space which the ring encircles?" "I think it must," said Tom; "and yet how can it be ever supported without touching the ring?" |