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wood or stone by means of a lever, placing the fulcrum as near the stone as they can, in order to gain power.
Boys balancing each other on a piece of wood over a gate, and adapting the length of the arms to their own weights.
Taking a spade, and supposing it to be pressed into the ground, and pulling at the handle in a direction perpendicular to it; the teacher asks where the fulcrum is points out it must be the surface of the ground—the arm the power— the earth pressing against the spade the weight. Show if the power (the man's arm) is exerted at an acute angle with the handle, power is lost, part of it being employed in forcing the spade deeper into the ground; if at an obtuse angle with the handle, or an acute angle with the handle produced, power is again lost, part of it being employed in dragging the spade out of the ground; that pressing at the handle at a right angle is to work at the greatest advantage: this they perfectly feel from their own experience; also the necessity of having the spade of a substance specifically heavier than the handle.
The poker in stirring the fire - a pronged hammer in drawing a nail (the teacher drawing one) —the axe when they place it in a cleft of wood edgewise, and press upon the handle to make the opening larger-a pair of scales, the steelyard-drawing water from a well by means of the windlass — the pump-handle, scissors, etc.
The knife—the blow of an axe in cutting down a treethe coulter of the plough, etc., belonging to the wedge.
In the same way on the inclined plane, when the power acts parallel to the plane, and taking for granted that the power is to the weight as the height of the plane to the length, or P: W::H: L; any three of which quantities being given, the fourth may be found.
Then, for instance, knowing the height of the plane and its length, with a given power they will calculate what weight can be raised, or for a given weight what power must be applied.
It is in working formula of this kind, where a little algebra is required, and this with a knowledge of a few elementary propositions in geometry, which the boys who
remain longest at school are getting here, that gives a practical usefulness to their education, which is of great value.
The teacher should point out what an immense addition to human power all these mechanical appliances are, and besides these, others of a more striking kind, such as wind, water, steam, etc.
On this subject, the following, taken from Babbage on the “Economy of Machinery,” and given as an experiment related by M. Rondelet, “ Sur l'Art de Bâtir," offers considerable instruction. A block of squared stone was taken for the subject of experiment:
lbs. 1. Weight of stone ......
1080 2. In order to drag this stone along the floor of the quarry,
roughly chiselled, it requires a force equal to .......... 3. The stone (Iragged over floor of planks required .......... 652 4. The same stone placed on a platform of wood, and dragged over a floor of planks required.......
606 5. After soaping the two surfaces of wood, which slid over
each other, it required ........ 6. The same stone was now placed upon rollers of three inches
diameter, when it required to put it in motion along the
floor of the quarry ...........
the same rollers placed between that and a plank floor,
From this experiment it results, that the force necessary to move a stone along
Part of its weight.
The rough chiselled floor of its quarry is nearly.......
From a simple inspection of these figures it will appear how much human labour is diminished at each succeeding step, and how much is due to the man who thought of the grease.
Care should be taken in introductory books containing formula to work from, the proofs of which the teacher perhaps does not understand, that the expressions are correct. I am led to make this observation from the following circumstance : when I first introduced this working from formulæ in the school here, I happened to go in one day when the boys were working out practical results between the power and weight of an inclined plane; this they were doing by taking the power to the weight, as the height of the plane to the length of the base, in the case of the power acting parallel to the plane; I was at a loss to conceive why master, boys, etc., should look so confident, even after I had pointed out to them the absurdity it led to in a particular case, instancing that if P:W:: H: length of the base,
H and P=W-
, when the base became nothing length of base and the plane vertical, the power, instead of being equal to
H the weight, became infinite, the expression becoming W—;
0 but taking it as the length of the plane, when the plane was vertical, L and H were equal, and the expression
would become P + W.--W. length of plane as it ought to be.
This I found arose from their having been reading a lesson on the inclined plane; and the error was, in the formula given in the note to the lesson ; the confidence of the boys in the auuhority of the bouk, made it rather amusing to observe the shyness with which at first they received my explanation.
The great art in teaching children is not in talking only, but in practically illustrating what is taught ; for instance, in speaking of the centre of gravity of a body, and merely saying it was that point at which, if supported, the body itself would be supported, might scarcely be intelligible to them; but showing them that a regular figure, like one of their slates, would balance itself on a line running down
the middle, the lengthway of the slate, and then again on another through the middle of that, and at right angles to it, they see, as the centre of gravity is in both lines, it must be where they cross; and accordingly, if this line be supported, the body will be at rest — this they understand.
Again, balance a triangle of uniform density on a line drawn from one of its angles to the middle of the opposite side -- the centre of gravity will be on that line — balance it again on a line drawn in the same way from one of the other angles — the centre of gravity of the body will be in the intersection of these two lines.
In the same way methods of finding the centre of gravity of other regular figures mechanically might be pointed out.
The teacher should also make himself acquainted with the theory of bodies falling by the force of gravity—that it acts separately and equally on every particle of matter without regard to the nature of the body that all bodies of whatever kind, or whatever be their masses, must move through equal spaces in the same time. This, no doubt, is contrary to common experience - bodies, such as feathers, etc., and what are called light substances, not falling so rapily as heavy masses - smoke, vapour, balloons, etc., ascending; all this to be accounted for from the resistance of the atmosphere.
The spaces described by a falling body being as the squares of the times that if it describes 16-feet in one second, in 2, 3, 4, etc. seconds it will describe 4, 9, 16, etc., multiplied into 164..
To show that while the spaces described in one, two, three, etc. seconds are as the numbers 1, 4, 9, 16, etc., those actually described in the second, third, fourth, etc,, successive seconds are as the odd numbers 3, 5, 7, 9, etc., showing very strikingly the accelerated motion of a falling body.
To apply this also to the ascent of bodies projected directly upwards, with a given velocity.
Again, the moving force of bodies being equal to the mass multiplied into the velocity: How a small body, moving with a great velocity, may produce the same effect as a large body with a small one-as a small shot killing a bird — a large weight crushing it to death.
Interesting observations of a simple kind might be made on the strength of timber-weights suspended on beams between supports, such as the walls of a building - these coming under the principle of the lever, etc.; also such simple things as the following might be asked: Why is it easier to break a two-foot rule flatwise than edgewise; and why joists are now always made thin and laid edgewise ? which our forefathers did not understand. Although the reasons are sufficiently simple, very few even amongst the tolerably well educated can give a satisfactory explanation of them. The usual answer, that “it breaks more easily because it is thinner” will not do.
Wood, and all fibrous matter, is much stronger in the direction of the fibre than across it, and the strength varies as the square of the dimensions in direction of the pressure, multiplied into the dimensions transverse to it, when the
th breadth x depth 2 length is given, or generally as the Tenooth
It is a curious fact, but completely proved by experiment, that hollow tubes are stronger than solid ones of the same quantity of material-how beautiful this provision of Nature, as shown in the structure of the bones of animals, more particularly in those of birds and the larger quadrupeds, giving them the greatest strength, and encumbering them with the least possible weight.
As a means of testing with accuracy and of forming some definite idea of the strength of the hollow stems of plants, etc., the following simple experiment, which I wit. nessed, by the late Professor Cowper, of King's College, London, is very instructive :
He placed a length of one inch of wheat straw in a vertical position in a hole bored in the lower of two parallel boards, held together by a hinge of the same height, one inch, and then brought down the upper part upon it. This he loaded with a load of sixteen pounds, without any appearance of breaking, and stated that he had known a straw bear as much as 35 lbs. placed in this position before it broke.