taught, as applying to practical purposes connected with their after-life.

However, I have myself no objection that this or any other ometry, a knowledge of which may be likely to advance the interest and the civilization of mankind, half as much as it does, should be taught to promising boys in our parish schools, whose parents have been able to keep them there to a sufficient age, and have acquirements enabling them to learn it-these will be exceptions, and not the rule.

But why among the words, supposed to be of suspicious termination, attack the ometries? they, of all others, are the most harmless-dealing in weight and measure of an exact quantitative kind; so demonstratively true, that there is no chance of getting wrong-no possibility of there being anti anything whatever. There may be something of wrongness in some of the ologies, as they leave room for the wanderings of fancy, and do not deal in measured quantity as the ometries do. Here scientific men may, and perhaps sometimes do, become bold and speculative to a degree which may startle those of a more sober-minded temperament, and who have not paid attention to the subject on which they treat; still, I think we may rest satisfied that where theories are advanced not based on truth, they will be but short-lived, and not do much mischief in the end.

Surely these objectors do not consider themselves as living in a railroad age-if they have ever travelled in the heavy Falmouth mail of olden times (for the distance between that time and this is, in social improvement as regards locomotion, not a part of a generation, but whole centuries)—or if they have ever gone between Paris and Geneva in a French diligence without stopping, let them call this to mind, and they will no longer object to trigonometry.

As an instance of the force of meaning in a word when it once gets good hold on the public mind-happening to go to a book sale in my own neighbourhood, where there was a copy of an early edition of the Encyclopædia Britannica, when it was placed on the table for sale, a man, employed by one of the booksellers in London, rather drily, perhaps cunningly, observed," Why, you won't find the word railroad in it.' Not another word was said; but after that, I observed there was not a bidder besides himself.

MECHANICS.

The teacher should understand the more simple properties of the mechanical powers, and if not equal to the mathematical proofs of them, he should be able to show their application in the tools they are in the habit of using, and in many other things of common life-such as the common steelyard-turning a grindstone-raising water from a well by means of a rope coiling round a cylinder, and the nature of the momentum of bodies-what is meant by the centre of gravity, &c. A skilful teacher, with models of the mechanical powers to assist him, will make this a subject of great interest. For instance, in the lever, assuming the power multiplied the distance from the fulcrum equals the weight multiplied its distance, he might take a rod four feet in length and divide into feet and inches; at one end he fixes a weight, and placing the fulcrum at different distances from the weight, shows how the theory and practice agree, by actually testing each particular case, showing that the calculated weight produces an equilibrium. This is a sort of proof by testing it in particular cases, and then by a process of induction assuming it to be generally true.

Then instance their own attempts at moving a block of 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 on 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-pair of scales, the steelyard-drawing water from a well by means of the windlass-the pumphandle, scissors, &c.

The knife-the blow of an axe in cutting down a tree-the coulter of the plough, &c. 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, which 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, &c,

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:

1. Weight of stone

2. In order to drag this stone along the floor of the quarry, roughly
chiselled, it required a force equal to

3. The stone dragged over a floor of planks required
4. The same stone placed on a platform of wood, and dragged over
a floor of planks required

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

Ibs.

1080

758

652

606

182

34

MECHANICS.

7. To drag it by these rollers over a wooden floor

8. When the stone was mounted on a wooden platform, and the same rollers placed between that and a plank floor, it required

From this experiment it results that the force necessary to

move a stone along

Part of its weight.

40

50

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 on 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, &c. 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, and P = W. when the base became nothing and the plane vertical, the power, instead of being equal to the weight, became infinite, the expression becoming W. but taking it as the length of the plane, when the

H

0

H length of base'

plane was vertical, L and H were equal, and the expression

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 authority of the book, 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 intelligble 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 length way 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 point 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, &c., and what are called light substances, not falling so rapidly as heavy masses- -smoke, vapour, balloons, &c., 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 161 feet in one second, in 2, 3, 4, &c., seconds it will describe 4, 9, 16, &c., multiplied into 16.

To show that while the spaces described in one, two, three, &c. seconds are as the numbers 1, 4, 9, 16, &c., those actually described in the second, third, fourth, &c. successive seconds are as the odd numbers 3, 5, 7, 9, &c., showing very strikingly the accelerated motion of a falling body.