pendicular to the plane and the other parallel to it, the latter will represent the amount of force acting to give motion down the plane, or that which has to be sustained by the weight P. Draw D S in the direction in which gravity acts, that is, perpendicular to the horizon, and assume it to represent the weight, then its two components will be D N perpendicular to the inclined plane and N S. Thus the actual weight of the body is to its tendency downwards, or the weight to be supported, as the line DS is to SN; but as a little inspection will convince us that the triangle D S N is similar to A B C, it follows that DSSN:: A B: BC, from which we conclude that the weight in this machine is to the power as the length of the plane is to its height. From this proportion, which is sufficient to solve most questions, we can deduce a form simpler still: since P: W:: BC: BA, P must BC be equal to W x = W. sin a, so that to estimate BA

the power we need only multiply the weight by the sine of the angle at which the plane is inclined to the horizon.

7. All hills upon turnpike roads, and gradients on railroads, are inclined planes, and the force exerted in surmounting them can be readily calculated. Thus suppose the traction on a horizontal portion of a railroad to amount to 10lbs. per ton; this we may consider constant for the same velocity, but when the locomotive arrives at a gradient of 1 foot in 224, it has an increased work ofth of a ton, or 10 lbs. to accomplish, making in all 20lbs. per ton: thus we see that even by so slight an elevation the work of the engine is doubled.

When a sloping plank is used for ascending a height, battens, or small pieces of timber, are nailed across to prevent the feet from slipping, and the stairs of our house are only a farther extension of this principle.

8. This machine may be used to raise a weight in a different manner by giving motion to the plane itself; it is then called the moveable inclined plane. In this case (fig. 19) the plane is pushed under the resistance R, by a force acting parallel to its base, in the direction P X. Resolving the resistance into a force perpendicular to the plane and one parallel to P X, the latter,

find

NS, will represent the power required for equilibrium ; so that, reasoning as in the last instance, we may that the power is to the resistance as the height of the plane is to its base. Many cutting tools, such as the

chisel, plane, &c., are constructed on this principle, but its most important application is in the screw, which gives to it the same advantage of continuous action that the wheel and axle does to the lever.

9. THE SCREW.-This consists of a small inclined plane wrapt round a cylinder, and may be familiarly exhibited by twisting a section of a plane cut in paper round a lead pencil. This is all that is necessary in screws for penetrating, such as those used by carpenters, and corkscrews; but when it is used for giving pressure or lifting weights, an additional contrivance is necessary. In this case the projecting plane, called the thread, of the screw is fitted into a corresponding groove cut in the inside of a nut, and the power is applied by means of a lever fitting into either the nut or the head of the screw.

The amount of force is easily calculated when we consider the distance between two threads as the height of an inclined plane, and the circumference of the cylinder as the length of it; we then find by the theory of the moveable inclined plane (see sec. 8), that the power is to the resistance as the distance between two threads is to the circumference of the cylinder; or when we use a lever, to the circumference of the circle described by its extremity. By means of a fine screw and a long lever, an enormous pressure or lifting power can be secured;

and until the invention of the hydrostatic press (to be afterwards described), this machine was the most powerful that could be employed for these purposes. 10. THE WEDGE.-Another form of the inclined

plane is the wedge, employed for splitting or rending timber, or for giving a small lift to a great weight. It may be either of the form figured at p. 247, or double, with a common base in the centre. The latter form, which is that most frequently employed in rending, because its action is equable on both sides, is here represented. Although in its structure the wedge is exactly similar to the inclined plane, its mechanical action is different, as the force applied is generally percussion instead of pressure, and on this account it is not expedient at present to enter upon a calculation of the results produced through its agency.

Fig. 20.

EDWARD PURCELL.

LIFE OF BENJAMIN FRANKLIN.

BY JAMES S. WHITE.

LESSON I.

1. FRANKLIN tells us that his father, among the instructions given to him when a boy, frequently repeated this proverb of Solomon, "Seest thou a man diligent in his calling, he shall stand before kings, he shall not stand before mean men." "I thence," continues Franklin, "considered industry as a means of obtaining wealth and distinction, which encouraged me,-though I did not think that I should ever literally stand before kings, which, however, has since happened; for I have stood before five, and even had the honour of sitting down with one, the king of Denmark, to dinner." Benjamin Frank

lin, whose words have just been quoted, and who, by the most honourable means, and the practice of the highest virtues, rose from an obscure origin to great distinction in his native country and in the world at large, was born of humble parents at Boston, in New England, in the month of January 1706. He was the youngest son of seventeen children, and, showing an

early readiness in learning to read, was destined by his father to the service of the church; and accordingly he was sent at eight years of age to a grammar-school, where he rose rapidly in his class. But in less than a year he was removed to an inferior school, as his father, being burdened with a numerous family, was unable to support the more expensive education which was necessary to fit his son for the church. Here he learned to write a good hand very soon, but failed entirely in arithmetic; and at ten years old he was

taken away to help his father in his business, which was that of a tallow-chandler and soap-boiler. At this early age the school-education of Franklin was brought to a close the admirable cultivation, which his mind subsequently underwent, was due to his own unassisted efforts in the midst of considerable difficulties.

2. Little Franklin, disliking his father's trade, wanted to go to sea, but his father refused his consent. It was now that he taught himself to swim, an accomplishment which was a great source of recreation to him, and which he highly recommends in his writings. He continued to be employed in his father's business till he was twelve years old; but his dislike to the trade not abating, another business had to be chosen for him. Young Franklin's early taste for reading had become a real passion. All the money that came into his hands was laid out in the purchase of books. He was particularly fond of voyages and travels. His father's little library, consisting chiefly of controversial books, was read with avidity. This bookish inclination at length determined his father to make him a printer; and, with some little hesitation on Franklin's part, who still had a hankering for the sea, he was bound apprentice to his brother James. In a short time he made a great progress in the business; and he now had access to more and better books. "Often," says he, "I sat up in my chamber reading the greatest part of the night, when the book was borrowed in the evening and to be returned in the morning, lest it should be found missing." Now it was that Franklin began to acquire the art of prose-writing, to his success in which he mainly attributed his advancement in life. He bought an odd volume of the Spectator; and he used to take some of the papers, and making short hints of the sentiments in each, lay them by a few days, and then, without looking at the book, he tried to complete the papers again. By comparing his Spectator with the original, he discovered some of his faults and corrected. them. Now it was, too, that he resumed the study of arithmetic, which he had twice failed in learning when. at school. All his former difficulties had vanished, and,