Читать книгу The Library of Work and Play: Mechanics, Indoors and Out - Fred. T. Hodgson - Страница 6

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The cement walk being finished to the satisfaction of all concerned, and the admiration of the neighbours, Fred turned his thoughts to the building of a boat house and workshop. It was decided to make it 16 feet wide and 22 feet long, as these dimensions would suit the timbers in the old barn, and be ample for stowing away the boat and allowing space for a work bench.

Lines for a foundation were set out, and stakes driven in the ground at the corners, alongside the cement walk and pier. A trench about two feet deep was dug on the two sides and ends; and in this were laid large rocks and stones, in a single course all round. Nick, who was quite handy at this kind of work, built up a wall of smaller stones laid in cement mortar. This mortar was composed of one part of cement to five of sand, and made quite thin and easy to spread. When the wall was high enough, about level with the highest part of the ground, it was levelled off by using smaller stones and plenty of cement mortar. The level was obtained by laying a straight plank flat on the top of the cement finishing, and then applying an ordinary spirit-level. Any errors in the level of the wall showed at once, and were made right by adding more mortar, or by taking some off the top of the wall.

Fig. 8. Framing studding

Timbers from the old barn were next pressed into service, chestnut wood that had served as girths and beams. Two pieces were cut, 22 feet long, and two of 16 feet. The ends were then halved, as shown in Fig. 8—the simplest method of framing a corner—and the timbers were spiked and so squared as to make right angles at the corners.

Fred then took the old window and door frames, and measured off on the foundation timbers the outside distance where each one was to be placed. He put the double doors in the end of his boat house, next to the river front. The other door and windows were set in the best places to provide an entrance opening on the cement walk, light above the work bench, and views over the river and grounds. Fred decided to build his house ten feet high; so a quantity of studding, 2 × 4 inches in section, was taken out from the walls of the barn, and cut exactly ten feet long. These were to form the side walls between the corners, doors, and windows. Heavier studs were found in the barn, and Fred wisely used them next to the windows and doors.

Fig. 9. Side of boat house frame

These heavy studs were set up in the places marked on the timber sills, also at the four corners, and were toe-nailed at the bottom to hold them in place. They were then made vertical or plumb, by aid of a spirit-level, and the corners were braced temporarily to hold them in that position. The picture (Fig. 9) shows how the side of the building next to the cement work looked when the studding was all in place. The dark ends shown are the joists on which the floor is laid. The lower joists were made from timbers taken from the barn floor, 2 × 8 inches wide and long enough to reach across the building. The joists on top were 2 × 6 inches, by 16 feet long. These latter floor beams were set about 15 inches apart, ready to receive the flooring plank, which was nailed solid to them. You will notice that cross pieces of studding are nailed between the studs at the window openings. These form the tops and bottoms of the window frames. The spaces above and below are also filled in with short pieces of studding, to nail the clapboards to, as shown. The ends of the building were finished as shown in Fig. 10, a small window being left in each to admit light and air, also lumber, poles, or other stuff that could be put into the loft through these openings. Inside the building a trapdoor was to be left, so that Fred or George could get up to take in or hand out the stuff.

Fig. 10. End of boat house frame

The end (Fig. 10) shows how Fred and Nick, with George's help, built that portion, the collar beam, O O, and the rafter being seen, while the details in Fig. 8 give larger sketches of the manner of doing the work. The stone-work, as built by Nick, for foundation walls, is shown in both Figs. 9 and 10.

All the clapboards having been taken off the barn and old sheds, the better portions were selected for covering the outside of the new frame, and a lot of old boards were used for lining the inside of the walls and nailing on to the rafters. The next thing was to lay on the shingles. These had been provided some days before by Mr. Gregg, who had figured out the number required. He found the roof would measure 24 feet in length, including the projections over the ends of gables, and that the length of the rafters was 17 feet each, including the overhanging eaves or cornice. This made the whole stretch of length on both sides of the roof 34 feet. Multiplied by 24 feet, the length of the roof, this was 816 feet. To cover an area of 816 feet about 8,000 shingles would be required, as 100 surface feet require nearly 1,000 shingles, laid 4 inches to the weather, according to the usual custom. Mr. Gregg explained to Fred what is meant by the term "weathering," applied to shingles, clapboards, slates, or anything similar. The "weathering" part of a shingle is that portion of it exposed to the weather, when in place on the roof. It makes no difference how wide or how narrow a shingle may be, it is that portion showing from the lower end of one shingle to the lower end of the next one above it, that is the "weathering." This is generally four inches wide and it runs from end to end of the roof. Another thing Mr. Gregg explained—the term, "a square of shingling." "In this case, as in flooring, clapboarding or similar work, a square is an area 10 × 10 feet; or 100 superficial feet. In nailing down shingles," went on Mr. Gregg, "the nails should be driven so that the next course or layer will cover up the nail heads, thus protecting them from rain and damp, and preventing them from rusting. When laying the shingles, after the first courses are on, which should be laid double at the eaves, a string or chalk line must be stretched from one end of the roof to the other, four inches up from the ends of the first courses. This string or chalk line may first be rubbed over with chalk or soft charcoal, and when drawn tight from each end, it may be 'struck' or 'snapped' by raising it up in the middle and letting it strike the roof suddenly so that a mark will be left on the shingles from end to end. This will be the guide for the thick ends of the shingles to be laid against when nailing on the next course, and the process must be continued until the ridge, or top of the roof, is reached. When you paint your boat house, don't forget the roof, for a good coat of paint on the shingles will lengthen the life of the roof fully five years."

Fred, to whom these instructions were more particularly given, told his father he understood the whole matter, and he was directed to go on with the work. In the meantime the father ordered the shingle-nails required; five pounds for each thousand shingles, or forty pounds altogether.

The building being small, the whole work was soon completed, windows put in, doors hung, and floors laid; and Mr. Gregg was greatly pleased with the manner in which Fred had managed the job.

Photograph by Frank H. Taylor

Boat House and Workshop

"A Good Coat of Paint on the Shingles Will Lengthen the Life of the Roof Fully Five Years."

The next thing was to take down the heavy timbers of the barn, still standing. Fred saw at once that they were too heavy to be removed without mechanical aid or more human help, so he brought from his father's stable a rope and set of pulley-blocks like the ones shown in Fig. 11. Nick, who had seen some service at sea, hooked the block into a loop formed by a short piece of rope tied over a limb projecting from one of the trees. The question of lifting the timber now was an easy one, as another short rope was tied to the heavy post W, in this case the weight P being the power. Each of the blocks shown contains pulleys which make the relation of the weight to the power as one to four. The weight being sustained by six cords, each bears a sixth and a weight of six pounds will be kept in equilibrium by a power of one pound. The blocks used in a system of this character are called single if there is one pulley in each, double if there are two, treble if there are three, and quadruple if there are four.

Fred, George, Nick, and Jessie who liked to help whenever she could, counted for four times their number when they all pulled together on the rope P. It was astonishing to the youngsters how easily the heavy timbers were taken down and piled in a nice heap.

Two timbers, each about twenty-five feet long, were chosen and marked, to be used for slides or ways, on which the proposed boat could be hauled in and out of the boat house. It was quite a distance from the timber to the river end of the boat house, and, the former being heavy, Fred decided to make an inclined plane of planks—of which there was an abundance—so that the timbers could be slid or rolled down to the river. It took but a few minutes to lay the planks, and as the incline was gentle, rollers were used and the timbers went down as easily as the big rock had done. This pleased the younger children very much.

"When papa comes home," said Jessie, "I'm going to get him to tell me about the 'inclined plane' as well as the ropes and pulleys."

The two timbers were rolled into the river and floated to the boat house, where one end of each was raised to the floor level at the doorway and made fast; the other end sank to the bottom, where Nick dug down and made a bed for it to rest in. These beds were made deep enough to bury the ends, and large stones were then thrown in to keep them from moving, but these were not allowed to reach within 18 inches of the surface of the water, which was then at its lowest mark. The timbers were kept about three feet apart, ample space to admit of any ordinary launch or row boat being taken into the boat house.

"Oh, Fred," said Jessie, "do you think those two sticks will be strong enough to hold the boat while you are pulling it up?" "Why, yes; strong enough to hold a dozen boats no larger than the one we intend having made. I don't know how much weight these timbers will support, nor how heavy our boat will be with the engine in it, but I'm sure the timbers are strong enough."

Jessie's question, however, caused Fred to think over the matter, and he set to work to find out how to tell the strength of timber beams. He discovered that to be able to determine the strength of beams and wooden pillars under all sorts of conditions required considerable training in mechanics and mathematics, but that the case before him was comparatively easy. A general rule for finding the safe carrying capacity of wooden beams of any dimensions, for uniformly distributed loads, is to multiply the area of section in square inches, by the depth in inches, and divide their product by the length of the beam in feet. If the beam is of hemlock, this result is to be multiplied by seventy, ninety for spruce and white pine, one hundred and twenty for oak, and one hundred and forty for yellow pine. The product will be the number of pounds each beam will support. For short-span beams, the load may be increased considerably. Fred, who had some knowledge on the subject, acquired at the training school, determined to pursue his studies in this direction.

In talking over the matter of nails with his father, their holding power was mentioned, and Mr. Gregg told Fred of a test that had been made some time ago by the U. S. Ordnance Department, where cut and wire nails had been tested respectively, showing a decided superiority for the former, both in spruce, pine, and hemlock. Thus in spruce stock nine series of tests were made, comprising nine sizes of common nails, longest 6 inches, shortest 1³⁄₈ inches; the cut nails showed an average superiority of 47.51 per cent.; in the same wood six series of tests, comprising six sizes of light common nails, the longest 6 inches and the shortest 1¹⁄₈ inches, showed an average superiority for cut nails of 47.40 per cent.; in 15 series of tests, comprising 15 sizes of finishing nails, longest 4 inches and shortest 1¹⁄₈ inches, a superiority of 72.22 per cent. average was exhibited by the cut nails; in another six series of tests, comprising six sizes of box nails, longest 4 inches and shortest 1¹⁄₄ inches, the cut nails showed an average superiority of 50.88 per cent.; in four series of tests, comprising four sizes of floor nails, longest 4 inches and shortest 2, an average superiority of 80.03 per cent. was shown by the cut nails. In the 40 series of tests, comprising 40 sizes of nails, longest 6 inches and shortest 1¹⁄₈ inches the cut nails showed an average superiority of 60.50.

Speaking of the ropes used in blocks, while taking down the old barn timbers, Mr. Gregg suggested that it would not be a bad idea if the boys were taught a few general items concerning hempen ropes; so he asked them to memorize the following: A rope ¹⁄₄ inch in diameter will carry 450 pounds, and 50 feet of it will weigh one pound. If ⁵⁄₈ inch in diameter, it will carry 3,000 pounds and 7 feet will weigh one pound. When a rope is ³⁄₄ inch in diameter, it will carry 3,900 pounds, and 6 feet will weigh 1 pound. A rope one inch in diameter, the same as we have in our blocks, will carry 7,000 pounds, and 3 feet 6 inches will weigh one pound. "It is not likely that sizes greater than these will ever be used by you. If they are, you can obtain a fair knowledge of their strength by finding their areas, and comparing them with the areas of the ropes given, taking the rope having one inch in diameter, as a constant example."

Wire ropes are much stronger than hempen ones, whether made of steel, brass, or bronze. The care and preservation of ropes is deserving of consideration, particularly in localities where the atmosphere is destructive to hemp fibre. Such ropes should be dipped when dry into a bath containing 20 grains of sulphate of copper per gallon of water, and kept soaking in this solution some four days, before they are dried. The ropes will thus have absorbed a certain quantity of sulphate of copper, which will preserve them for some time, both from the attacks of animal parasites and from rot. The copper salt may be fixed in the fibres by a coating of tar or by soapy water. In order to do this the rope is passed through a hot bath of boiled tar, drawn through a ring to press back the excess of tar, and suspended afterwards on a staging to dry and harden.

The figures given are intended for new manila ropes, and do not hold good for ropes made of inferior hemp. It is always safer never to load a rope to more than 60 per cent. of its capacity, and not even this much when it is old and weathered.

Jessie reminded her father of his promise to give them some information regarding the power of blocks and tackle and the qualities of the inclined plane. Accordingly, Fred, George, and Jessie joined their father in his den after supper, and George placed his blackboard in a convenient place with chalk, rule, and other requisites.

When all were seated, the father said: "Some time ago I tried to explain to you the uses of the lever in quite a number of different situations; to-night I'm going to show you how the various ropes and pulley blocks are made to do service for mankind. These devices are used very generally, especially in building operations, where heavy beams, girders, or blocks of stone have to be raised. On board ship, it is the favourite mechanical power by which rigging is raised, cords and ropes tightened, and goods lifted from or lowered into the hold.

Fig. 11. Blocks and tackle

"The pulley, the main feature of the third mechanical power, may be explained almost on the same principle as the lever, as you will see upon examining the sketch (Fig. 11) I now make on the blackboard.

"The pulleys seen in the blocks around which the rope runs may be considered so many levers whose arms are equal, and whose centres are fulcrums.

"In describing this power, it will perhaps be better to begin with the first and simplest form of the combination. The pulley, weight, and rope I show now (Fig. 12) is the simplest form of making use of this power. It is called a snatch-block and often employed for drawing water from wells, or for hoisting light weights. It is very handy, but we do not get any additional power from it, though we get a change of direction and quick movement. From its portable form, its low cost, and the handiness with which it can be applied, this arrangement is one of the most useful of our mechanical contrivances.

Fig. 12. Theory of block and tackle

"When pulleys are adjusted, as I show you in this sketch (Fig. 13), the block which carries the weight is called a movable pulley, and the whole, as shown, a system of pulleys.

Fig. 13. Double block and tackle

"In this illustration, suppose the weight is 20 pounds. It is supported by two cords, A and B; that is, the two sections of the cord support 10 pounds each. Now, the cord being continuous, the power must be 10 pounds.

"We leave out of consideration the weight of pulley and the friction of the various parts.

"We have seen that the weight is sustained by two cords; if, therefore, it has been raised two feet, each cord must be shortened two feet. To do this, the power P must run down four feet. To get the full value of this machine the cords must be parallel.

"If we increase the number of movable pulleys, as sketched at Fig. 14, to three, the relation of P to W will be as 1 to 8 and the distance through which P will travel will be eight times that through which W is raised.

Fig. 14. Multiple blocks and tackle

"If we apply this principle to the sketch (Fig. 11), which illustrates the blocks you used to-day in lifting the large timbers, and which is the usual form of pulley employed to lift heavy weights, you will notice that there is a four-sheave block at the top, and a three-sheave block at the bottom, with the end of the rope fixed from the top block. The three-sheave block is movable. A power of 10 pounds will, with this form of pulley, balance a weight of 60 pounds.

"Suppose a block of stone weighing 8,000 lbs. is to be raised to the top of a wall and we use a system of pulleys where each of the two blocks has four pulleys; we shall find that it will require a power of 1,000 pounds to raise it.

"Now, as to the inclined plane: this is called the fourth mechanical power, and it is not in any way related to the lever, but is a distinct principle. Some writers on the subject reduce the number of mechanical powers to two, namely, the lever and the inclined plane. The advantages gained by this are many for just so much as the length of the plane exceeds its perpendicular height is an advantage gained. Suppose A B C (Fig. 15), I make in the sketch, is a plane standing on the table. If length A B is three times greater than the perpendicular height C B then a cylinder at R P may be supported upon the plane A B by a power equal to a third of its own weight. That is, a block of that weight would prevent the roller or cylinder from going farther. From this we gather that one third of the force required to lift any given weight in a perpendicular direction will be quite sufficient to raise it the same height on the plane; allowance, of course, must be made for overcoming the friction, but then, you see, you will have three times the space to pass over, so that what you gain in power, you will lose in time. We see the use of the inclined plane every day we pass a building under construction, where the workmen wheel bricks, mortar, and other materials from the street to the floors above, using long planks for the plane or tramway. Merchants, too, often make use of an inclined plane when rolling heavy boxes and packages from the street to the floors of their warehouses.

Fig. 15

"An excellent, practical illustration was given you to-day when Nick and Fred built the ways on which the proposed boat is to be slid into the new house. It would require five or six strong persons to lift the boat bodily into the new house; but I expect two or three will easily slide it up into the building on the ways; and by arranging a winch—another mechanical contrivance—at one end of the boat house, Fred, or George, for that matter, will be able to haul the boat up. The winch for this purpose will be a very simple affair, merely a ready adaptation of the wheel and axle, as I will show you later. Now, however, we are talking about inclined planes, and to illustrate its early application to the building arts, it is only necessary to tell a few things we know regarding the moving and raising of the great stones used in building the Pyramids. For centuries it was a mystery how the heavy stones in these structures had been placed in their present positions. Recent investigations have led many scientific men to believe the stones were taken up inclined planes, on rollers, and then put in place by the workmen, who moved them to the different sides of the building on strong timber platforms, where rollers, or rolling trucks, carried the load. According to one authority, there are the remains of the approach to an inclined plane near the Great Pyramid, which, if continued at the angle, as now seen, would rise to the apex. According to this writer, the foot of the plane was more than a mile from the building, fifty or sixty feet wide, and had been one huge embankment, formed of earth, sand, and the clippings and waste of stone made by the workmen. This, of course, would be an expensive and a tedious method, but in those days time and labour went for little. Every time a course of stones was laid and completed, the plane was raised another step, to the height of the next tier of stones. The same angle of incline was probably maintained during the whole period of erection, and this angle, you may rest assured, was made as low and easy as possible; for the Egyptian engineers were not slow in adapting the easiest and quickest methods available.

"This method of conveying the heavy stones to their places in the Pyramids was simple and effective, with no engineering difficulties that could not be readily overcome. Moreover, it was really the very best method considering the narrow limits of their appliances.

"You may ask, 'How were these big stones carried to the foot of the inclined plane?' The quarries, in some cases, were five hundred miles distant, and most of the stones had to be brought across the Nile to the works. We know from the monuments, and from the papyrii that have come down to us from remote periods, that many of the stones were brought down the river on large rafts or floats, and on barge-like vessels; and we also know that many of the larger ones were hauled or dragged down from the quarries at Assowan to Memphis, alongside the river, a distance of 580 miles. This is particularly true of the obelisks, for all along an old travelled road evidences have lately been found that these stones had been taken that way, and that resting places for the labourers had been provided at stations about twelve miles apart, along the whole distance. It has been estimated that a gang of men—say forty—well provided with rollers, timbers, ropes, and necessary tools, could easily roll an obelisk like that in Central Park, New York, twelve miles in twelve hours; and doubtless this was the system employed in conveying those immense stones that great distance.

"A large number of obelisks were erected near Memphis, though there are none there now, for the Greek and Roman engineers, at the command of the rulers, took a number down and carried them to the city of Alexandria; but we have less knowledge of how these later engineers transferred the stones to the newer city, than we have of the methods of the older. The beautiful column known as Pompey's Pillar was once an obelisk, and was transformed into a pillar, by either Greek or Roman artisans, it is not clear which. The work of putting those huge stones in place was not easy, as Commander Gorringe discovered when he stood the New York obelisk in the place it now occupies.

"But let us get back to our inclined plane.

"I have shown you how a weight or roller acts on the incline, but I did not explain it clearly, nor in a scientific way, as I do not want to puzzle or confuse you with terms and problems you cannot understand. I will, however, give you another illustration or two on the subject, in which another factor plays a part, namely—gravitation. Let us suppose you have two golf balls laid on a table that is perfectly horizontal or level in every direction; they will remain at rest wherever placed, but if we elevate the table so that the raised end is half the length of the top higher than the lower end, the balls will require a force half their weight to sustain them in any position on the table. But suppose they are on a plane perpendicular to the table top, the balls would descend with their whole weight, for the plane would not contribute in any respect to support them; consequently they would require a power equal to their whole weight to hold them back. It is by the velocity with which a body falls that we can estimate the force acted upon it, for the effect is estimated by the cause. Suppose an inclined plane is thirty-two feet long, and its perpendicular height sixteen feet, what time should a ball take to roll down the plane, and also to fall from the top to the ground by the force of gravity alone? We know that by the force of attraction or gravitation, a body will be one second in falling sixteen feet perpendicularly, and as our plane in length is double its height at the upper end, it will require two seconds for the ball to roll down from top to bottom. Suppose a plane sixty-four feet in perpendicular height, and three times sixty-four feet, or one hundred and ninety-two feet long; the time it will require a ball to fall to the earth by the attraction of gravitation will be two seconds. The first it falls sixteen feet, and the next forty-eight feet will be travelled in the same time, for the velocity of falling bodies increases as they descend. It has been found by accurate experiments that a body descending from a considerable height by the force of gravitation, falls sixteen feet in the first second, three times sixteen feet in the next; five times sixteen feet in the third; seven times sixteen feet in the fourth second of time; and so on, continually increasing according to the odd numbers, 1, 3, 5, 7, 9, 11, etc. Usually, the increase of velocity is somewhat greater than this, as it varies a trifle in different latitudes. In the example before us we find that the plane is three times as long as it is high on a perpendicular line; so that it will take the ball to roll down that distance (192 ft.) three times as many seconds as it took to descend freely by the force of gravity, that is to say, six seconds.

"The principle of the inclined plane is made use of in the manufacture of tools of many kinds, as in the bevelled sides of hatchets, axes, chisels and other similar tools, the examples of which are in a great measure related to this power, though many of them partake largely of the wedge, of which we shall now have something to say.

Fig. 16. Action of the wedge

"The wedge may be a block of wood, iron, or other material, tapered to a thin edge, forming a sort of double inclined plane, A P B, (Fig. 16) where their bases are joined, making A B the whole thickness of the wedge at the top. In splitting wood as is shown in the illustration, R R being the wood, the wedge must be driven in with a large hammer or heavy mallet which impels it down and forces the fibres of the wood to separate and open up. The wedge is of great importance in a vast variety of cases where the other mechanical powers are of no avail, and this arises from the momentum of the blow given it; which is greater beyond comparison than the application of any dead weight or pressure employed by the other mechanical powers. Hence, it is used in splitting wood, rocks, and many other things. Even the largest ships may be raised somewhat by driving wedges below them. Often, in launching a vessel, wedges are used to start it on its way. And they are also used for raising beams or floors of houses where they have given way by reason of having too much weight laid upon them. In quarrying large stones, it is customary to wedge or break off the rock by first drilling a number of holes on the line of cleavage. Wooden wedges are then driven tightly into these and left there until they get wet, when they expand and split off the rock as required. This method of quarrying large stones was well known to the old Egyptians, and employed by them in quarrying their famous obelisks.

"Owing to the fact that the power applied to force a wedge is not continuous, but a series of impulses, the theory of the wedge is less exact than that of the other mechanical powers. Considering the power and the resistance on each side, however, as three forces in equilibrium, it may be demonstrated that the

Resistance (R) equals P × Length of equal side/Back of wedge

Then the mechanical advantage will be—

R/P equals Length of equal side/Back of wedge

So that by diminishing the size of the back and increasing the length of the side—that is, diminishing the angle of penetration—the mechanical power of the wedge is increased. While I did not intend to inflict you with arithmetical or algebraical formulæ, I have been compelled to give you that simple example which I know you can all work out, as it is concise, and the same would be long and tedious if rendered in text."

Next morning, as Fred and his father were out on the new place early, looking over the boat house, the slide for the boat, and some other matters, Mr. Gregg suggested that a winch be placed at the upper end of the house, to haul the boat out of the water. He also suggested that Fred prepare for work on the boat at once, and provide himself with all the tools and materials necessary. He promised to call on a friend of his in the city, who is a noted boat builder, and ask him the best method to adopt in building the craft.

"Perhaps," said the father, "it might be a good plan to buy a full set of shapes or patterns from some one of the professional boat builders who advertise such. They are sold at a very low rate—being made of paper—and many firms sell all the material that is required to build a boat complete; with the sweeps, ribs, and curved stuff cut out to the required shape and numbered all ready to set up.

"What we want, Fred," continued the father, "is a boat sixteen or eighteen feet long, just the size of the one belonging to your friend, Walter Scott; that is plenty large enough for all our purposes. His boat can stand as a kind of a model for you to work after in case you do not thoroughly understand the patterns you are to get, or the manner of arrangement. The gasolene motor we'll order from some manufacturer, with whom we'll arrange to install it, with a suitable propeller and necessary attachments."

Fred was quite satisfied with all his father had said and started to get ready. Jessie began to question him about several things she did not fully understand in her father's talk the night previous. Fred explained matters, made them quite clear to her, and then asked her to get her memorandum book and write down the following, which he said, she would often find useful: "There are six mechanical powers, two of which father has not told us about, but will no doubt do so, before long. These are called, the Lever, Pulley, Wheel and Axle, Inclined Plane, Wedge, and Screw. The Screw and the Wheel and Axle, you have yet to hear about. Now, study carefully the following rules:

"The Lever.—Rule: The power required is to the weight as the distance of the weight from the fulcrum is to the distance of the power from the fulcrum.

"The Pulley.—A fixed pulley gives no increase of power. With a single movable pulley the power required will equal half the weight, and will move through twice the distance. Increasing the number of pulleys, diminishes the power required. Rule: The power is equal to the weight, divided by the number of folds of rope passing between the pulleys.

"The Wheel and Axle.—Rule: The power is to the weight as the radius of the axle is to the length of the crank or radius of the wheel.

"The Inclined Plane.—Rule: The power is to the weight as the height of the plane is to the length.

"Wedge.—Rule: Half the thickness of the head of the wedge is to the length of one of its sides as the power which acts against its head is to the effect produced on its side.

"The Screw.—Rule: As the distance between the threads is to the circumference of the circle described by the power, so is the power required to the weight."

Fred told George also to copy the foregoing in his memorandum book, so that he would be able to work out any problems for himself.